Download Xiaomin Nie scattering on silicon nitride waveguides Surface

Surface enhanced coherent anti-Stokes Raman
scattering on silicon nitride waveguides
Xiaomin Nie
Supervisors: Prof. dr. ir. Roel Baets, Prof. dr. ir. Günther Roelkens
Counsellor: Haolan Zhao
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Photonics Engineering
Department of Information Technology
Chairman: Prof. dr. ir. Daniël De Zutter
Faculty of Engineering and Architecture
Academic year 2014-2015
ii
Surface enhanced coherent anti-Stokes Raman
scattering on silicon nitride waveguides
Xiaomin Nie
Supervisors: Prof. dr. ir. Roel Baets, Prof. dr. ir. Günther Roelkens
Counsellor: Haolan Zhao
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Photonics Engineering
Department of Information Technology
Chairman: Prof. dr. ir. Daniël De Zutter
Faculty of Engineering and Architecture
Academic year 2014-2015
iv
Preface
Writing this thesis has become an unforgettable experience in my life. There would be
no chance for me to finish this thesis without the constant help from my supervisors and the
unconditional support of my family and friends.
First of all, I want to express my sincere thanks to my supervisor, Haolan, Zhao for his
guidance, encouragement and support throughout this thesis. Whenever I met problems in
theory study, simulation or experiment, he can always provide useful information and lead me
to find the right solution. Also, my appreciations go to Stephane Clemmen for his whole-hearted
guidance in both theory study and simulation. Most importantly, I want to thank two of my
promotors, Prof. dr. ir. Roel Baets and Prof. dr. ir. Gunther Roelkens for giving me the
opportunity to do my master thesis in the photonics research group. I am very grateful that
they can spare their valuable time to set meeting with me and share their instructive idea in the
discussion. Many thanks also to all the other people in the group who have offered help to me.
In the meanwhile, I am rather thankful for having all the support from my close friends
Boyang, Shao and Xiaoning, Jia. Their warm encouragements always help me go through hard
time.
Finally, I would like to thank my parents. Although being thousands miles away, their love
and support is wonderful and uplifting. The conversations with them are great spiritual boosts
that give me the strength to face the challenges encountered in both learning and living.
Xiaomin Nie, 2015
v
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the limitations of the copyright have to be respected, in particular with regard to the obligation
to state expressly the source when quoting results from this master dissertation.
Xiaomin Nie, June 2015
Surface Enhanced Coherent Anti-Stokes Raman Scattering on
Silicon Nitride Waveguides
by
Xiaomin Nie
Thesis submitted to obtain the academic degree of
Master Science of Photonics Engineering (MSPE)
academic 2014–2015
Promotor: Prof. Dr. Ir. Roel Baets, Prof. Dr. Ir. Gunther Roelkens
supervisor: Ir. Haolan Zhao, Dr. Stephane Clemmen
Faculty of Engineering and Architecture
University Gent
Department of Information Technology
Photonics Research Group
Abstract
Coherent Anti-Stokes Raman Spectroscopy (CARS) is attracting significant attention recently
as a non-invasive nonlinear spectroscopy. CARS possesses a much higher sensitivity compared
with Spontaneous Raman Spectroscopy and has been widely used in biological applications
although usually bulky equipment are involved. In this thesis, we propose to miniaturized the
CARS experiment on chip. In the first part, we want to present the theory of waveguide-based
CARS and investigate the feasibility of it. In the second part, we move to an enhanced version
of CASR, i.e. the Surface Enhanced CARS (SECARS), where mental nanoparticles (NPs) are
involved.
Keywords
On-chip, Coherent Anti-Stokes Raman Spectroscopy, Four-Wave Mixing, Surface Enhanced Coherent Anti-stokes Raman Spectroscopy, Localized surface plasmon Resonance
Surface Enhanced Coherent Anti-Stokes Raman Scattering on Silicon
Nitride Waveguides
Xiaomin Nie
Supervisor(s): Roel Baets, Gunther Roelkens, Haolan Zhao, Stephane Clemmen
Abstract— Coherent Anti-Stokes Raman Spectroscopy
(CARS) is attracting significant attention recently as a noninvasive nonlinear spectroscopy. CARS possesses a much higher
sensitivity compared with Spontaneous Raman Spectroscopy
and has been widely used in biological applications although
usually bulky equipment are involved. In this thesis, we
propose to miniaturized the CARS experiment on chip. In the
first part, we want to present the theory of waveguide-based
CARS and investigate the feasibility of it. In the second part,
we move to an enhanced version of CASR, i.e. the Surface
Enhanced CARS (SECARS), where mental nanoparticles
(NPs) are involved.
Keywords— On-chip, Coherent Anti-Stokes Raman Spectroscopy, Four-Wave Mixing, Surface Enhanced Coherent Antistokes Raman Spectroscopy, Localized surface plasmon Resonance
with a sample and generate an anti-Stokes field Eas at the
frequency of
ωas = 2ωp − ωs
(1)
I. INTRODUCTION
Spectroscopic techniques are widely used in both chemical
biological research to identify molecules by their spectral fingerprint, such as Fluorescence Spectroscopies, Raman Spectroscopies and Fourier Transform Infrared Spectroscopies (FTIR). Among them, Raman-based technique is
most promising in bio-sensing in which field it enjoys several
advantages. Firstly, Raman spectroscopy is a non-invasive,
label-free technique which requires nearly no sample preparation and very small sample volume. Moreover, Raman
spectroscopy can be used to analyze sample in aqueous
solutions since water will not bring much interference.
Because of the low efficiency of spontaneous Raman
scattering, different enhancement technologies are developed
for efficient Raman sensing. Coherent Anti-Stokes Raman
Spectroscopy (CARS) is one of the most popular enhancement technology, which has been studied intensively based
on the microscopy system [1]. This microscopy-base CARS
usually needs cumbersome and expensive instrumentation,
and requires sophisticated alignment.
The recently developed spectroscopy-on-chip technologies
of silicon photonics actually provide a way to to miniaturize
the spectroscopy and make it less expensive [2]. In this article, the feasibility of CARS generation based on a dispersion
engineered silicon-nitride waveguide is investigated. And
furthermore, we attempt to achieve an enhanced version of
CARS, i.e. Surface Enhanced Coherent Anti-Stokes Raman
Spectroscopy (SECARS) also based on the platform of the
silicon-nitride waveguide.
A. Anomalous Dispersion
II. WAVEGUIDE - BASED CARS
CARS is intrinsically a four-wave mixing (FWM) process.
A pump field Ep (ωp ) and a Stokes probe Es (ωs ) interact
This interaction is typical a third-order nonlinear process
which happens through the third-order nonlinearity χ(3) . One
can express the anti-Stokes signal as
Ias ∝ |χ(3) |2 L2 Ip2 Is sinc2 (κL/2)
(2)
where Ii is the optical intensity at frequency ωi (i = p, s
and as), κ is the net phase mismatch and L is the interaction
length. One can see from this equation that waveguide-based
CARS enjoys the advantage of long interaction length while
calls for a small κ.
The net phase mismatch κ has contributions result from
material dispersion, waveguide dispersion and nonlinear effects. For a perfect phase matching, we can write the phase
matching condition as
1
β2 (ωp )Ω2 = −γP0
(3)
2
where β2 the second order derivative of propagation constant
β, which describes the group-velocity dispersion (GVD). Ω
is the Raman shift defined by ωp − ωs . γ is the nonlinear
parameter and P0 is the pump power.
In stead of using β2 , group-velocity dispersion (GVD) is
often quantified by parameter D, which is defined as
2πc
β2
(4)
λ2
Then we can see from equation (3) that perfect phase
matching can only be achieved when the pump wavelength
lies in the small anomalous dispersion regime, where D has
a small positive value.
D=−
B. Dispersion Engineered Silicon-Nitride Waveguide
The total GVD consists material contribution and waveguide dispersion. For the silicon-nitride ridge waveguide, we
found from the simulation that by etching the SiO2 substrate
underneath silicon nitride core, one can compensate the
strong material dispersion by the waveguide dispersion and
therefore get positive D in the interested wavelength range.
Since we want to use evanescent field of the guided mode
for CARS generation, it is necessary to check the dispersion
after cladding the underetched waveguide with bio-material.
In sketch of the cross section of the structure shown in
figure 1, a monolayer of nitrothiophenol (NTP) is coated
on the surface of an underetched waveguide. The size of the
waveguide core is fixed with height of 300 nm and width of
500 nm and the etch depth is set to be 150 nm.
(QNLSE), we end up with the photon flux f (Ω) at antistokes frequency (CARS signal) which can be related to the
injected Stokes photon flux by
E
D
(5)
f (Ω) == |ν(z, Ω)|2 a0 (−Ω)a†0 (−Ω) + |ς(Ω)|2
where
D ς(Ω) describesEthe spontaneous Raman contribution
and a0 (−Ω)a†0 (−Ω) denotes the injected Stokes photon
flux averaged over coherent state. The photon flux is the
number of photons per unit time and frequency, in the unit
of photons/s/Hz. In the weak pump region, ν(z, Ω) can be
expressed as
β 2 Ω2
z) exp(iβ1 Ω)
(6)
2
where γr is the nonlinear parameter, P is the pump power,
z is the interaction distance and χ is the normalized Raman
response function.
We calculated the power of CARS signal for different
sets of parameters. The required parameters for getting
signal above the detection limit (1 pW) are summed in
table 1. Unfortunately, due to fabrication uncertainty one
ν(z, Ω) = −γr P zχsinc(
Fig. 1. A sketch of the underetched Si3 N4 waveguide cladded with a NTP
monolayer(green).
For varying cladding thickness the GVD curves resulted
from simulation are shown in figure 2. We can see that
increasing cladding thickness would red shift the curve and
move the first ZDW to the longer wavelength side. This
means that given a pump wavelength, the cladding should
be enough thin to ensure anomalous dispersion (D>0). For
example, if we choose to work at 750 nm, the cladding
should not be thicker than 30 nm.
Parameter
Value
GVD
pump power
Stokes probe
waveguide length
γr
-0.004 ∼ -0.002 ps2 m−1
10 ∼ 100 mW
1 ∼ 5 dB/nm
1 cm
1 m−1 W−1
TABLE I
PARAMETERS OF CARS.
can hardly reduce GVD to such a small level at a chosen
pump frequency even with the underetched waveguide. This
would be a problem because with large GVD, non-flat kerr
background would impede the detection of CARS signal.
Another problem is that with the laser source available in
our lab, the pump power coupled into waveguide is weaker
than 10 mW. According to our experience, the coupled power
is usually at the level of 1 mW. This would lead to CARS
signal at level of 0.1 pW, which is below the detection limit.
III. S URFACE E NHANCED CARS (SECARS)
Fig. 2. The GVD curves of underetched waveguide with varying cladding
thickness as shown in the legends. The size of the waveguide core are fixed
with height of 300 nm and width of 500 nm and the etch depth is set to be
150 nm.
C. CARS feasibility
CARS generation based on the optical waveguide can be
calculated analytically and many different parameters can
influence the strength of CARS signal in a nonlinear way.
Starting for the quantum nonlinear Schrodinger equation
With the combination of CARS and plasmonic surface enhancement on nanostructured surfaces, another enhancement
technique, namely Surface Enhanced Coherent Anti-Stokes
Raman Spectroscopy (SECARS), now attracts growing attentions.
In SECARS, localized surface plasmon resonances
(LSPRs) can locally enhance the electric fields and allow
SECARS to achieve single-molecule detection sensitivity.
Comparing with waveguide CARS, another advantage of
SECARS is that phase matching is automatically fulfilled.
The interaction length is limited by the size of ’hotspot’
which is usually in the nanometer scale. As a result, the
total phase mismatch that scales with the interaction length
will be negligible small.
To calculate the overall SECARS signal, one needs to
know the distribution of the enhanced electromagnetic field
strength inside the nonlinear medium which is deposited
at the vicinity of the metallic nanoparticles (NPs). The
estimation of the local field enhancement is not trivial as
the distribution of local field varies strongly with the geometry of the nano-structure. However, finite-difference time
domain (FDTD) algorithm provides a solution to analyze the
structures by numerically solving a set of coupled Maxwell’s
equations in differential form. With the help of FDTD
simulation tool, the local field distribution can be obtained,
allowing further calculations of SECARS signal strength.
In our work, silver NPs carried by the calcium carbonate
(CaCO3 ) micro-beads are the Raman active center for SECARS generation. As the model substance, NTP molecules
are bonded to silver NPs to form a monolayer, providing
Raman information. We consider that a droplet of water
containing large amount of Ag-CaCO3 beads are dripped
onto the silicon nitride waveguide.
To model the structure for simulation, we consider a
configuration that is realistic in fabrication and can provide
large efficiency in SECARS generation. In this model, a
CaCO3 bead carrying two silver NPs is positioned on top of
the core of a silicon-nitride waveguide. We assume that the
two silver NPs have hemisphere shape with the same radius
and are set close to each other, creating a gap in between.
We calculated the SECARS signal strength for varying gap
between the two hemispheres in the case of different radius
of the hemisphere. The results are shown in figure 3.
radius 30nm
radius 35nm
10000
radius 25nm
1000
power (pW)
100
10
enough to be detected. The strongest signal power we can
get at the detector is 58.52 pW in the optimum case of 7 nm
gap and 30 nm radius. Away from this optimum situation,
we still have a large parameter space where the SECARS
signal is detectable.
B. SECARS Experiment
After the simulation and calculation, we tried to experimentally measure the SECARS signal. Raman setup is used
for the measurement, where the Ti:sapphire laser emitting at
765 nm works as pump and supercontinuum light provides
a broadband Stokes probe above 775 nm.
6500
6000
5500
counts
A. SECARS Simulation and Calculation
5000
4500
4000
3500
600
620
640
660
680
700
720
740
760
780
wavelength (nm)
Fig. 4. spectrum obtained with the chip when both the Ti-sapphire laser
and Supercontinuum source are switched on. The integration time is 1 s.
A measured spectrum is shown in figure 4. In this spectrum, lots of features can be observed. Among them, the most
obvious one is the sharp peak at 765 nm, which is caused
by the Ti:sapphire pump laser.
Unfortunately, after careful study, we found that none
of these features can be related to anti-Stokes signal of
the analyte. A possible reason could be that although the
supercontinuum light is collected by the objective lens, it
might not have been coupled into the waveguide.
IV. CONCLUSIONS
1
0.1
0.01
4
6
8
10
12
gap distance (nm)
Fig. 3. Power of SECARS signal that coupled into the fundamental TE
mode of the waveguide is calculated for varying gap distance between the
two hemispheres with different radius. The dash line marks the required
power level that is decided by the collecting efficiency and detection limits.
One can see in the figure that SECARS signal strength
varies with the gap distance and radius.
Considering the collecting efficiency of 1% and detection
limit of 1 pW, we draw a dash horizontal line at power of
100 pW in figure 5.7. Above this dash line the signal is strong
Through the theoretical calculation, we found that
waveguide-based CARS is currently not feasible in our lab.
The main reason is that the laser available currently in
our lab cannot provide enough power. According to the
calculation, pump power coupled into the waveguide should
at least be 10 mW, while in our lab, the coupled power is
usually at the level of 1 mW. With this low coupled power,
the signal strength is below the detection limit, even when
waveguide has proper dispersion. Another reason is that due
to fabrication and processing uncertainty, in practice it is very
difficult to have the small anomalous GVD at the desired
wavelength range.
As for SECARS, while the simulation result is promising,
the experiment result however is not as good. Anti-stokes
signals are not observed in the resulting spectrum. The
possible reason could be the improper optical design, though
further investigation should be conducted to really figure out
the cause.
R EFERENCES
[1] Cheng, J. X. and Xie, X. S. (2004). Coherent anti-Stokes Raman
scattering microscopy: instrumentation, theory, and applications. The
Journal of Physical Chemistry B, 108(3), 827-840.
[2] Baets, R., Subramanian, A. Z., Dhakal, A., Selvaraja, S. K., Komorowska, K., Peyskens, F., ... and Le Thomas, N. (2013, March).
Spectroscopy-on-chip applications of silicon photonics. In SPIE OPTO
(pp. 86270I-86270I). International Society for Optics and Photonics.
CONTENTS
xi
Contents
List of Abbreviation
xiii
1 Introduction
1.1
1
Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
Scattering Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Spontaneous Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.3
Stimulated Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . .
4
Raman Spectroscopy and Enhancement Technologies . . . . . . . . . . . . . . . .
5
1.2.1
Surface Enhanced Raman Spectroscopy (SERS) . . . . . . . . . . . . . . .
6
1.2.2
Tip-Enhanced Raman Spectroscopy (TERS) . . . . . . . . . . . . . . . .
8
1.2.3
Resonance Raman Spectroscopy (RRS) . . . . . . . . . . . . . . . . . . .
9
1.2.4
Coherent Anti-Stokes Raman Spectroscopy (CARS) . . . . . . . . . . . .
10
1.2.5
Surface Enhanced Coherent Anti-Stokes Raman Spectroscopy (SECARS)
13
1.3
On-chip Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.4
Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.2
2 Theory of Coherent Anti-Stokes Raman Scattering (CARS)
18
2.1
Generalized Nonlinear Schrödinger Equation (GNLSE) . . . . . . . . . . . . . . .
18
2.2
Four-Wave Mixing(FWM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.3
CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.4
Phase Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3 Waveguide Dispersion Engineering and Supercontinuum Generation (SCG) 27
3.1
Material GVD
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
CONTENTS
xii
3.2
Ridge Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.3
Underetched Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.4
Underetched Waveguide with Cladding . . . . . . . . . . . . . . . . . . . . . . . .
33
3.5
Supercontinuum Generation (SCG) . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4 CARS Case Study and Limitation
37
4.1
Quantum Nonlinear Schrödinger equation (QNLSE) . . . . . . . . . . . . . . . .
37
4.2
Media Response and Nonlinear Parameter . . . . . . . . . . . . . . . . . . . . . .
39
4.3
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.4
Conclusion
44
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Surface Enhanced Coherent Anti-Stokes Raman Scattering (SECARS)
5.1
5.2
5.3
Theory of SECARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
5.1.1
Localized Surface Plasmon Resonance (LSPR) . . . . . . . . . . . . . . .
48
5.1.2
SECARS Signal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
Simulation of Local Field Enhancement . . . . . . . . . . . . . . . . . . . . . . .
50
5.2.1
A Short Introduction to FDTD Algorithm . . . . . . . . . . . . . . . . . .
50
5.2.2
Model the Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
5.2.3
Local Field Enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
5.2.4
Coupling Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
SECARS Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5.3.1
Calculation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5.3.2
Calculation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
6 Fabrication
6.1
6.2
47
61
Silicon Nitride Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
6.1.1
Chip Cleavage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
6.1.2
Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.1.3
Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
Silver Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
6.2.1
Synthesis of CaCO3 Beads . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
6.2.2
Silver Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
CONTENTS
6.2.3
xiii
NTP Monolayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Experiment of SECARS
65
66
7.1
Raman Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
7.2
Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
7.3
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
7.4
Measured Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
7.4.1
Measured Result of SECARS . . . . . . . . . . . . . . . . . . . . . . . . .
70
7.4.2
Measured Result of SERS . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
8 Conclusion and Future Prospects
75
8.1
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
8.2
Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Bibliography
78
List of Figures
88
List of Tables
89
CONTENTS
xiv
List of Abbreviation
SERS
Surface Enhanced Raman Spectroscopy
TERS
Tip-Enhanced Raman Spectroscopy
RRS
Resonance Raman Scattering
CARS
Coherent Anti-Stokes Raman Spectroscopy
SECARS
Surface Enhanced Coherent Anti-Stokes Raman Spectroscopy
LPCVD
Low-Pressure Chemical Vapor Deposition
PECVD
Plasma-Enhanced Vapor Deposition
GNLSE
Generalized Nonlinear Schrödinger equation
FWM
Four Wave Mixing
GVD
Group Velocity Dispersion
SCG
Supercontinuum Generation
TE(M)
Transverse Electric (Magnetic)
ZDW
Zero Dispersion Wavelength
NTP
Nitrothiophenol
QNLSE
Quantum Nonlinear Schrödinger Equation
LSPR
Localized Surface Plasmon Resonance
NPs
Nanoparticles
FDTD
Finite-Difference Time Domain
SPPs
Surface Plasmon Polarization
DUV
Deep Ultra-Violet
IPA
Isopropyl Alcohol
FIB
Focused Iron Beam
SEM
Scanning Electron Microscopy
INTRODUCTION
1
Chapter 1
Introduction
Spectroscopic techniques are widely used in both chemical biological research to identify molecules
by their spectral fingerprint, such as Fluorescence Spectroscopies, Raman Spectroscopies and
Fourier Transform Infrared Spectroscopies.
Among them, Raman-based technique is most
promising in bio-sensing in which field it enjoys several advantages. Firstly, Raman spectroscopy
is a non-invasive, label-free technique which requires nearly no sample preparation and very
small sample volume. Moreover, Raman spectroscopy can be used to analyze sample in aqueous
solutions since water will not bring much interference.
Because of the low efficiency of spontaneous Raman scattering, different enhancement technologies are developed for efficient Raman sensing. In this chapter, we will first explain several
basic principles that help with the understanding of the work in this thesis. Then, we will review
the Raman spectroscopic technique and various enhancement schemes. After that, a section is
dedicated to photonics on chip. At the end of this chapter, the outline of this thesis will be
given.
1.1
1.1.1
Basic Principles
Scattering Processes
Scattering is a process referring to the physical interaction between light and physical fluctuation. After interaction, the photon could have a different propagation direction and/or different
frequency than the incident photon. There are multiple different scattering processes arising
1.1 Basic Principles
2
from various fluctuations (figure 1.1).
As shown in part (b) of figure 1.1,scattering processes can have different spectral features
depending on the origin of scattering. Brillouin scattering is the scattering of light from sound
waves, Rayleigh scattering (or Rayleigh-center scattering) is the scattering of light from static
density fluctuations and Rayleigh wing scattering (that is, scattering in the wing of the Rayleigh
line) is scattering the from fluctuations in the orientation of anisotropic molecules. Among them,
Raman scattering is most interesting to us, which results from the interaction of light with the
vibrational modes of the molecules.
It is worth mentioning some of the scattered light has lower (higher) frequency than the
incident light, and is by definition called Stokes (anti-Stokes) component.
Figure 1.1: Light scattering processes (a) schematic diagram of scattering, (b) Typical observed
spectrum. This diagram is reprinted from [2]
.
1.1.2
Spontaneous Raman Scattering
Raman scattering was first discovered by C. V. Raman and K. S. Krishnan in liquids[1], and
by G. Landsberg and L. I. Mandelstam in crystals[3] and finds now various applications in
chemical analysis and bio-detection. Raman scattering refers to the interaction of light with the
1.1 Basic Principles
3
vibrational modes of the scatter molecules.
Quantum mechanics gives an elegant and straightforward explanation to Raman scattering
in which Raman scattering can be considered as the inelastic scattering of photons by optical
phonons. Molecule can have vibrational modes with different frequencies. And a phonon is the
quantization of one of such vibrational modes. Similar as other quanta, phonon has energy
E = h̄Ωvibration
(1.1)
where, Ωvibration represent the angular frequency of one of the vibrational modes, and h̄ is the
reduced Plank’s constant.
In non-resonance Raman scattering, the system is first excited by the incident photon to a
virtual state. As the virtual state is not stable, the system will soon rest back to a stable state by
emitting a photon. In one possible case which is called Stokes scattering, the system is initially
at ground state and ends up at a vibrational state, emitting a photon with lower frequency than
the incident one (ωs < ωl ). In another case called anti-Stokes scattering, the system begins at a
vibrational state and decays back to the ground state, let out a photon with higher frequency
(ωas > ωl ). In both Stokes and Anti-Stokes scattering, energy conservation requires that:
ωl = ωs + Ωvibration or ωas = ωl′ + Ωvibration
(1.2)
Virtual State
ωl′
ωs
ωas
ωl
Ωvibration
Ground State
Figure 1.2: Energy diagram for Stokes and anti-Stokes Raman scattering.
It is important to notice the difference between scattering and fluorescence. Raman scattering
is not a resonant effect and can happen with arbitrary incident frequency. Instead of being
1.1 Basic Principles
4
directly excited to a vibrational state, the molecule is excited by the incident photon to a
virtual state, which exists because of the distortion of the electron cloud and can have various
energy levels[4].
However, spontaneous Raman scattering is a weak process. Even for condensed matter the
scattering cross section per unit volume is only approximately 106 cm−1 . Hence, in propagating
through 1 cm of the scattering medium only approximately 1 part in 106 of the incident photon
will be scattered through Raman process.
1.1.3
Stimulated Raman Scattering
In spontaneous Raman scattering, the excited system drops to lower energy state spontaneously
and emitting a photon with random phase or polarization. On the other way around, stimulated
Raman scattering happens when the excited system interacts with incident photon and decays
back to lower energy level by emitting a photon identical with the incident one.
This is typically a very strong scattering process, more than 10% of the energy of the incident
laser beams can be converted into the Stokes frequency. And instead of emitting nearly isotropic
as in the case of spontaneous Raman scattering, the stimulated process leads to emission in a
narrow cone in the forward and the backwards direction.
Figure 1.3: Stimulated Raman scattering. [2]
To understand the origin of stimulated Raman scattering, one can consider the positive
feedback between the two processes depicted in figure 1.3. In part (a) of figure 1.3, the laser is
modulated by the refractive index fluctuation cause by the vibration of molecule at frequency
1.2 Raman Spectroscopy and Enhancement Technologies
5
Ω0 . Sidebands at frequency ωa = ωl + Ω0 and ωs = ωl − Ω0 will be generated. In part (b) of
figure 1.3, the laser and the Stokes signal will generate a beat which can coherently excite the
molecular oscillation at frequency Ω0 = ωl − ωs . These two processes continue reinforce each
other leading to stronger Stokes signal and also stronger molecular vibration.
1.2
Raman Spectroscopy and Enhancement Technologies
Although with low efficiency, spontaneous Raman scattering is easy to trigger in practice.
Base on spontaneous Raman scattering, a non-invasive, label-free technique called Raman spectroscopy is often used to detect the vibrations of molecular bonds. The schematic of a typical
Raman spectroscopic apparatus is shown in figure 1.4. This technique also proves a novel way
for imaging. For this purpose, the laser wavelength typically employed is in or at the edge of
visible range, This will surely improve the lateral resolution of better than half the wavelength
(250-350 nm), which is similar to that achieved in fluorescence imaging, and is far superior
to the minimum resolution (0.1-10 mm) achievable with medical diagnostic techniques such as
ultrasound, Magnetic Resonance Imaging, Positron Emission Tomography, or x-ray imaging.
Figure 1.4: A schematic diagram to demonstrate typical Raman spectrometer, reprinted from
[5].
The difference between the frequency of the incident laser light and that of the red-shifted
light, is equal to the frequency of the vibrational bond which has been excited. Each molecule has
1.2 Raman Spectroscopy and Enhancement Technologies
6
their unique of Raman spectrum as its fingerprint [6]. These Raman peaks correspond to various
molecular bonds, for example, the C-H, C=C, O-H and aromatic ring in certain biomolecule.
Such a Raman spectrum from a single live cell is shown in figure 1.5. [5]. The frequency shifts
are usually recorded in wavenumbers (cm−1 ).
Raman shift (cm−1 ) =
1
1
−
λincident λscattered
(1.3)
Figure 1.5: This figure is reprinted from [5] to give an example of unprocessed Raman spectrum of
live cells. To obtain this image, parameters of 300 seconds acquisition time, 785 nm illumination
and approximately 100 mW illumination power is employed.
1.2.1
Surface Enhanced Raman Spectroscopy (SERS)
It was first observed by Fleischmann et al. [7] that Raman scattering is enhanced from pyridine
molecules adsorbed on silver electrode surfaces in 1974. Later in 1977, Jeanmaire et al. [8]
employed roughened silver electrode and found similar results, which led them to propose an
electric field enhancement mechanism. In the same year, Creighton et al. [9] reported similar
results independently and suggested that the observed enhancement is due to interaction of
molecular electronic states of molecule with the metal surface. As shown in part (a) of figure
1.2 Raman Spectroscopy and Enhancement Technologies
7
1.6, this effect was later known to all as Surface Enhanced Raman Scattering (SERS).
The enhancement of Raman spectra of molecules locate near a metal can be mainly explained
by two mechanisms (part (c) of figure 1.6). In the electromagnetic mechanism, the enhancement
is induced by surface plasmon resonances generated on the roughened metal surface. In addition,
the chemical enhancement raise from chemisorption-induced molecular resonance can also be a
contribution.[12].
Electromagnetic mechanism indicates that SERS spectra will not be different from the Raman spectra of free molecules. In electromagnetic mechanism, localized surface plason resonance
(LSPR), the excitation of surface plasmons by incident light at the surrounding of metallic nanostructures, is responsible for the enhancement. An example of SERS spectrum of Rhodamine
6G in silver hydroxylamine colloid is compared with its normal Raman spectrum in part (b)
of figure 1.6. In obtaining the normal Raman spectrum a higher concentration of 4 orders of
magnitude than that in SERS spectrum is employed and the intensity is multiplied by a factor
of 100. We can easily find the same features in both spectra.
Figure 1.6: Pictures reprinted from [13] to demonstrate: (a) The difference between Raman
and SERS phenomena. (b) Spectrum of Rhodamine 6G acquired by SERS measurement at the
vicinity of silver hydroxylamine colloid (red line) and from spontaneous Raman spectrum. (c)
A schematic explanation of the electromagnetic and chemical enhancements in SERS.
1.2 Raman Spectroscopy and Enhancement Technologies
8
LSPRs are excited through the interactive between light and metals. The interaction is
strongly related to the nanostructure properties. As a result, the electromagnetic enhancement
is also determined by the size, shape and optical property of the nanostructure of the metal.
Besides, the plasmonic resonance frequency and bandwidth also depend on the surrounding
medium (refractive index).
The total enhancement in SERS process includes two separate enhancement processes as
shown in part (c) of figure 1.6. The first one is the enhancement of incident pump field around
the surface of metal. And the second contribution is the enhancement of emission of Raman
signal.
The overall enhancement of SERS signal depends on the frequency of incident filed and
Raman Stokes signal. When both frequencies match the plasmonic resonance frequencies, the
maximum enhancement can be achieved at the metallic surface. It is reported that the electromagnetic enhancement is dominated to the dramatic enhancement of the signal in SERS and
can be up to 1010 − 1011 [11].
1.2.2
Tip-Enhanced Raman Spectroscopy (TERS)
Tip enhanced Raman scattering (TERS) is the combination of SERS and Raman-atomic force
microscope(AFM) analysis. Coated with SERS active metal antiparticles, the tip of AFM
functions as a plasmonic antenna. TERS enhancement is based on the same physical principle
as SERS. The difference is that the enhancement is confined to a tiny area under the tip. For
this reason, TERS can offer true nanometer scale spatial resolution for Raman and a resolution
of around 10 nm is reported in the imaging performed on carbon nanotubes [14].
However, to achieve good TERS results, the laboratory environment must be very stable
and mechanical isolation is often necessary. In general, TERS measurement needs significant
investment both in equipment and time. Successful TERS measurements have only been made
on limited sample types. For other samples, TERS signal can be even hard to achieve. Biological
molecules with lower Raman scattering cross section, will need several seconds per spectrum.
In additional, the absorption induced heating of the gold tip can limit the usable illumination
power to such a low level as 50 µW. Higher power will cause the boiling of a water film around
the tip apex [15].
1.2 Raman Spectroscopy and Enhancement Technologies
1.2.3
9
Resonance Raman Spectroscopy (RRS)
While typical Raman spectroscopy is performed within visible and near-infrared range, anther
enhanced Raman spectroscopic technique, resonant Raman (RR) spectroscopy, works mainly in
UV range.
In figure 1.7, the energy diagrams of RR scattering and its non-resonance counterpart are
shown. The photon absorbed by the molecule has higher energy in RR scattering than in the
non-resonance one. The result is that rather than being excited to a virtual energy state, the
molecule in RR scattering is excited to one of its excited electronic transitions. The associated
vibrational modes will then have an increased Raman scattering intensity.
It is reported that vibrational Raman bands attributed to a specific molecular species or
chromophore in a complex mixture can be selectively enhanced by RR spectroscopy. In the
work of H. S. Kim et al. [16], V = O and V − O stretching modes in monomeric O = V − (OAl)3
surface are selectively enhanced by RR scattering at 220 nm and 287 nm. As shown in figure
1.8, signal corresponds to V = O band is strongly enhanced by 220 nm expiation while V − O
overtones are very weak at these excitation frequencies. In contrast, an strong enhancement
is found for V − O signal when the pump laser is at 287 nm, in which case the V = O signal
is relatively weak. The difference manifests that RR spectroscopic technique can enhance the
scattering signal when the incident laser frequency matches the resonance frequency of electrons
in certain band.
Figure 1.7: the energy diagram of non-resonance Raman process and resonance Raman process.
However there are two drawbacks which can limit the applicability of this technique. One is
1.2 Raman Spectroscopy and Enhancement Technologies
10
Figure 1.8: For alumina supported vanadium oxide monomers: The upper spectrum shows
resonance Raman enhancement of V-O signal at 287 nm. The middle spectrum shows resonance
Raman enhancement of V=O signal at wavelength 220 nm. And the bottom spectrum is the
spontaneous Raman spectrum of same molecule as reference. This figure is reprinted from [16]
photo-degradation that happens at certain pump wavelength due to the strongly absorption of
the resonant components. Another restriction is that inorganic samples mainly have electronic
resonance frequency in deep UV range, where the proper laser source is rare and expensive.
1.2.4
Coherent Anti-Stokes Raman Spectroscopy (CARS)
Coherent Anti-Stokes Raman Spectroscopy (CARS), was first proposed by Maker and Terhune
at Ford Motor Co. in 1965 [23]. CARS is intrinsically a four-wave mixing (FWM) process. A
pump field Ep (ωp ) and a Stokes probe Es (ωs ) interact with a sample and generate an anti-Stokes
field Eas at the frequency of
ωas = 2ωp − ωs .
(1.4)
The energy diagrams of CARS is shown in figure 1.9. The molecule is excited from ground
state to a virtual state by absorbing a photon with frequency ωp . After that, a photon with
frequency ωs induces transition of molecule to a vibrational state. The molecule then absorbs
another pump photon with frequency ωp and transits to a higher virtual state. And by emitting
a photon at anti-Stokes frequency ωas , the molecule will return back to the ground state.
1.2 Raman Spectroscopy and Enhancement Technologies
11
Virtual State
ωp
ωs
ωas
ωp
Ωvibration
Ground State
Figure 1.9: Energy diagram of CARS.
As a third-order nonlinear process, the CARS intensity is related to the intensity of pump
and Stokes probe through the third-order susceptibility χ(3) ,
Icars ∝ χ(3) Ip2 Is
(1.5)
The third-order susceptibility χ(3) in general has various contributions. If we only consider the
vibrationally resonant contribution corresponding to the process shown in figure 1.9, χ(3) can
be expressed by [21]
χ(3) =
AR
Ω2 − (ωp − ωs )2 + iΓR (ωp − ωs )
(1.6)
where Ω is the vibrational frequency and Γ is the half width at half-maximum of the Raman
line.
Being a FWM process, CARS generation normally requires phase matching. The phasematching condition takes the expression [22]
l < lc =
π
π
=
|∆k|
kas − (2kp − ks )
(1.7)
where kp , ks , kas are the wave vectors of pump, Stokes probe and anti-Stokes signal. The
interaction length should be smaller than the coherent length lc , within which constructive
interference will continuously build up CARS signal, and at which the CARS signal reaches the
maximum [17, 18, 19, 20].
CARS has several advantages over spontaneous Raman scattering. First of all, conventional
Raman relies on the spontaneous transition. The signal is the incoherent addition of light
1.2 Raman Spectroscopy and Enhancement Technologies
12
scattered by individual molecules. While CARS relies on a coherently driven transition. Once
phase-matching condition is fulfilled the power signal quadratically grows with distance.
Secondly, spontaneous Raman signal is detected on the Stokes side of incident radiation.
Since fluorescence also emits in Stokes band, the fluorescent background might affect the signal
to noise ratio. On the other hand, CARS detects the scattering signal on the blue side, which
is free from fluorescence.
Figure 1.10: The illustration of an advanced CARS microscope reprinted from [29]. This microscopy can perform both forward-detected CARS (by PMT1) and backward-detected CARS
(by PMT2). PH, pinhole; DM, dichroic mirror; L, lense; PMT, photomultiplier.
In 1982, at the Naval Research Laboratory, the application of CARS was first demonstrated
in imaging with a noncollinear beam geometry [24]. In 1999, it was revisited by researchers with
a collinear beam configuration at the Pacific Northwest National Laboratory [25]. Nowadays,
the development and applications of CARS can be found in wide scientific disciplines.
In figure 1.10, a high-speed, multifunctional CARS microscope is sketched. The pump and
Stokes probe with frequency ωp and ωs are two picosecond laser pulses in the near IR range.
The sources can be generated from two synchronized Ti:sapphire lasers [26] or a synchronously
pumped optical parametric oscillator system [27]. After being collinearly combined, the two
beams go into the scanner and are focused on the sample. The forward signal is collected by a
1.2 Raman Spectroscopy and Enhancement Technologies
13
condenser and detected by PMT1. The backward reflected signal is detected by PMT2. When
working with only the pump beam, this system can also be used for generating and detecting
spontaneous Raman signals. In this case, Raman signals generated at the sample will be directed
by DM into the spectrometer for spectra recording.
However, CARS also has shortcomings. First, the equipment for CARS measurement is more
complex and expensive than that for spontaneous Raman. The need to sweep the Stokes probe
requires expensive tunable laser or broadband supercontinuum source. In conventional CARS
measurement, two synchronized pulses are employed. The two pulses should overlap in both
space and time, which makes sophisticated temporal and spatial alignment necessary.
Most of all, CARS generation also has background problems. The electronic contribution
in the third-order susceptibility χ(3) can induce coherent nonresonant background which is independent of Raman shift [21]. This nonresonant background is mixed with the chemically
specific resonant signal, limiting the sensitivity of CARS detection. Several approaches have
been developed to solve this problem. One is the polarization CRAS. The difference between
the polarization properties of the resonant CARS signal and its non-resonant counterpart makes
it possible to reject the non-resonance background by putting an analyzer before the detector.
However, for materials of which the difference is small, rejecting non-resonance background will
also reject a large part of the resonant signal. Other approaches such as epi-CARS, time-resolved
CARS and spatial phase control CARS can also help to suppress the nonresonant background.
But, in the same time, the required sophisticated optical design could limit their application.
1.2.5
Surface Enhanced Coherent Anti-Stokes Raman Spectroscopy (SECARS)
With the combination of CARS and plasmonic surface enhancement on nanostructured surfaces, another enhancement technique, namely Surface Enhanced Coherent Anti-Stokes Raman
Spectroscopy (SECARS), now attracts growing attentions. Although CARS itself is a good enhancement technique over conventional Raman spectroscopy, its sensitivity is still not enough
in single molecule detection. Playing the same role as in SERS, LSPRs can locally enhance the
electric fields and allow SECARS to achieve single-molecule detection sensitivity.
We refer to the energy diagram shown in figure 1.11 to illustrate the transition and field dependence of SECARS and compare it with other Raman processes. By employing appropriately
1.2 Raman Spectroscopy and Enhancement Technologies
14
Figure 1.11: Energy diagram of different Raman process. gi stands for the field enhancement at
different frequencies. This figure is reprinted from [30]
.
designed nanostructure, the input frequencies ωp , ωs and output frequency ωas can experience
enhancement. The enhancement factor as also shown in figure 1.11 is given by
GSECARS =|gp |4 |gs |2 |gas |2
(1.8)
=|E(ωp )/E0 (ωp )|4 |E(ωs )/E0 (ωs )|2 |E(ωas )/E0 (ωas )|2
The enhancement is significant when any of photons ωp , ωs or ωas is in resonance with the
localized plasmonic field supported by certain nanostructure. And when all three photons are in
resonance with the plasmonic modes of nanoparticle in same spatial location, the enhancement
reaches maximum [32, 33, 34] and can be theoretically as high as 1012 [31]. In a recent work, Y.
Zhang et al. reported an enhancement of about 11 orders of magnitude relative to spontaneous
Raman by exploiting the unique light harvesting properties of plasmonic Fano resonances [35].
As illustrated in figure 1.12, their nano-structure is optimized to have resonance at pump
frequency, Stokes frequency and anti-Stokes frequency [35]. To perform SECARS measurement,
they split the laser beam from a Ti:sapphire pulse laser (Mira 900, Coherent Inc.) into two
beams. One of the beam functions as pump beam and the other beam is propagating inside
nonlinear photonic crystal fiber to generate continuum Stokes beam .Then they focus these two
horizontally polarized, collinear and coherent pulse trains onto the sample. The detection of
SECARS signal is done by collecting the transmission and after which it was analysed by a
1.2 Raman Spectroscopy and Enhancement Technologies
15
Figure 1.12: Pictures reproduced from [35] to introduce their works. The gold quadrumer is
shown in inset. (a) The upper and lower spectrum show experimental and simulation results
with (black) and without (red) the p-MA. (b)A schematic diagram of the charge distribution of
the subradiant(top) and superradiant modes(bottom). (c) Field enhancement at the different
frequencies : anti-Stokes (left), pump (middle) and Stokes (right). (d) SECARS enhancement
map with the maximum enhancement factor about 1.5×1010 in the central gap using FDTD
simulation.
1.3 On-chip Spectroscopy
16
spectrometer. In this experiment, phase matching for efficient nonlinear build-up is automatically fulfilled mainly due to its short interaction length. Their simulation and experiment result
indicated that with horizontally polarized excitation and after functionalization of a monolayer
of paramercaptoaniline (p-MA) molecules, the maximum enhancement factor can reach about
1.5×1010 in the central gap.
1.3
On-chip Spectroscopy
Spectroscopy is an important technology in the field of sensing. By detecting the ”fingerprint”
of the molecules, spectroscopy can give us relatively adequate information for the substance
identification as well as concentration determination. Yet, conventional spectroscopy involves
cumbersome and expensive instrumentation, and requires sophisticated alignment. To miniaturize the spectroscopy and make it less expensive, one way is to integrate the key part of the
optical functionality onto a chip [37, 38].
The already existing technologies in advanced CMOS fabrication can be directly employed to
fabricate photonic integrated circuits. Optical components including passive waveguides, optical
modulator and bonded III-V semiconductor layers have already been reported on the platform
of 200-300 mm silicon-on-insulator (SOI) wafer [39, 40, 41, 42]. In bio-sensing applications the
interested wavelengthes mainly lie in the wavelength range from 750 to 1200 nm, which is defined
by the protein absorption region (>750 nm) and the water absorption wavelengthes (<1200 nm)
[36]. However, silicon is transparent only above 1100 nm, which makes the SOI platform seemly
not suitable for bio-sensing applications. This difficulty is soon solved by the development of
Silicon-Nitride (Si3 N4 ) waveguide.
Si3 N4 is suitable for bio-sensing for its transparency in visible and near infrared(NIR) region
and its high refractive index. In Si3 N4 waveguide, the high refractive index contrast can enhance
the absorption of the guided mode by the particles at the core and cladding interface and also
increase the efficiency of coupling light emitted by these particles into the guided mode[48].
Besides, very low material loss in the interested wavelength range is reported in the Si3 N4
waveguide fabricated by low-pressure chemical vapor deposition (LPCVD)[43, 44] and also by
low temperature plasma-enhanced chemical vapor deposition (PECVD) [45].
All these good performances have made Si3 N4 waveguide attractive in on-chip spectroscopy.
1.4 Outline of Thesis
17
Actually, some works have already been reported recently on the silicon nitride based spontaneous Raman spectroscopy [46] and surface enhanced Raman spectroscopy [47].
1.4
Outline of Thesis
In this master thesis, we want to investigate the feasibility of CARS generation based on silicon
nitride waveguide. The main purpose is to accomplish the on-chip CARS generation, and into
the detail, our battle plan can be divided into two parts.
In the first part, we will focus on the CARS generation based on the silicon-nitride waveguide.
The theory of CARS based on nonlinear propagation of radiation described by the Generalized
Nonlinear Schrödinger Equation (GNLSE) is first introduced chapter 2. Waveguide based CARS
generation enjoys several advantages over microscopic CARS generation. Among then, the most
important improvement is the relatively long interaction length which can be up to centimeter
level. Yet, to really realize this benefit, one must be careful with the phase matching condition
and engineering of waveguide dispersion in inevitable. We will show how we do this in chapter
3. In chapter 4, we will investigate the feasibility of CARS generation based on the available
sources in our lab.
In the second part, we move to an enhanced version of CARS, i.e. Surface Enhanced Coherent
Anti-Stokes Raman Spectroscopy (SECARS). We will introduce the theory of SECARS and
discuss the simulation in chapter 5. Then in chapter 6, we will present the fabrication detail
involved in this thesis work. The experimental investigation of SECARS will be reported in
chapter 7.
THEORY OF COHERENT ANTI-STOKES RAMAN SCATTERING (CARS)
18
Chapter 2
Theory of Coherent Anti-Stokes
Raman Scattering (CARS)
2.1
Generalized Nonlinear Schrödinger Equation (GNLSE)
In general, the propagation of optical pulse in dispersive and nonlinear waveguide is described by
the Generalized Nonlinear Schrödinger Equation (GNLSE). The time-domain GNLSE is given
by [53]
(
)(
)
∫ ∞
∑ in+1 ∂ n A
1 ∂
∂A α
′
′ 2
′
+ A−
βk n = iγ 1 + i
A(z, T )
R(T )|A(z, T − T )| dT . (2.1)
∂z
2
n!
∂T
ω ∂T
−∞
n≥2
In obtaining this equation, the spacial dependence of electric file E(x, y, z) is separated as
E(x, y, z) = F (x, y)A(z)
(2.2)
where F (x, y) is the normalized transverse mode profile and A(z) is the amplitude varying slowly
along the direction of propagation.
The variable T is the time in co-moving frame and is defined as
T = t − β1 z
(2.3)
where β1 is the reciprocal of group velocity.
In GNLSE, the linear propagation effect is described at the left-hand side, where α in the
second term is the linear attenuation coefficient and βn is the dispersion coefficients to the n-th
2.2 Four-Wave Mixing(FWM)
19
order. At The right-hand side of GNLSE, nonlinear effect is introduced by nonlinear parameter
γ, which is defined as
γ=
n2 (ω)ω
cAeff
(2.4)
where n2 is the nonlinear refractive index and Aeff is the mode effective area. R(t) is the
response function of the medium which in general consists instantaneous Kerr response and
delayed Raman response. One can write R(t) as
R(t) = (1 − fr )δ(t) + fr hr (t)
(2.5)
where δ(t) is the instantaneous Kerr response function and hr (t) is the Raman response function.
The time derivative ∂/∂T models the nonlinear dispersion and response for the effects such as
self-steepening and optical shock formation.
2.2
Four-Wave Mixing(FWM)
Four-wave mixing (FWM) is a third-order nonlinear effect. Two pump lasers with frequency
ωpump1 and ωpump2 are injected into nonlinear medium together with another beam (ωidle ). They
interact with nonlinear medium through the third-order nonlinearity χ(3) and generate signal at
new frequency ωsignal . FWM is a typical parametric mixing process where energy conservation
and phase matching must be fulfilled
∆ω = ωsignal + ωidle − ωpump1 − ωpump2 = 0;
(2.6)
∆k = ksignal + kidle − kpump1 − kpump2 = 0.
(2.7)
The energy diagram of a degenerated FWM is shown figure 2.1, where the two pump laser
beams have the same frequency, i.e. ωpump1 = ωpump2 .
In general, the discussion of degenerated FWM in nonlinear waveguide should base on
GNLSE given by equation (2.1). In this section, however, we want to use a reduced NLSE
to model the degenerated FWM. We neglect the losses and dispersion and only take into account the instantaneous Kerr response. Equation (2.1) then becomes
∂A
= iγA(z, T )|A(z, T )|2 .
∂z
(2.8)
2.2 Four-Wave Mixing(FWM)
20
Figure 2.1: The energy diagram of degenerated FWM process
In undepleted assumption, we consider a strong pump P0 which remains undepleted during the
interaction. The general solutions of a set of coupled amplitude equations based on equation
(2.8) can be written as [51]
B3 (z) = (a3 egz + b3 e−gz )exp(−jκz/2)
(2.9)
B4 (z)∗ = (a4 egz + b4 e−gz )exp(−jκz/2)
(2.10)
where the subscript 3 and 4 correspond to the idle and signal respectively. The cross phase
modulation induced by pump P0 is included in Bj (z)
Bj (z) = Aj (z)exp(−2jγP0 z)
(2.11)
where j=1,2. The net phase mismatch κ has both linear and nonlinear contribution and is given
by
κ = ∆k + 2γP0 .
(2.12)
√
g = γP0 − (κ/2)2 .
(2.13)
The parametric gain g is defined by
2.3 CARS
21
Parameter aj and bj are determined by the given boundary condition. In our discussion, we
assume that a strong pump and a weak signal are injected into the waveguide. Furthermore, we
make another assumption that we are working in the low gain region where κ >> γP0 . This is
usually the case because perfect phase matching for a high parametric gain is rarely achieved in
practice. After some calculation, we get the signal power at the output (z = L)
P4 (L) = (γP0 L)2 P3 (0)sinc2 (κL/2).
(2.14)
From this equation, we can see that the signal at new frequency can be generated by degenerated
FWM and the signal strength quadratically depends on the pump power and linearly depends
on idle power. If κ = 0, it is also shown in equation (2.14) that the signal grows quadratically
as the propagation distance increases . We can see now that the phase matching is important
because if the net phase matching κ is too large, signal can only be built up in a very short
distance and therefore be rather weak.
2.3
CARS
Figure 2.2: The energy diagram of CARS process
We show the energy diagram of CARS in figure 2.2. The process can be understood as
following. The molecule is initially at the ground state. A pump beam excites the molecule to a
virtual state which theoretically cannot be occupied since it is not an eigenstate of the molecule.
2.3 CARS
22
However, it can work as an intermediate state which makes the transitions between otherwise
uncoupled real states possible. As shown in figure 2.2, when the frequency difference between
pump beam and Stokes beam matches the vibrational frequency Ωv , the virtual states can couple
the vibrational eigenstate and ground state of the molecule together and help generate signal at
new frequency given by
ωas = ωp + Ωv .
(2.15)
CARS is a degenerated FWM process. The theory employed in section 2.2 can be used to
describe CARS after some modification. That is now we should take into account both the
instantaneous Kerr response and delayed Raman response. In this case, equation (2.8) becomes
∂A
= iγk (1 − fr )A(z, T )|A(z, T )|2
∂z
∫
∞
+ iγr fr (A(z, T )
−∞
h(T ′ )|A(z, T − T ′ )|2 dT ′ )
(2.16)
where fr is the fractional contribution of the delayed Raman response and h(t) is the Raman
response function.
It is studied in [50] that the imaginary part of the Fourier transform of h(t) is related to
Raman gain spectrum. In practice, h(t) is deduced from the Raman gain spectrum with the use
of Kramers-Kronig relations.
Although it is not easy to find the analytic form of Raman response function, several attempts
have already been made. One of them is the damped oscillation model [49]. In this model, the
response function is expressed as
h(t) =
τ12 + τ22
exp(−t/τ2 )sin(t/τ1 )Θ(t).
τ1 τ22
(2.17)
It is worth noting that there is a heaviside function Θ(t) in this expression. This is required by
causality that there should be no response at the time before the arriving of the stimulation.
In Fourier domain, the imaginary part of the response function is of lorentz line shape,
which peaks at angular frequency of 1/τ1 and has bandwidth at half width of maximum of 1/τ2
(angular frequency).
It would be too cumbersome to give the detailed theory of FWM based on equation (2.16).
Actually, we can make use of equation (2.14). We consider P4 as the power of anti-stokes signal,
P0 as power of pump laser and P3 as power of Stokes probe. Noting that power can be directly
2.3 CARS
23
related to the intensity and the nonlinear parameter γ is proportional to the corresponding third
order susceptibility, we can get to the conclusion that anti-Stokes signal can be expressed as
Ias ∝ |χ(3) |2 L2 Ip2 Is sinc2 (κL/2).
(2.18)
The third-order nonlinearity χ(3) is composed of both Raman contribution and Kerr contribution
(3)
χ(3) = χk + χ(3)
r
(3)
(3)
where the two contributions χk and χr
(2.19)
are included in equation (2.16) by γk and γr respec-
tively.
Kerr contribution is a non-resonance electronic contribution which has no dependency on the
Stokes frequency and will not give information about the vibrational structure of the molecules.
Therefore, this contribution often refers to a non-resonance background.
Figure 2.3: CARS line shape the horizontal dash line represent the non-resonance background
and the vertical dash line is positioned at the vibrational frequency Ωv
(3)
As for the Raman contribution, the responsible χr
χ(3)
r =
Ω2v
takes following form
Ar
− (ωp − ωs )2 + iΓs (ωp − ωs )
(2.20)
where Ar is a constant related to Raman scattering cross section, Γr and Ar are the frequency
and linewidth of the Raman line. Assuming the pump frequency ωp is fixed, it is clear that the
Raman contribution will vary with different Stokes frequency.
2.4 Phase Matching
24
In the case κL << π, the combination of both contributions generates a CARS line shape
against a flat non-resonant background. Such a CARS line shape is shown in figure 2.3 where a
resonant peak appears at the blue-shifted side and a negative contrast feature comes out on the
red side.
2.4
Phase Matching
As seen from the solution given by equation (2.18), CARS generation is efficient only when the
propagation distance L is smaller than π/κ. Beyond this distance the sinc term becomes so
small that the CARS signal is too weak to be detected.
The net phase mismatch κ has three contributions and can be written as
κ = ∆km + ∆kw + ∆knl
(2.21)
where ∆km , ∆kw , ∆knl are the phase mismatch resulting from material dispersion, waveguide
dispersion and nonlinear effects, respectively.
The material contribution can be written as
∆km = n0 (ωs )
ωp
ωs
ωas
+ n0 (ωas )
− 2n0 (ωp )
c
c
c
(2.22)
where n0 (ωj ) with j=s, as and p is the material refractive index at corresponding frequency.
Normally, it is hard to change these terms because for a given material the dispersion curve is
usually fixed.
The origin of the second contribution can be understood as a frequency dependent change
in refractive index due to waveguiding. We can write this term in a similar form as equation
(2.22)
∆kw = ∆n(ωs )
ωp
ωs
ωas
+ ∆n(ωas )
− 2∆n(ωp ) .
c
c
c
(2.23)
This term can be modified by waveguide design as the waveguide dispersion curve depends
strongly on the structure of waveguide.
In practice, it is not easy to investigate the two contributions separately. Instead, we combine
them together by writing the total refractive index as
n(ωj ) = n0 (ωj ) + ∆n(ωj )
(2.24)
2.4 Phase Matching
25
where j= s, as and p. With this expression, we can write the linear phase mismatch which is
the combination of the contribution of material and waveguide.
∆kl = β(ωs ) + β(ωas ) − 2β(ωp )
(2.25)
where β(ωj ) is the propagation constant defined as n(ωj )ωj /c. Using Taylor expansion, β(ωs )
and β(ωas ) can be expanded at pump frequency ωp
∑ 1
1
β(ωs ) = β(ωp ) − Ωβ1 (ωp ) + Ω2 β2 (ωp ) +
(−Ω)n βn (ωp )
2
n!
n>2
∑ 1
1 2
β(ωas ) = β(ωp ) + Ωβ1 (ωp ) + Ω β2 (ωp ) +
Ωn βn (ωp )
2
n!
(2.26)
n>2
where Ω = ωas − ωp = −(ωs − ωp ) is the frequency shift and βn is the nth-order derivative of
β. If we only concern dispersion to the second order and neglect all higher order terms, we can
write the linear phase mismatch as
∆kl = β2 (ωp )Ω2 .
(2.27)
For a perfect phase matching, κ is zero, which means the linear and nonlinear phase mismatch
should add up to be zero. Taking into account that the nonlinear phase mismatch is 2γP0 , we
can write the phase matching condition as
1
β2 (ωp )Ω2 = −γP0
2
(2.28)
Figure 2.4: (a), the cross section of a typical slot waveguide with silicon nitride as core material
and silicon as substrate. (b) the cross section of a same waveguide after under etching
2.4 Phase Matching
26
Instead of using β2 , group-velocity dispersion (GVD) is often quantified by parameter D,
which is defined as
D=−
2πc
β2 .
λ2
(2.29)
We canthen see from equation (2.28) that perfect phase matching can only be achieved when
the pump wavelength lies in the anomalous group velocity dispersion regime, where D is positive.
A typical silicon nitride waveguide is shown in the figure 2.4. For such a waveguide, D is
negative within the interested wavelength range because of the strong material GVD. According
to equation (2.28), it is difficult to get phase matching in this waveguide. However by etching
the SiO2 substrate underneath silicon nitride core (structure shown in part b of figure 2.4) we
found that positive D is achievable. A detailed investigation will be dedicated to this approach
in chapter 3.
WAVEGUIDE DISPERSION ENGINEERING AND SUPERCONTINUUM GENERATION (SCG) 27
Chapter 3
Waveguide Dispersion Engineering
and Supercontinuum Generation
(SCG)
Optical waveguide is a structure to guide light wave propagation. Basically, a dielectric waveguide has a longitudinally extended high-index optical region which is called the core. The media
transversely surround the core, usually with lower refractive index, are the cladding. In most of
the case, optical wave is confined within the core region and propagates in the waveguide along
the longitudinal direction.
By definition, dispersion is the frequency dependency of phase velocity at which an optical
wave propagates. In optical waveguide, dispersion has two contributions, i.e. material dispersion
and waveguide dispersion. The former is the change in refractive index with optical frequency
in a homogeneous material. In a waveguide, however, optical wave is propagating in an inhomogeneous structure. The distribution of optical field in the core and the cladding depends on the
frequency. This would lead to an additional frequency dependence of the phase velocity, which
is termed as waveguide dispersion.
In the propagation of optical pulse in waveguide, rather than dispersion, one would be more
concerned about the group velocity dispersion (GVD). GVD describes the wavelength dependence of the group velocity at which the pulse of light propagating in a transparent medium.
Just as dispersion, GVD also has material and waveguide contributions. The material GVD is
3.1 Material GVD
28
often characterized by the GVD parameter D which is usually in the unit of (ps/km/nm) and
defined as
D=
−λ d2 n(λ)
c dλ2
(3.1)
where n(λ) is the refractive index of bulk material and c is the speed of light in free space.
3.1
Material GVD
The core material of the waveguide involved in our work is Si3 N4 . Predominantly, Si3 N4 is
deposited by low-pressure chemical vapor deposition (LPCVD) or plasma-enhanced chemical
vapor deposition (PECVD) technique. To obtain the GVD curves of these two type of Si3 N4 ,
one approach is to fit the wavelength dependent refractive index with polynomial function and
calculate the second order derivative at each wavelength. Following this approach, we plot the
curves of GVD in figure 3.1 for Si3 N4 deposited by LPCVD and PECVD.
Figure 3.1: The curve of material group velocity dispersion for Si3 N4 deposited by low-pressure
chemical vapor deposition (LPCVD) and plasma-enhanced chemical vapor deposition (PECVD)
technique.
3.2 Ridge Waveguide
29
The fitting and plotting are limited in the wavelength range of 600-900 nm covering the
visible and near infrared region we are interested in. Within this window, we would like to have
a wavelength region where the total GVD is positive (anomalous dispersion with D > 0) and
weak (D has small absolute value).
The total GVD is the sum of material GVD and waveguide GVD. The material GVD of
Si3 N4 as shown in figure 3.1 is strong and negative. Compensation can be done by engineering
waveguide GVD. But one would prefer to have a good start point, i.e. a relatively weak material
GVD. In this consideration, LPCVD Si3 N4 is a better choice.
Once the material GVD is fixed. The total GVD is only determined by the waveguide GVD,
which is controlled by the geometry of waveguide. In the following sections, we will investigate
the total GVD of LPCVD Si3 N4 waveguide with different geometries.
3.2
Ridge Waveguide
In this section, the waveguide under concern is a ridge waveguide consisting a Si3 N4 waveguide
core, a silica undercladding and a silicon substrate. The cross section of the ridge waveguide is
shown in figure 3.2.
In a properly designed ridge waveguide, light can propagate in transverse electric (TE) mode
or in transverse magnetic (TM) mode. Different mode has different GVD and in the following
discussion we will focus on fundamental TE mode of the reason that we found this mode has
the most desirable GVD we want.
When playing with the height H and the width W, one should also keep in mind that the
size of the core must be realistic for fabrication. In this aspect, H up to 300 nm is possible and
the W should be larger than 300 nm. For waveguide with different core size, optical design tool
FIMMWAVE is used to solve the fundamental TE mode and calculate the curve of total GVD.
The simulation wavelength is limited in the range of 600-900 nm as we are interested in only
the visible and near infrared region.
The curves of GVD for height H fixed at 300nm are plotted in figure 3.3 with different width
W. It can be observed that as the core becomes wider, the curve becomes steeper. If we can
somehow raise the curve (proved later), a flat curve would allow a wide region of weak anomalous
dispersion and thus be preferable.
3.2 Ridge Waveguide
30
Figure 3.2: A sketch of ridge Si3 N4 waveguide.
In figure 3.4, We plot the GVD curves with fixed W for example at 500 nm and varying H.
From the result we can see that a weaker GVD dispersion is achieved by increasing the height
of the core.
Figure 3.3: The GVD curves of ridge waveguide with height H fixed at 300 nm and width W
varying from 500 nm to 600 nm
As a conclusion, the strong material dispersion as shown in figure 3.1 can be compensated
3.3 Underetched Waveguide
31
Figure 3.4: The GVD curves of rectangle waveguide with width W fixed at 500 nm and the
height H taking 270, 280, 290 and 300 nm.
by the waveguide GVD to certain extent. However, we also notice that within the parameter
space allowed by the fabrication, we cannot obtain a waveguide with anomalous dispersion.
3.3
Underetched Waveguide
Apart from optimizing the size of Si3 N4 core, waveguide dispersion can be further engineered
by removing part of the silica underneath the core. Underetching the silica increases the indexcontrast experienced by the waveguide mode and improves the mode confinement. As a result,
the waveguide dispersion becomes stronger providing the possibility to further compensate material dispersion and obtain the anomalous total GVD. In this section, we will investigate the
dispersion of underetched waveguide. The schematic cross-section of such a waveguide is shown
in figure 3.5.
The height H and the width W of the core is fixed at 300 nm and 500 nm respectively.
Fundamental TE mode of waveguide with different etch depth is solved at different wavelength,
for which we calculate the GVD parameter D and plot the GVD curves in figure 3.6.
3.3 Underetched Waveguide
32
Figure 3.5: A sketch of the underetched Si3 N4 waveguide.
Figure 3.6: The GVD curves of waveguide with different etch depth varying form 50nm to
175nm. W and H is set to be 500 nm and 300 nm.
From the figure, it can be easily observed that with increasing etch depth, the GVD curve is
shifted upwards. For example, when the etch depth is 125 nm, we find zero GVD at wavelength
of 775 and 870 nm, and between which an anomalous dispersion (D > 0) regime appears.
Moreover, the pillar width is fixed to study the influence of making waveguide wider. The
3.4 Underetched Waveguide with Cladding
33
pillar width is defined by the subtraction of two times of the etch depth from the core width
W. We fixed the pillar width at 200 nm, in which case, the GVD is positive and also weak
(0 < D < 200ps/nm/km) for W = 500 nm. The GVD curves are plotted in figure 3.7 for
varying core width from 500 to 600 nm. In this figure, we found that increasing core width
would shift the first zero dispersion wavelength (ZDW) to the longer wavelength side and also
make the curve steeper, leading to a narrow wavelength range in which 0 < D < 200ps/nm/km.
Therefore, making the core too wide should be avoided, though, based on our experience, a
wider core often provides lower coupling and propagating loss.
Figure 3.7: The GVD curves of waveguide with fixed pillar of 200 nm. W varies from 500 to
600 nm and H is 300 nm.
3.4
Underetched Waveguide with Cladding
Optical power is not perfectly confined in the waveguide core. The evanescent tail of guided
mode can extend outside the waveguide core, forming a evanescent field at the close vicinity
of the core. The evanescent field can be scattered the bio-molecules attached to the waveguide
core. The scattered light is then evanescently coupled back to the waveguide as in the case of
3.5 Supercontinuum Generation (SCG)
34
Raman sensing [46]. For guided mode with proper GVD, the evanescent field can also be used
to detect the CRAS signal of the attached bio-material.
In this section, we assume the bio-material, for example, nitrothiophenol (NTP) with refractive index of 1.68, forms a thin monolayer on the surface of the waveguide. A sketch of the
cross section of the structure is shown in figure 3.8. The underetched waveguide is covered by
a green cladding which stands for the NTP monolayer. The size of the waveguide core is fixed
with height of 300 nm and width of 500 nm. And the etch depth is set to be 150 nm.
Figure 3.8: A sketch of the underetched Si3 N4 waveguide cladded with a NTP monolayer(green).
For different cladding thickness, the GVD curves are plotted in figure 3.9. We can see that
increasing cladding thickness would red shift the curve and move the first ZDW to the longer
wavelength side. This means that given a pump wavelength, the cladding should be enough
thin to ensure anomalous dispersion (D>0). For example, if we choose to work at 750 nm, the
cladding should not be thicker than 30 nm.
3.5
Supercontinuum Generation (SCG)
Supercontinuum generation (SCG) refers to the process of drastic expansion of the spectra of
the input source. This process is the co-product of several nonlinear effects [53] when the pulse
is propagating in the anomalous GVD region and experiences near zero GVD. Small anomalous
GVD allows soliton formation and propagation which is the fundamental of spectral broadening.
The requirement of small anomalous dispersion makes SCG proper for verifying the disper-
3.5 Supercontinuum Generation (SCG)
35
Figure 3.9: The GVD curves of underetched waveguide with varying cladding thickness as shown
in the legends. The size of the waveguide core are fixed with height of 300 nm and width of
500 nm and the etch depth is set to be 150 nm.
sion engineering approach discussed in the previous section. For this purpose, we etched a ridge
Si3 N4 waveguide, as shown in figure 3.2, with core height of 300 nm and and width of 500 nm
to get an underetched waveguide as shown in figure 3.3. The etch depth is 150 nm which gives
us a pillar width of 200 nm. The fabrication details will be introduced in later chapter.
Figure 3.10: The waveguide loss in the wavelength range of 600-950 nm measured by a cutback
measurement
Waveguide loss can also be a limiting factor in SCG. Before performing SCG, We measured
3.5 Supercontinuum Generation (SCG)
36
Figure 3.11: Spectra of the underetched waveguide at different launched peak power. For clarity
the spectra are deliberately shifted vertically to avoid overlap.
the waveguide loss use a commercial supercontinuum source (NKT superK EXR-4). The result
is plotted in figure 3.10.
With waveguide loss around 11 dB/cm in the wavelength window we interested in, this
waveguide is ready for SCG generation. The output spectra of this underetched waveguide are
shown in figure 3.11 for different pump power. We refer to the work of H. Zhao et al. [54] for
more details. Through SCG, we can conclude that the dispersion engineering approach discussed
in section 3.3 is, in practice, capable of enhancing the waveguide dispersion to compensate the
strong material dispersion and in the end bringing the anomalous GVD into the interested
wavelength window.
CARS CASE STUDY AND LIMITATION
37
Chapter 4
CARS Case Study and Limitation
In this chapter, we show that CARS generation based on the optical waveguide can be calculated
analytically and that many different parameters can influence the strength of CARS signal in
a nonlinear way. In the first section, we would like to give a brief introduction to this analytic
algorithm. Then in the second section, we will talk about the media response function and
investigate the nonlinear parameter. Some computing results will be presented in third section
which would provide insight into the influence of different parameters. Finally, we give some
conclusions at the end of this chapter.
4.1
Quantum Nonlinear Schrödinger equation (QNLSE)
The simulation of CRAS generation is based on the analytical solution of Quantum Nonlinear
Schrödinger equation (QNLSE). Like the GNLSE introduced before, QNLSE can describe the
propagation of pulse in nonlinear dispersive medium. QNLSE takes the form
2
∑
√
∂ψ(z, t)
in+1
∂n
= {(
βn n ) + ϵi fr γh̄ω0 Γ(z, t)
∂z
n!
∂t
n=1
∫ ∞
+ iγh̄ω0
R(t − t′ )ψ † (z, t′ )ψ(z, t′ )dt′ }ψ(z, t).
(4.1)
−∞
The first term at the right hand side describes the effect of dispersion. The term including Γ(z, t)
refers to thermal Raman effect which, in classical regime, is very small and can be treated as a
perturbation. Here we use a factor ϵ to follow this perturbation term. The third term models
the response of medium which includes both the Kerr and Raman response.
4.1 Quantum Nonlinear Schrödinger equation (QNLSE)
38
Without perturbation, the solution for the propagation of monochromatic beam can be
written as
ψ(z) =
√
∫
F exp(iFϱz) with ϱ = γh̄ω0
∞
−∞
R(t − t′ )dt′ .
(4.2)
In this solution, F is the flux of pump photons, which can be directly related to the power of
laser P = F h̄ω0 .
Now we add a perturbation A(z,t) into the solution, and change equation (4.2) into
√
ψ(z) = [ F + ϵA(z, t)]exp(iFϱz).
(4.3)
Inserting this solution back into equation (4.1) and linearizing in ϵ gives us
4
∑
√
√
∂A(z, t)
in+1 ∂ n A(z, t)
=(
βn
)
+
i
f
γh̄ω
F Γ(z, t)
r
0
∂z
n!
∂tn
n=1
∫ ∞
R(t − t′ )(A† (z, t′ ) + A(z, t′ ))dt′ .
+ iγh̄ω0
(4.4)
−∞
Rather than in the time domain (z, t), it is more convenient to solve this equation in Fourier
domain (z, ω). To move into Fourier domain, new new variables should be introduced,
∫ +∞
1
′
R(t − t ) =
χ(Ω)e−Ω(t−t ) dΩ
2π −∞
∫ +∞
1
a(z, ω + Ω)e−Ωt dΩ
A(z, t) = √
2π −∞
∫ +∞
1
′
Γ(z, Ω)e−Ω(t−t ) dΩ
Γ(z, t) = √
2π −∞
′
(4.5)
Where the variable a(z, ω + Ω) is the Fourier transform of A(z, t), whose frequency is shifted
by Ω from the monochromatic pump frequency ω. After some calculations, we come to the
solution
a(z, Ω) = µ(z, Ω)a0 (Ω) + ν(z, Ω)a†0 (−Ω)
∫ z
√
+ P γfr
iΓ(z ′ , Ω)[µ(z − z ′ , Ω) − ν(z − z ′ , Ω)]dz ′
(4.6)
0
where
β2 Ω2 + γP χ
sinh(ρz) + cosh(ρz)] exp(iβ1 Ω)
2ρ
γP χ
sinh(ρz) exp(iβ1 Ω)
ν(z, Ω) = i
ρ
√
β 2 Ω4
ρ(Ω) = − 2
− β2 Ω2 γP χ.
4
µ(z, Ω) = [i
(4.7)
4.2 Media Response and Nonlinear Parameter
39
In the solution (4.6), a0 (Ω) and a†0 (−Ω) are related to the initially injected photon flux at
anti-Stokes and Stokes frequency. The third term again describes the spontaneous Raman effect.
From the solution, if we assume no initial injection at anti-stokes frequency, the generated
photon flux f (Ω) at anti-stokes frequency can be related to the injected Stokes photon flux by
⟨
⟩
f (Ω) = a(Ω)a† (Ω)
⟩
⟨
= |ν(z, Ω)|2 a0 (−Ω)a†0 (−Ω) + |ς(Ω)|2
Where ς(Ω) stands for the spontaneous Raman term,
(4.8)
∫z
√
P γfr 0 iΓ(z ′ , Ω)[µ(z − z ′ , Ω) − ν(z −
z ′ , Ω)]dz ′ and ⟨...⟩ denotes the averaged over coherent state. The photon flux is the number of
photons per unit time and frequency, in the unit of photons/s/Hz.
From equation (4.8) and the expression of ν(z, Ω) in the definition (4.7), one can find that
the generated signal at anti-stokes frequency is governed by GVD (β2 ), Pump power (P), Stokes
⟨
⟩
seeds (fStokes , defined as a0 (−Ω)a†0 (−Ω) ), nonlinear parameter gamma (γ), media response
function (χ) and interaction distance z in a nonlinear way. In the following sections, we would
study these factors in detail.
4.2
Media Response and Nonlinear Parameter
As mentioned in chapter 2, media response contains Kerr and Raman contributions. In time
domain, Kerr contribution is an instantaneous response, while the Raman response has time
delay nature. In frequency domain, we can write
γχ =γk + γr χr
(4.9)
=γr (η + χr )
where η is the factor that evaluate the ratio of Kerr contribution and Raman contribution. The
complex Raman response function χr can be obtained from the Fourier transform of h(t) defined
in (2.17). The imaginary part of χr has a Lorentzian line shape and determines the peak position
and bandwidth of Raman gain.
Raman nonlinear parameter γr can be estimated by gr /2Aeff , with Aeff the effective area and
gr the gain coefficient. The later is obtained from the spontaneous efficiency S,
gr =
8πc2 ωp
S
h̄ωs4 n2 (N + 1)∆ω
(4.10)
4.3 Simulation Results
40
With this definition, we can write γr as
γr =
2
λ3 σC
× Ffrac
Aeff πh̄cn2 (N + 1)Γr
(4.11)
where Γr is the bandwidth, N is the Boltzmann thermal population factor depends on the
temperature and frequency shift, σ is the Raman cross-section and C is the volume number
density. We also take into account that not all the power is launched into the bio-material by
putting a factor Ffrac into equation 4.11.
We assume the pump is at 765 nm and consider NTP’s prominent Raman peak at 1335 cm−1
(N O2 bond) [55] with bandwidth assumed to be 300 GHz. For the Raman cross-section, it is
safe to take the value of 10−30 cm2 sr−1 as most molecules have larger value than this one [35].
The parameters need to estimate γr is tabulated in table 4.1 4.1.
Parameter
Value
λ
765 nm
σ
10−30 cm2 sr−1
C
5.3×1021 cm−3
Aeff
0.18 µm2
n
1.9
N
0.00166
Γr
300 GHz
Ffrac
0.1
Table 4.1: Parameters for the estimation of γr
Inserting these parameters into equation (4.11), we get γr of 1.4 W−1 m−1 . Although this
estimation is not very precise, it could nevertheless give us an idea about the order of magnitude
of the Raman nonlinear parameter.
4.3
Simulation Results
The simulation is based on the solution in equation (4.8). In the following discussion, we consider
Raman peak at frequency shift of 40 THz (about 1335 cm−1 , the domain Raman peak of NTP)
and bandwidth of 300 GHz and we set γr = 1W−1 m−1 and η = 4. The injected Stokes flux is at
4.3 Simulation Results
41
the level of 107 photons/Hz/s which is converted from power density of 1 dBm/nm, generated
by a supercontinuum source.
As mentioned before, many parameters can simultaneously influence the anti-Stokes spectrum in a nonlinear way. We would like to first study the influence of GVD (β2 ) on the spectrum.
For now, we fix the interaction distance z0 =1 cm and set P0 = 0.1 W. In figure 4.1, signal spectrum for different values of GVD with β2 = −0.034 ps2 m−1 is plotted.
1 ΜW
0.1 Β2
Β2
Power
1 nW
10 Β2
1 pW
20
40
frequency shift W HTHzL
60
80
Figure 4.1: The anti-Stokes spectrum for different GVD: 0.1β2 , β2 and 10β2 . At the frequency
shift of 40 THz a CARS line shape can be observed most obviously in the case of 0.1β2 . The
interaction distance is fixed at z0 = 1 cm and γr = 1m−1 W−1 , P = 0.1W.
One can find CARS line shape at frequency shift of 40 THz, sitting on top of the Kerr
background. The kerr background exhibits a sinc line shape, which origins from the the expression of ν(z, Ω), where the hyperbolic sinh function can be replaced by a sinc function when
γr P << β2 Ω2 ,
ν(z, Ω) = −γr P zχsinc(
β2 Ω2
z) exp(iβ1 Ω).
2
(4.12)
We can see from the figure that, for small GVD, i.e. 0.1β2 , kerr background is flat at the
position of CARS line shape. In this case it is easy to observe the CARS feature.
4.3 Simulation Results
42
However, when the GVD increases, the sinc line shape shrinks and the bandwidth of the
central peak decreases. In the case of large GVD, β2 or 10β2 , the CARS signal is inundated
by the background of fast kerr oscillations. As we can also see from figure 4.1, this non-flat
background would make it difficult to detect the CARS signal.
The interaction distance z can also influence the bandwidth of the central peak of the sincshaped background. This time, we fix GVD at β2 and plot the spectrum for 0.1z0 , z0 and
10z0 in figure 4.2. Comparing this results with what shown in figure 4.1, one can find that the
bandwidth of the central peak is actually determined by the production of GVD and interaction
distance.
Additionally, the interaction distance z also has influence on the level of the central peak
of the sinc background. In equation (4.12), we show that ν(z, Ω) is linearly proportional to
the interaction distance z, which would lead to a quadratic dependency of the strength of the
spectrum on the interaction z. This dependency is also shown in figure 4.2.
10 z0
1 ΜW
z0
Power
1 nW 0.1 z0
1 pW
20
40
frequency shift W HTHzL
60
80
Figure 4.2: The anti-Stokes spectrum for different interaction distance: 0.1z0 , z0 and 10z0 , where
z0 = 1 cm. The GVD is fixed at β2 = −0.034 s2 m−2 and γr P = 0.1m−1 .
The influence of pump power is investigated for fixed interaction distance of z0 and GVD of
0.1β2 . In this situation, the bandwidth of central peak of sinc line is broad enough to provide a
flat background for CARS signal. We plot the spectrum with pump power set to be 0.1P0 , P0
4.3 Simulation Results
43
and 10P0 in figure 4.3. We found the the quadratic dependency of the background level on the
pump power. In this regard, the pump power has the same influence on the spectrum as the
interaction distance does.
10 P0
Power
1 ΜW
P0
1 nW
0.1 P0
20
40
60
frequency shift W HTHzL
Figure 4.3: The anti-Stokes spectrum for different pump power: 0.1P0 , P0 and 10P0 , where
P0 = 0.1 W . The GVD is fixed at 0.1β2 = −0.0034 ps2 m−1 and γr = 1m−1 W−1 .
Yet, an obvious difference is that the pump power within the considered range has no influence on the bandwidth of the kerr background. In figure 4.2, we see that the background level
quadratically scales with the interaction distance, while the CARS signal does not behave in
the same manner. This is because the evanescent nature of the sinc function’s oscillation tail
provides an additional attenuation to the CARS signal. On the other hand, as the CARS signal
is located at the flat central peak of the background, the sinc function will not have important
influence on the CARS signal. This allows the CARS signal to scale quadratically with the
power.
We plot the spectrum for different injected Stokes flux with pump power fixed at P0 = 0.1 W,
GVD fixed at 0.1β2 = −0.0034 ps2 m−1 and interaction distance of z0 = 1 cm in figure 4.4. The
linear dependency can be easily found in the figure, which matches the prediction of equation
4.8.
Eventually, it is also interesting to compare CARS signal with the anti-Stokes signal in
4.4 Conclusion
44
1 ΜW
Power
10 fStokes
fStokes
0.1 fStokes
1 nW
20
40
60
frequency shift W HTHzL
Figure 4.4: The anti-Stokes spectrum for different injected Stokes flux: 0.1fStokes , fStokes and
10fStokes , where fStokes = 107 photons/Hz/s. The GVD is fixed at 0.1β2 = −0.0034 ps2 m−1 and
γr = 1m−1 W−1 , P = 0.1W.
spontaneous Raman. The latter can be obtained by removing the Stokes seeding. For pump
power fixed at P0 = 0.1 W, GVD fixed at 0.1β2 = −0.0034 ps2 m−1 and interaction distance of
z0 = 1 cm, we plot the spectra of CARS signal (fStokes = 107 photons/Hz/s) and Spontaneous
anti-Stokes signal (fStokes = 0) in figure 4.5. We measured in the figure that the CASR signal
is at the level of 103 pW while spontaneous signal is negligible small, at the level of 10−5 pW.
This leads to the conclusion that with large Stokes seeding flux, one can simply neglect the
contribution of spontaneous Raman scattering in CARS generation.
4.4
Conclusion
From the previous sections, we found that GVD plays an important role in CARS generation.
Given fixed interaction distance, it can determine bandwidth wherein the kerr background is
flat. With sufficiently small GVD, the flat region would extend to the frequency where CARS
signal generated. In such a case, the sinc function will not bring attenuation to the CARS signal.
The influence of the interaction distance z is more complicated. It’s production with GVD
determines the background bandwidth while on the other hand, it can also decide the height of
4.4 Conclusion
45
10 6
Power HpWL
10 3
10 0
10-3
10-6
10-9
20
40
60
frequency shift W HTHzL
Figure 4.5:
The anti-Stokes spectrum of CARS signal with Stokes flux of fStokes =
107 photons/Hz/s (up) and Spontaneous Raman signal with fStokes = 0 (below) The GVD
is fixed at 0.1β2 = −0.0034 ps2 m−1 and γr = 1m−1 W−1 , P = 0.1W.
the central peak of the kerr background.
Furthermore, we found that when the bandwidth of background is broad enough, CARS
signal, sitting on the flat kerr line, scales quadratically with the pump power (P) and has linear
dependency on the strength of Stokes injection.
Parameter
Value
GVD
-0.004 ∼ -0.002 ps2 m−1
pump power
10 ∼ 100 mW
Stokes probe
1 ∼ 5 dB/nm
waveguide length
1 cm
γr
1 m−1 W−1
Table 4.2: Parameters of CARS.
In practice, we estimate that only 1% of the signal can be collected by the spectrometer.
The detection accuracy of the spectrometer can go down to 1 pW. For signal stronger than this
4.4 Conclusion
46
limit, the required parameters are summed in table 4.2.
Unfortunately, due to fabrication uncertainty one can hardly reduce GVD to such a small
level even with the underetched waveguide. This would be a problem because as discussed
before, with large GVD, non-flat kerr background would impede the detection of CARS signal.
Another problem is that with the laser source available in our lab, the pump power coupled into
waveguide is weaker than 10 mW. According to our experience, the coupled power is usually
at the level of 1 mW. This would lead to CARS signal at level of 0.1 pW, which is below the
detection limit.
For these reasons, we think CARS generation based on the underetched waveguide is currently not feasible. Thus, we decide to move to the surface enhanced coherent anti-Stokes Raman
Scattering (SECARS), about which we will discuss in next chapter.
SURFACE ENHANCED COHERENT ANTI-STOKES RAMAN SCATTERING (SECARS)
47
Chapter 5
Surface Enhanced Coherent
Anti-Stokes Raman Scattering
(SECARS)
As introduced already in chapter 1, Surface Enhanced Coherent Anti-Stokes Raman spectroscopy
(SECARS), by exploiting the surface enhancement mechanism of metallic nano-particles (NPs),
can provide strong Raman signal allowing single-molecule detection.
Comparing with waveguide CARS, another advantage of SECARS is that phase matching
is automatically fulfilled. In SECARS, the interaction length is limited by the size of ’hotspot’
which is usually in the nanometer scale. As a result, the total phase mismatch that scales with
the interaction length will be negligible small.
Looking back to the two main problems we have in the waveguide CARS, we found that SECARS actually provides solutions for both of them. The strong enhancement effect in SECARS
overcomes the disadvantage of the low laser power. Additionally, we do not need to engineer
the dispersion since phase matching is automatically achieved in SECARS.
5.1
Theory of SECARS
The surface enhancement mechanism in SECARS origins from the Localized Surface Plasmon
Resonance (LSPR). We will first give a brief introduction to the theory of LSPR.
5.1 Theory of SECARS
5.1.1
48
Localized Surface Plasmon Resonance (LSPR)
Plasmon can be understood as a collective oscillation of electron gas in a bulk metal. The
oscillation is caused by the external electric field at the plasma frequency
√
ne2
ωplasma =
mε0
(5.1)
where n and e are the electron density and electron charge, ε0 is the permittivity in free space
and m is the mass of electron.
At metal-dielectric interface, there can exist a propagating mode called surface plasmon
polaritons (SPPs). SPPs is a surface wave involving both the motion of conductive electron in
the metal (plasmon) and electromagnetic (EM) waves in the dielectric (polariton).
The boundary conditions for EM wave propagating at the interface of two material characterized by dielectric function ε1 and ε2 are given by Maxwell’s equation. The conditions lead to
the dispersion relation for a wave propagating on the surface.
√
ω
ε1 ε2
k|| =
c ε1 + ε2
(5.2)
where k|| is the component of wave number parallel to the interface. For a dielectric with real
and positive ε2 , it is necessary to have a negative ε1 . This condition is fulfilled by metal. If we
neglect attenuation, free electron model of an electron gas expresses the metallic function as
ε1 (ω) = 1 −
2
ωplasma
ω2
(5.3)
where ωplasma is plasma frequency given by equation (5.1). One can see that the permittivity
ε1 (ω) becomes negative for ω < ωplasma .
Surface plasmon provides a way to confine electric energy within a very thin layer at the
metal-dielectric interface. We will see later this confinement can cause a huge enhancement of
EM intensity in the localized surface plasmons (LSP) based on metal nano-particles (NPs).
Localized surface plasmon(LSP) is the collective oscillation of free electrons when a surface
plasmon is confined within a NP whose size is smaller than the wavelength of incident light. At
proper frequency, this collective oscillation of electrons can resonate with the driving electric
field in a similar manner as a spring-mass system attains resonance under external periodic
driving force. When localized surface plasmon resonance (LSPR) is triggered by the incident
5.1 Theory of SECARS
49
optical field, enhanced dipole moment and charge separation would happen, which leads large
electric field near the particle.
It is worth noting that the frequency of LSPR strongly depends on the composition, size,
geometry, dielectric environment and particle particle separation distance of NPs. In the simplest
case of nano-sphere, the particle can be considered as a dipole with electric polarizability given
by [52]
α = 4πε0 R3
ε(ω) − εm
ε(ω) + 2εm
(5.4)
where εm is the dielectric constant of embedding medium which is usually real and taken independently of frequency. ε is the complex dielectric constant of the metal particle. Then the
electric field at the vicinity of particle can be expressed as
E = E0 + 4πε0 R3
ε(ω) − εm
εm E0
ε(ω) + 2εm
(5.5)
Where E0 represents the incident electric field. At resonance frequency, ε(ω) + 2εm reaches
minimum and a large resonant enhancement of the electric field will happen.
5.1.2
SECARS Signal
Normally when two NPs are positioned close to each other, a large local electric field enhancement can be obtained in the interparticle junctions. This EM enhancement can be used to
enhance CARS signal. As used for Raman spectroscopy, the intensity of CARS signal is related
to the intensity of pump and Stokes probe in the following form
Icars ∝ |χ(3) |2 Ip2 Is
(5.6)
In the case of SECARS, the enhanced intensity should take into account the enhancement at
frequencies of the pump, Stokes probe and the anti-Stokes signal. Thus, the overall enhancement
factor GSECARS can be written as
GSECARS = |gp |4 |gs |2 |gas |2
(5.7)
where gj = E(ωj )/E0 (ωj ) (j = p, s, as) is the field enhancement factor at corresponding
frequency.
To calculate the overall SECARS signal, one needs to know the distribution of the enhanced
electromagnetic field strength inside the nonlinear medium which is deposited at the vicinity of
the metallic NPs.
5.2 Simulation of Local Field Enhancement
50
The estimation of the electromagnetic enhancement is not trivial as the distribution of local
field varies strongly with the geometry of the nano-structure. However, finite-difference time
domain (FDTD) algorithm provides a solution to analyze the structures by numerically solving
a set of coupled Maxwell’s equations in differential form. With the help of FDTD simulation
tool, the local field distribution can be obtained, allowing further calculations of SECARS signal
strength.
5.2
5.2.1
Simulation of Local Field Enhancement
A Short Introduction to FDTD Algorithm
Maxwell’s equations are the fundamental principles in the world of electromagnetism, which
relate the temporal variation of E-field to the spatial change of H-field and vice versa. According
to Maxwell’s equations, the temporal change in the E-field (the time derivative) is determined
by the spatial variance of the H-field (the curl).
Same time-stepping relation is applied in the FDTD algorithm. At each spatial point, the
updating of E-field in time depends on both the value of the E-field stored at that point and
the numerical curl of the spatial distribution of H-field around that point. In a similar manner,
the H-field is also updated. By iterating E-fields and H-fields alternatively, FDTD can then
simulate the continuous electromagnetic waves propagating in the pre-defined numerical grid.
FDTD algorithm is first proposed by Kane Yee in the year of 1966 [56]. In his paper,
Yee proposed a way to spatially stagger the vector components of the E-field and H-field. As
illustrated in figure 5.1, the electric field components lie along the edges of one cube, while the
magnetic field vectors form the normal to the faces. In another cube, the magnetic field vector
instead situates along the edge and the E-vector crosses the middle of the face normally. In this
way, the E-field and H-field are spatially staggered together. These unit cells are now known as
Yee’s cells.
Temporally, Yee also proposed a leapfrog scheme. In this scheme, the updating of E-field
and H-field are staggered in the way that E-field is updated in the middle of each time-step of
successive H-field updates.
Based on Yee’s scheme, FDTD algorithm has been developed into many simulation tools.
FDTD method itself has been proved to be very robust and can be used to directly solve
5.2 Simulation of Local Field Enhancement
51
Figure 5.1: A sketch to demonstrate the staggered electric and magnetic field in Yee’s cells.
Maxwell’s equations in various situations with satisfying accuracy.
5.2.2
Model the Structure
In our work, silver (Ag) nanoparticles (NPs) carried by the calcium carbonate (CaCO3 ) microbeads are the Raman active center for SECARS generation. As the model substance, NTP
molecules are bonded to silver NPs to form a monolayer, providing Raman information. In
figure 5.2, we show a SEM picture of the Ag-CaCO3 beads. The gray particle with diameter of
about 1.5 µm is the CaCO3 bead. One can also see from the picture that several small bright
silver NPs are deposited on the surface of the CaCO3 bead.
We consider that a droplet of water containing large amount of Ag-CaCO3 beads are dripped
onto the silicon nitride waveguide. As the Ag-CaCO3 beads randomly moving in the liquid, some
of them would by chance rest on the waveguide. In that case, the evanescent tail of the guided
waveguide mode can trigger the plasma modes of the silver NPs and lead to SECARS generation.
In reality, the situation can be rather complicated. Ag-CaCO3 bead can rest at any position
5.2 Simulation of Local Field Enhancement
52
Figure 5.2: A SEM picture of Ag-CaCO3 micro-beads.
on the waveguide. There could be only one silver NP that is efficiently coupled to the evanescent
field, while it is also possible that more than one NP are actually engaged. Also, it is hard to
determine exactly the size of the NPs and in what manner they aggregate.
In our simulation, we consider a configuration that is realistic in fabrication and can provide
large efficiency in SECARS generation. In this model, a CaCO3 bead carries two silver NPs that
are positioned close to each other. We assume that the two silver NPs have the same hemisphere
shape, with radius of 30 nm. Although the size of the CaCO3 bead (diameter at micron level)
is often larger than the dimension of the waveguide (width of 800 nm), only a small part of the
bead can experience the evanescent field and has influence on the SECARS. For this reason, we
can simplify the CaCO3 bead to a small cuboid characterized by it refractive index (1.6). The
structure is demonstrated in figure 5.3.
Now we bring the Ag-CaCO3 structure onto the silicon nitride waveguide. We assume
that the two NPs are positioned side by side perpendicular to the longitudinal direction of the
waveguide. The Ag-CaCO3 structure is further assumed to rest in the middle of the waveguide.
5.2 Simulation of Local Field Enhancement
53
Figure 5.3: The structure of Ag-CaCO3 bead in the simulation
In this configuration, the fundamental TE mode of the waveguide can excite the LSPRs between
the two NPs and result in large local field enhancements.
Taking a cross-section in y-z plane, we show the structure by the distribution of refractive
index. In figure 5.3, CaCO3 bead is colored by green. Attached to the green rectangle are
the two hemisphere NPs now shown as half circle. A layer of NTP (4 nm) is coated on the
surface of the NPs. Underneath, the yellow-colored region is the silicon nitride waveguide. The
background is the water with refractive index of 1.33.
5.2.3
Local Field Enhancement
We set up a simulation with the geometry parameters shown in the table 5.1 to study the
local field enhancement. These parameters are chosen so that the structure is realistic from the
fabrication point of view.
To resolve the nanostructure, finer mesh should be set in the corresponding volume. However,
as one goes to smaller mesh size, the memory and computing time of FDTD simulation increases
dramatically. In our simulation, mesh size of 1 nm in all direction is chosen as a trade-off between
resolution and computing resource.
The source in the simulation is a broadband mode source covering wavelength range from
0.5 to 1 micron. This mode source would calculate the fundamental TE mode of the waveguide
and inject it into the waveguide.
5.2 Simulation of Local Field Enhancement
54
Figure 5.4: The cross-section of the Ag-CaCO3 bead resting on the silicon nitride waveguide.
Parameter (nm)
Value
waveguide width
800
waveguide thickness
300
radius of the hemisphere
30
gap between the two hemispheres
10
thickness of the NTP monolayer
4
Table 5.1: Parameters of the structure.
We show in figure 5.4 the field distribution in cross-sections (x-y plane) 1 nm away from
the lower surface of CaCO3 cuboid. We defined the field enhancement as E(ω)/E0 (ω), the ratio
of electrical fields with and without the presence of NPs. Between two NPs, strong local field
enhancement is observed in the so-called ”hot spot” inside the gap.
As we want to study the Raman signal of NTP molecules, we should only care about the field
inside the NTP monolayer. In the cross-section, the area corresponds to the NTP monolayer is
covered by the rings as shown in figure 5.4.
5.2 Simulation of Local Field Enhancement
55
Figure 5.5: Field enhancement in the cross-section 1 nm away from the lower surface of CaCO3
cuboid. The area corresponds to the NTP monolayer is covered by the rings.
5.2.4
Coupling Efficiency
In SECARS generation, nonlinear polarization is induced by this enhanced local field in the
nonlinear medium. The nanostructure can be treated as a dipole source emitting at anti-Stokes
frequency. It is necessary to mention that not all of the power radiated by the dipole is coupled
into the waveguide. We define the coupling efficiency η as
η=
Pw
Ptot
(5.8)
where Ptot is the total power emitted by the dipole and Pw is the power coupled into the
fundamental TE mode of the waveguide. We want to first investigate the coupling efficiency of
dipole source with different direction.
We use lumerical FDTD to simulate the coupling and calculate the efficiency η. In the
simulation, a dipole source emitting at anti-Stokes frequency is placed 20 nm above the silicon
nitride waveguide in the middle as shown in figure 5.6. The direction of the dipole is along x
axis. As before, the simulation background is water, we set the background index as 1.33. We
use an auto non-uniform mesh with mesh accuracy of level 4 in this simulation, which is tested
to have enough accuracy yet ask for little simulation resource.
We use the combination of a mode expansion monitor and frequency-domain field and power
monitor to record the power in the fundamental TE mode of the waveguide and calculate the
efficiency η at 20 µm away from the dipole source. The simulation time is 500 fs which allows
5.3 SECARS Calculation
56
Figure 5.6: Structure for the simulation and calculation of the coupling efficiency. The dipole is
put above the waveguide.
light to travel to the monitor. The coupling efficiency η for a x-oriented dipole is calculated to
be 4.4% based on the direction.
Same simulation was conducted with y-oriented and z-oriented dipole. For these two dipole,
the coupling efficiency is extremely small, both at the level of 10−6 .
5.3
5.3.1
SECARS Calculation
Calculation Approach
The power of SECARS signal can be deduced from the nonlinear polarization induced by the
pump and Stokes field through the third order susceptibility. The nonlinear polarization usually
has components along x, y and z direction in a Cartesian coordinate system. Since the coupling
efficiency of y-oriented and z-oriented dipole is negligible small. We would only consider the x
component of the nonlinear polarization, and write it as PNL . Another assumption is that the
(3)
we only take into consideration of the diagonal component χxxxx of the third order susceptibility,
(3)
and denote it by χCARS . As a result, we will only take the x component of the electrical field in
the following discussion.
The calculation is based on the enhanced local field solved by lumerical FDTD. At every
5.3 SECARS Calculation
57
point inside the NTP monolayer, the nonlinear polarization is calculated by
(3)
PNL = g(ωas )ε0 χCARS E(ωp )E(ωp )E(ωs )
(5.9)
where g(ωas ) is the field enhancement E(ωas )/E0 (ωas ) at anti-Stokes frequency and E(ωi ) is the
(3)
enhanced local field at frequency ωi . χCARS is the third order Raman susceptibility which can
be estimated by
(3)
χCARS =
∂σ
)ωv
4π 2 ε0 c4 (Nl − Nu )( ∂Ω
h̄ωs4 [ωv2 − (ωp − ωs )2 + iΓ(ωp − ωs )]
(5.10)
where
• ε0 is the vacuum permittivity,
• c is the speed of light in free space,
•
∂σ
∂Ω
is the Raman scattering cross-section,
• ωv is the frequency of targeted vibrational mode,
• Nl − Nu is the population difference between the lower and upper levels of the targeted
transition and can be approximated by the number density,
• ωs and ωp are the frequency of Stokes probe and Pump, respectively,
• Γ is the bandwidth of the Raman peak.
For NTP’s prominent Raman peak at 1335 cm−1 , ωv is 251 THz. The pump is at 765 nm,
which gives us ωp of 2463 THz. We consider ωp −ωs = ωv so that Stokes frequency ωs is 2212 THz.
(3)
For other parameters, we take the values from table 4.1 in chapter 4. The susceptibility χCARS
is then estimated to be 1.2 × 10−21 V2 /m2 , using equation 5.10.
Nonlinear polarization is induced in the NTP monolayer coated on the NPs. We can treat the
nanostructure as a dipole source emitting at anti-Stokes frequency. Once we get the distribution
of polarization inside the monolayer, we can calculate the total dipole moment (p) by integrating
the nonlinear polarization in the monolayer (PNL ).
∫∫∫
p=
monolayer
PNL (ωas )dV
(5.11)
5.3 SECARS Calculation
58
For a dipole source, the emitted power can be related to the dipole moment. After obtaining
the dipole moment through equation (5.11), we can next calculate the total power radiated by
the dipole with the following equation
Ptot =
5.3.2
|p|2 nω 4
12πε0 c2
(5.12)
Calculation Results
From the discussion above, the power of SECARS signal coupled into the fundamental TE mode
of the waveguide can be expressed as

Pw =
(3)
nε0 ω 4 χCARS
η
12πc2


∫∫∫
2

g(ωas )Ep 2 Es dV
(5.13)
monolayer
where Ei is the short of E(ωi ).
Parameter (nm)
Value
waveguide width
800
waveguide thickness
300
radius of the hemisphere
25
gap between the two hemispheres
5
thickness of the NTP monolayer
4
Table 5.2: Parameters of the structure
Based on the local enhanced field distribution obtained from the simulation with structure
parameters tabulated in table 5.2, Pw is calculated to be 1117.6 pW. With the assumption that
only 1% of this power can be collected by the detector, we still have a power of 11.2 pW. This
is already above the detection limit in our lab.
Furthermore, we also conducted simulation for structures with varying gap between the two
hemispheres in the case of different radius of the hemisphere. We plot the coupled power Pw as
function of different parameters in figure 5.7.
For a given value of radius, one can see in the figure that SECARS signal strength varies
strongly with the gap distance. When the radius of the hemisphere is set to be 30 nm, the peak
value of signal strength is 5852 pW with gap distance of 7 nm. Even a small deviation from
5.3 SECARS Calculation
59
radius 30nm
radius 35nm
10000
radius 25nm
1000
power (pW)
100
10
1
0.1
0.01
4
6
8
10
12
gap distance (nm)
Figure 5.7: Power of SECARS signal that coupled into the fundamental TE mode of the waveguide is calculated for varying gap distance between the two hemispheres with different radius.
The dash line marks the required power level that is decided by the collecting efficiency and
detection limits.
this gap distance could decrease the power dramatically. According to the simulation, for gap
distance of 8 nm and 6 nm, the power of signal are respectively 1658 pW and 844.8 pW.
The strength of SECARS signal depends on the enhanced local fields at three different frequencies, i.e. ωp , ωs and ωas . One cannot simply explain the peak signal strength as having
maximum local field enhancement at one of these frequencies. Actually, we found in the simulation that the maximum enhancement at one frequency is compensated by a weak enhancement
at another frequency, resulting a non-peak SECARS signal. In fact, one can get a peak value of
the SECARS signal only when the enhancements at all three frequencies are relatively large at
the same time.
Also, one can find that the peak value and peak position (gap distance) of SECARS signal
5.3 SECARS Calculation
60
vary with the radius of the hemisphere. For radius of 25 nm and 35 nm, the peak signal power
is 2301 pW at gap distance of 6 nm and for radius of 35 nm, the peak value is 591 pW at gap
distance of 8 nm. This indicates that the size of the hemisphere also plays a important role in
determining the strength of SECARS signal.
Another important aspect we want to discuss is the power level of SECARS signal. Considering the collecting efficiency of 1% and detection limit of 1 pW, we draw a dash horizontal
line at power of 100 pW in figure 5.7. Above this dash line the signal is strong enough to be
detected. The strongest signal power we can get at the detector is 58.52 pW in the optimum
case of 7 nm gap and 30 nm radius. Away from this optimum situation, we still have a large
parameter space where the SECARS signal is detectable.
FABRICATION
61
Chapter 6
Fabrication
In this chapter, we will introduce some details about the fabrication involved in this thesis. We
start with the silicon nitride waveguide, and then describe the processing details for the underetched waveguide. After this, we will briefly describe the fabrication of the silver nanoparticles
used in SECARS.
6.1
Silicon Nitride Waveguide
The silicon nitride waveguide mentioned in chapter 4 is fabricated through IMEC standard
CMOS pilot-line. The chip starts with a thick bare silicon wafer, which works as the stubstrate,
providing a foundation to build on.
With high refractive index (about 3.47), the silicon substrate should be separated from the
waveguide core. For this purpose, a layer of silicon dioxide (SiO2 ), having refractive index of
1,45, is then deposited by the high-density plasma chemical vapor deposition (HDP-CVD) on the
substrate. The thickness of this SiO2 layer is about 1.6 µm, which would give enough buffering
to avoid the substrate leakage.
On top of this SiO2 layer, the core material, silicon nitride is deposited via low pressure
chemical vapor deposition (LPCVD) to for a thin film of 300 nm thick. Deep ultraviolet (DUV)
lithography and dry etching are employed to define the waveguide.
6.1 Silicon Nitride Waveguide
6.1.1
62
Chip Cleavage
In our clean-room, the arrived wafer is already diced into small chips for post-processing. Besides
the waveguide we are interested in, the chip also contains other structures. Since we want to use
a horizontal coupling setup to couple light into the waveguide, the chip should be first cleaved
to have a good facet which allows horizontal coupling.
However, the quality of cleavage is proved to be bad given the thickness of the chip. Mechanical grinding is usually adopted to make the chip thin enough for high quality cleavage. As
the structure on the chip would be damaged during the mechanical grinding process, we We
spin-coat a layer of AZ 9260 to prevent possible damage on the surface of the sample.
The first step is to clean to chip. We start by applying acetone to wash away the organics.
Isopropyl alcohol (IPA) is immediately followed to flush out acetone, as the high evaporation
rate of the latter might cause residuals on the chip. The chip will then be rinsed by deionized
water to remove the IPA. After that, we dry the chip with nitrogen gun.
Next step, we drip several drops of AZ 9260 on the chip, which is then rotated at 3000 rpm,
allowing the coating material to spread and form a coat layer. The chip is then baked at 100 ◦ C
for 3 minutes to solidify AZ 9260.
Now we clean a glass plate using IPA and Acetone, dry it and put it on a hotpot. As the
temperature reaches 120 ◦ C, we rub some purple wax on the surface of the glass plate and put
the chip on top of it, with the spin coated layer facing the glass plate. Then we bring the glass
plate to a metal slug for cooling. As the temperature decreases, the wax will solidify and the
chip will be fixed. The glass plate is then stuck to the lapping jig by vacuum. When sits on
the lapping plate, the jig can offer specified loads, which provides pressures not too low for
efficient grinding and not too high for the protection of the chip. The abrasive is the aluminum
oxide powder. We dissolve spoons of aluminum oxide powder into water and stir it to get a
homogeneous slurry, which is then constantly fed onto the lapping plate. As the lapping plate
rotates, the aluminum particles between the plate the substrate of the wafer would gradually
grind away the silicon.
After grinding, the chip is only about 300 micron thick. Now we can cleave the chip. Under
the microscope, we can find the structure column containing our waveguide. We scratch two
marks at the edge of the chip and press carefully on them to cleave the chip along its crystal
6.1 Silicon Nitride Waveguide
63
plane.
6.1.2
Etching
The cleaved chip is then dipped into diluted (1%) hydrofluoric (HF) acid, which shows high etching selectivity between SiO2 and LPCVD Si3 N4 (200:1). After 15 minutes, the SiO2 underneath
the Si3 N4 is partly removed while the latter is quasi-conserved.
Figure 6.1: Waveguide cross-section (within the yellow contour) pictured by SEM. Outside the
waveguide is the materials deposited for FIB to create this cross-section
6.1.3
Inspection
Eventually, we want to have a inspection of the waveguide we just processed. This allows us to
know the real structure of the underecthed waveguide and get insight into the approach of HF
etching.
To do the inspection, we bring the cleaved chip to the focused iron beam (FIB). A cross
sections is then created by FIB precisely at the position of the waveguide we want to investigate.
Subsequently, Scanning Electron Microscopy (SEM) is employed to image the cross section.
In the SEM image shown in figure 6.1, the underetched waveguide is marked by the yellow
contour. We measured the etching depth is about 126 nm. Taking into account that the
6.2 Silver Nanoparticles
64
waveguide is etched in the diluted HF for 15 minutes, we calculated the etching rate is about
8 nm/min.
6.2
Silver Nanoparticles
As mentioned before the silver (Ag) nanoparticles are carried by calcium carbonate (CaCO3 )
particles. The CaCO3 -Ag beads are fabricated by Alexey Yachshenok in the lab of prof. Andre
Skirtach (Dept. Molecular Biotechnology, Ghent University). In this section, we will give a
short introduction to the fabrication details.
6.2.1
Synthesis of CaCO3 Beads
The CaCO3 particles are chemically generated by the salt metathesis reaction of sodium carbonate (Na2 CO3 ) and calcium chloride (CaCl2 ).
Water solutions of both CaCl2 and Na2 CO3 are first prepared. Next, ethylene glycol (EG)
is added to both solutions. The presence of EG with different volume percentage in the solution
would allow us to control the size of the generated CaCO3 particles. The fresh prepared CaCl2
and NaCO3 solution with equal concentration are mixed in equal volumes. The mixture is then
stirred in a magnetic stirrer for 15 minutes at stirring rate of 500 rpm without heating. After
that, the precipitated CaCO3 particles are washed with ethanol and dried in an oven.
6.2.2
Silver Nanoparticles
Silver nanoparticles are chemically generated by silver mirror reaction. Tollens’ reagent, freshly
prepared by mixing AgNO3 solution with ammonium hydroxide (NH4 OH), is used to conduct
this reaction. When the reducing agent is added into Tollens’ reagent, the diamminesilver(I)
complex ([Ag(NH3 )2 ]+ ) in the reagent would be reduced to elemental silver and NH4 OH. The
elemental silver will then precipitate out of solution. With the CaCO3 particles synthesized
before pre-immersed in the Tollens’ reagent, the precipitates of elemental silver would selfassumable into nanoparticles and grow at the surface of the CaCO3 particles. Carrying silver
nanoparticles, the beads are now functionalized.
6.2 Silver Nanoparticles
6.2.3
65
NTP Monolayer
To grow a monolayer on the surface of silver NPs, the CaCO3 -Ag beads is immersed into 1 mM
solution of 4-nitrotiophenol in ethanol. The solution are then shaken for a few hours, during
which the thiol-group (-SH) of the NTP would bind to surface of silver NPs and in that way
form a monolayer. After that, excessive NTP is washed out with pure ethanol by centrifugation
for more than 3 times each of 5 minutes and at acceleration of 1000 g.
EXPERIMENT OF SECARS
66
Chapter 7
Experiment of SECARS
7.1
Raman Setup
In our experiment, we use Raman setup for the measurement of SECARS signal. To introduce
Raman setup, we refer to figure 7.1, where we plot the schematic of Raman setup in the alignment
configuration. In this configuration, the light source is a tunable Ti:sapphire laser pumping at
785 nm. The beam coming out from the laser box is reflected by a mirror (M1) to a periscope.
The latter rises the laser beam to a proper height so that it can go through all the following free
space optics. The laser beam is then expanded by the lens system composing L1 and L2. After
the expansion, the laser beam is split into two by a 50:50 beam-splitter (BS1). The transmitted
one would be reflected by another beam-splitter (BS2) to the objective. This beam will then go
through the objective (50×, NA = 0.2) and the aspheric lens (ASPL), which has focal length of
8mm and NA of 0.5. After reflected by M3 and then M2, part of the light can transmit through
BS1 and eventually hit the camera. On the other hand, another beam that is reflected by BS1
would also end up into the camera. The route is however reversed and can be consequently
marked by M2, M3, ASPL, objective, BS2, BS1, M4 and camera.
7.2
Alignment
In the alignment, the first step is to align the objective with the ASPL . We first want to make
the focus plane of the objective overlaps with that of the ASPL so that we can see two spots
in the display window of the camera when the pump laser is switched on. For this purpose,
7.2 Alignment
67
one should tune the distance between the objective and the aspherics lens. As the Objective is
fixed, this is done by moving the ASPL along the propagation direction (z direction) of the laser
beam. Once the two spots are observed clearly in the display window, we can move the ASPL
in x-y plane to overlap the two spots. For fine alignment, the pump laser is tuned to 800 nm.
At this wavelength, light can pass through the dichronic mirror inside BS2 and be detected by a
power meter, which is not shown in the figure 7.1. ASPL is again adjusted in x,y and z direction
to optimize the power received by the power meter.
Figure 7.1: Schematic plot of Raman setup in alignment configuration. Ti:saf is the short of
the Ti:sapphire laser. BS1 is a 50:50 beamsplitter. BS2 is actually a dichronic mirror reflecting
wavelengths shorter than 790 nm. PH: pinhole; L, lens; M, mirror; ASPL, aspheric lens.
After the optimization, we move the ASPL apart from the objective along z axis without
changing its coordinates in x-y plane. This would allow us to put the chip on the stage, which is
located between the objective and aspherical lens. Now, we want to couple the light from both
side into a reference waveguide on the chip. At this step, the laser is tuned back to 785 nm. By
blocking PH2, the light will go to the chip only through the objective. We can now move the
chip along z axis to make sure the light is focused on the facet of the chip. Then we can shift
7.3 Measurement
68
the chip in x-y plane to couple the light into the reference waveguide. With a second camera
right above the chip, one can also observe the chip directly and know if the light is coupled into
the reference waveguide. Done with this side, we open PH2 and put a blocker between BS1 and
BS2. Now the light only go through the ASPL. To focus the light on the facet of the chip, we
move the ASPL along z axis and try to couple the light into the reference waveguide, we rotate
the chip along x axis and y axis. We found that in doing so, we lost the alignment at the other
side. So when the ASPL side is aligned, one should go back to the objective side. Repeating
these procedures for several times, we can couple the light into the reference waveguide from
both side. Again, we tune the laser to 800 nm and use the power meter to measure the optical
power of the light passing through BS2. After this fine alignment, the Raman setup is ready for
measurement.
7.3
Measurement
In the measurement configuration, we want to couple the light coming from supercontinuum
source into the optical path. As shown in figure 7.2, we put a dichronic mirror (DM) in the
optical path. This DM reflects long wavelengths and transmits short wavelengths with a steep
cutoff at wavelength of 775 nm for TE polarized light at incidence angle of 45◦ . Light coming
from supercontinuum source with wavelength longer than 775 nm is reflected into the Raman
setup collinearly with the Ti:sapphire laser beam. These two beams are then coupled into the
waveguide on the chip using end-fire coupling via the ASPL. Coming out from the other end
of waveguide, signals along with pumps are collected by the objective. Light with wavelength
longer than 790 nm would go through the dichronic mirror inside BS2 and be measured by a
spectrometer (D1). The short wavelength light is, on the other hand, directed into another
spectrometer (D2) by a mirror (M4).
In the experiment, A droplet of water containing large amount of Ag-CO3 beads is applied
on top of the 800 nm wide silicon nitride waveguide. The analyte is the NTP monolayer coated
on the surface of silver NPs. To have SECARS signal, the Ti:sapphire laser, working as the
pump laser, is tuned to emit at 765 nm with power of 5 W. At this wavelength, the pump laser
would also be reflected by the dichronic mirror inside BS2 and then going to the spectrometer
D2 together with the anti-Stokes signal. To suppress the strong pump and make the anti-Stokes
7.3 Measurement
69
Figure 7.2: Schematic plot of Raman setup in measurement configuration. SC stands for supercontinuum source. D1 is a spectrometer to detect the Stokes signal and D2 is for anti-Stokes
signal. The filter is a short pass one transmitting wavelengths shorter than 755 nm. DM is
a short pass dichronic mirror with cut-off frequency of 775 nm. BS1 is a 50:50 beamsplitter.
BS2 is actually a long pass dichronic mirror reflecting wavelengths shorter than 790 nm. PH:
pinhole; L, lens; M, mirror; ASPL, aspheric lens.
signal easy to detect, we put a filter after M4, which transmit the wavelengths shorter than
755 nm. Furthermore, the supercontinuum source, with power density of 1.3 mW/nm, provides
a broadband Stokes probe above 775 nm, which is decided by the reflection window of DM. For
measuring the anti-Stokes spectrum , Andor spectrometer with iDUS416 camera is used. The
integration time is set to 1 s. We will discuss the measured result in the following section.
7.4 Measured Results
7.4
70
Measured Results
7.4.1
Measured Result of SECARS
The spectrum we acquired when both the Ti-sapphire laser and Supercontinuum source are
switched on is shown in figure 7.3.
In this spectrum, lots of features can be observed. Among them, the most obvious one is
the sharp peak at 765 nm, which is caused by the Ti:sapphire pump laser.
6500
6000
counts
5500
5000
4500
4000
3500
600
620
640
660
680
700
720
740
760
780
wavelength (nm)
Figure 7.3: Spectrum obtained with the chip when both the Ti-sapphire laser and Supercontinuum source are switched on. The integration time is 1 s.
Also, we can see other features from the spectrum at shorter wavelength range. However,
just by looking at this spectrum along, it is hard to tell what would be the causes of these
feathers.
To study these features, we do the same measurement again without the chip. The spectrum
is shown in figure 7.4. In this spectrum, besides the sharp peak caused by the Ti:sapphire
pump laser, other features can only be produced by the supercontinuum source. When compare
these two spectra, one might find some additional features in the first spectrum that cannot be
attributed to the supercontinuum source. This is the case particularly for the peak at around
648 nm.
7.4 Measured Results
71
13000
12000
11000
counts
10000
9000
8000
7000
6000
5000
4000
3000
600
620
640
660
680
700
720
740
760
780
wavelength (nm)
Figure 7.4: Spectrum obtained without the chip when both the Ti-sapphire laser and Supercontinuum source are switched on. The integration time is 1 s.
We show another spectrum in figure 7.5. This time, only supercontinuum source is switched
on. This spectrum is identical to the one shown in figure 7.3 only with the absence of the peak at
764 nm. Without the Ti-sapphire pump laser, same peak appears at around 648 nm, indicating
that this is not the anti-Stokes signal we are expecting.
Based on the data we have, it is difficult to determine the origin of the features shown in
figure 7.5. We suspect that these features may be brought by the short pass DM. Although this
DM is designed to transmit short wavelengths, it could be possible that still a small fraction of
short wavelength light is reflected into the optical path, which causes these strange features.
Another question is why we did not get any SECARS signal. A possible reason could be
that although the supercontinuum light is collected by the objective, it might not have been
coupled into the waveguide. The alignment procedures only guaranteed that the Ti-sapphire
beam is coupled into the waveguide. If the supercontinuum beam is not perfectly collinear with
the Ti-sapphire beam, one can doubt that the former is not coupled into the waveguide. This
could be the case in our setup. In fact we found that the reflection spot of the supercontinuum
light was not at the same position as that of the Ti:sapphire laser on the waveguide facet.
7.4 Measured Results
72
6500
6000
counts
5500
5000
4500
4000
3500
600
620
640
660
680
700
720
740
760
780
wavelength (nm)
Figure 7.5: Spectrum obtained with the chip when only the Supercontinuum source is switched
on. The integration time is 1 s.
7.4.2
Measured Result of SERS
The Raman setup shown in figure 7.2 can also be used to measure the Stokes signal. With
the silver NPs on the waveguide, we can measure the SERS signal without re-alignment. For
SERS measurement, supercontinuum source is switched off and only the Ti-sapphire pump laser
is coupled into the waveguide. The SERS signal is detected by Avantes spectrometer with
integration time of 10 s. Several SERS spectrum are shown in figure 7.6 together with the
reference (SERS8) which is obtained before applying Ag-CaCO3 beads to the waveguide. On
can obviously see a peak at 929.5 nm in all the spectra. Taking into account that the pump is at
764 nm, this peak has wavenumbers of 2330 cm−1 . Same value is found in the work of Dhakal
et al. [46] for the Raman emission from the Si3 N4 , which is the core material of the waveguide.
In order to observe signal peaks more clearly, we normalize all the 7 SERS spectrum and
subtract the reference. We take the average and get the normalized spectrum shown in figure
7.7.
We list the other peaks in table 7.1 and compare them with the peaks measured under
a confocal Raman microscope. One can see the peaks we obtained are roughly in consistent
7.4 Measured Results
73
6000
SERS1
SERS2
SERS3
SERS4
SERS5
SERS6
SERS7
SERS8
5000
counts
4000
3000
2000
1000
0
−1000
750
800
850
900
950
1000
wavelength (nm)
Figure 7.6: SERS spectra measured after we apply Ag-CaCO3 beads onto the waveguide. The
black spectrum, SERS8, is the reference obtained before the beads are applied. The integration
time is 10 s for all the spectra.
normalized signal strength (a.u.)
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
750
800
850
900
950
wavelength (nm)
Figure 7.7: Normalized SERS spectrum.
1000
7.4 Measured Results
74
wavelength (nm)
wavenumber (cm−1 )
Position of NTP peaks (cm−1 )
833.2
1087
1078
837.8
1154
1107
852.2
1355
1340
869.3
1586
1572
Table 7.1: The peaks measured in our experiment are listed in the first column. The corresponding wavenumbers are in the second column. NTP peaks measured under a confocal
Raman microscope are shown in the third column.
with the results measured under the confocal Raman microscope. The small shift of the peak
positions can be explained as the chemical changes in the molecule induced by the strong local
field [57].
CONCLUSION AND FUTURE PROSPECTS
75
Chapter 8
Conclusion and Future Prospects
In this master thesis dissertation, we investigated both the CARS generation and SECARS
generation based on the silicon nitride waveguide platform. The theoretical study of both
approaches are presented followed by the simulations and experiments. In this chapter, we want
to summarize the main conclusions we have come to and discuss what could be the improvement
in the future.
8.1
Conclusion
We focused on the waveguide-based CARS generation in the first part. Through theoretical
study, we found phase matching is really important in this approach, which calls for a small
anomalous GVD.
We show in chapter 3 that for a ridge waveguide, within the parameter space allowed by the
fabrication, anomalous dispersion cannot be obtained. Nevertheless, we found that by etching
the silica undercaldding beneath the Si3 N4 core, one can engineer the dispersion and get small
anomalous GVD in the wavelength range we are interested in. This approach is verified by
the success of SCG, for which a small anomalous GVD is the required condition. It is worth
mentioning that the work of SCG has led to a paper published in the Optics Letter [54]. Then
we coat the underetched waveguide with a thin monolayer of NTP. From the simulation result,
we found that with this additional cladding layer, the underetched waveguide can still have
small anomalous GVD in the interested wavelength range and therefore can be used for CARS
generation.
8.2 Future Prospects
76
The theoretical calculation in chapter 4 however indicates that waveguide-based CARS is
currently not feasible. The main reason is that the laser available currently in our lab cannot
provide enough power. According to the calculation, pump power coupled into the waveguide
should at least be 10 mW, while in our lab, the coupled power is usually at the level of 1 mW.
With this low coupled power, the signal strength is below the detection limit, even when waveguide has proper dispersion. Another reason is that due to fabrication and processing uncertainty,
in practice it is very difficult to have the small anomalous GVD at the desired wavelength range.
We next changed the research direction and studied the theory of surface enhanced CARS
(SECARS) on a Si3 N4 waveguide platform. We found that SECARS actually provides the
solutions for the problems we encountered in CARS. For one thing, low pump power is tolerable because of the strong electromagnetic enhancement in SECARS. For another, since the
interaction length is limited to several nanometers, SECARS do not ask for phase matching.
In our work, Ag-CaCO3 micro-beads as the Raman active center are applied to the Si3 N4
waveguide for SECARS generation. A model is developed for this nano-structure according
to fabrication. Based on this model, FDTD simulation is conducted to obtain the local field
distribution. Calculation is then performed to get the signal strength. The result is quite
satisfying as signal strength above detection limit is obtained in a large parameter space.
While the simulation result is promising, the experiment result however is not as good.
Anti-stokes signals are not observed in the resulting spectrum. The possible reason could be the
improper optical design, though further investigation should be conducted to really figure out
the cause. Unfortunately, this was not possible with in the timeframe of the thesis work.
8.2
Future Prospects
Since the desired experiment results of SECARS are not obtained due to the shortage of time,
one of the urgent future plans is to investigate the reasons and solve it. For this purpose, the
optical setup should be carefully checked or even be re-designed and if necessary, additional
optics should be purchased. After this, we can redo the measurement and hopefully compare
the results with our simulation.
Because CARS generation based on Si3 N4 waveguide is also a very promising topic, we would
also like to conduct experiments on it. To do this, we need to find a better laser source which
8.2 Future Prospects
77
can provide enough power to get strong Raman signal. Also, efforts should also be put into
improving the fabrication and searching for better approach that can more precisely control the
GVD.
BIBLIOGRAPHY
78
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Surface-Enhanced Spectroscopies 2014 conference, Germany, 2014.
[48] Baets, R., Subramanian, A. Z., Dhakal, A., Selvaraja, S. K., Komorowska, K., Peyskens, F.,
Le Thomas, N., “Spectroscopy-on-chip applications of silicon photonics.”, Proc. of SPIE;
pp. 86270I-86270I, 2013.
[49] Blow, K. J., Wood, D., “ Theoretical description of transient stimulated Raman scattering
in optical fibers.”, IEEE J. Quantum Electron.; 25, 2665, 1989.
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silica fibers.”, J. Opt. Soc. Am.; B 6, 1159, 1989.
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Wiley, New York, 1983.
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“Visible-to-near-infrared octave spanning suprcontinuum generation in a silicon nitride
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BIBLIOGRAPHY
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[55] Kang, L., Xu, P., Zhang, B., Tsai, H., Han, X., Wang, H. L. “Laser wavelength-and
power-dependent plasmon-driven chemical reactions monitored using single particle surface
enhanced Raman spectroscopy.”, Chemical Communications; 49(33), 3389-3391, 2013.
[56] Kane Yee. “Numerical solution of initial boundary value problems involving maxwell’s
equations in isotropic media.”, IEEE Transactions on Antennas and Propagation; 14 (3):
302307, 1966.
[57] Tabatabaei, Mohammadali, et al. “Optical Properties of Silver and Gold Tetrahedral
Nanopyramid Arrays Prepared by Nanosphere Lithography.”, The Journal of Physical
Chemistry C ; 117.28: 14778-14786, 2013.
LIST OF FIGURES
84
List of Figures
1.1
Light scattering processes (a) schematic diagram of scattering, (b) Typical observed spectrum. This diagram is reprinted from [2] . . . . . . . . . . . . . . . .
2
1.2
Energy diagram for Stokes and anti-Stokes Raman scattering. . . . . . . . . . . .
3
1.3
Stimulated Raman scattering. [2] . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.4
A schematic diagram to demonstrate typical Raman spectrometer, reprinted from
[5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5
5
This figure is reprinted from [5] to give an example of unprocessed Raman spectrum of live cells. To obtain this image, parameters of 300 seconds acquisition
time, 785 nm illumination and approximately 100 mW illumination power is employed.
1.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Pictures reprinted from [13] to demonstrate: (a) The difference between Raman
and SERS phenomena. (b) Spectrum of Rhodamine 6G acquired by SERS measurement at the vicinity of silver hydroxylamine colloid (red line) and from spontaneous Raman spectrum. (c) A schematic explanation of the electromagnetic
and chemical enhancements in SERS.
1.7
. . . . . . . . . . . . . . . . . . . . . . . .
the energy diagram of non-resonance Raman process and resonance Raman process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8
7
9
For alumina supported vanadium oxide monomers: The upper spectrum shows
resonance Raman enhancement of V-O signal at 287 nm. The middle spectrum
shows resonance Raman enhancement of V=O signal at wavelength 220 nm. And
the bottom spectrum is the spontaneous Raman spectrum of same molecule as
1.9
reference. This figure is reprinted from [16] . . . . . . . . . . . . . . . . . . . . .
10
Energy diagram of CARS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
LIST OF FIGURES
85
1.10 The illustration of an advanced CARS microscope reprinted from [29]. This microscopy can perform both forward-detected CARS (by PMT1) and backwarddetected CARS (by PMT2). PH, pinhole; DM, dichroic mirror; L, lense; PMT,
photomultiplier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.11 Energy diagram of different Raman process. gi stands for the field enhancement
at different frequencies. This figure is reprinted from [30]
. . . . . . . . . . . . .
14
1.12 Pictures reproduced from [35] to introduce their works. The gold quadrumer is
shown in inset. (a) The upper and lower spectrum show experimental and simulation results with (black) and without (red) the p-MA. (b)A schematic diagram of
the charge distribution of the subradiant(top) and superradiant modes(bottom).
(c) Field enhancement at the different frequencies : anti-Stokes (left), pump (middle) and Stokes (right). (d) SECARS enhancement map with the maximum enhancement factor about 1.5×1010 in the central gap using FDTD simulation. . .
15
2.1
The energy diagram of degenerated FWM process . . . . . . . . . . . . . . . . .
20
2.2
The energy diagram of CARS process . . . . . . . . . . . . . . . . . . . . . . . .
21
2.3
CARS line shape the horizontal dash line represent the non-resonance background
and the vertical dash line is positioned at the vibrational frequency Ωv
2.4
. . . . .
23
(a), the cross section of a typical slot waveguide with silicon nitride as core material and silicon as substrate. (b) the cross section of a same waveguide after
under etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
25
The curve of material group velocity dispersion for Si3 N4 deposited by lowpressure chemical vapor deposition (LPCVD) and plasma-enhanced chemical vapor deposition (PECVD) technique. . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.2
A sketch of ridge Si3 N4 waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . .
30
3.3
The GVD curves of ridge waveguide with height H fixed at 300 nm and width W
varying from 500 nm to 600 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
3.5
30
The GVD curves of rectangle waveguide with width W fixed at 500 nm and the
height H taking 270, 280, 290 and 300 nm. . . . . . . . . . . . . . . . . . . . . . .
31
A sketch of the underetched Si3 N4 waveguide. . . . . . . . . . . . . . . . . . . . .
32
LIST OF FIGURES
3.6
The GVD curves of waveguide with different etch depth varying form 50nm to
175nm. W and H is set to be 500 nm and 300 nm. . . . . . . . . . . . . . . . . .
3.7
86
32
The GVD curves of waveguide with fixed pillar of 200 nm. W varies from 500 to
600 nm and H is 300 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.8
A sketch of the underetched Si3 N4 waveguide cladded with a NTP monolayer(green). 34
3.9
The GVD curves of underetched waveguide with varying cladding thickness as
shown in the legends. The size of the waveguide core are fixed with height of
300 nm and width of 500 nm and the etch depth is set to be 150 nm. . . . . . . .
35
3.10 The waveguide loss in the wavelength range of 600-950 nm measured by a cutback
measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.11 Spectra of the underetched waveguide at different launched peak power. For
clarity the spectra are deliberately shifted vertically to avoid overlap. . . . . . . .
4.1
36
The anti-Stokes spectrum for different GVD: 0.1β2 , β2 and 10β2 . At the frequency
shift of 40 THz a CARS line shape can be observed most obviously in the case of
0.1β2 . The interaction distance is fixed at z0 = 1 cm and γr = 1m−1 W−1 , P = 0.1W. 41
4.2
The anti-Stokes spectrum for different interaction distance: 0.1z0 , z0 and 10z0 ,
where z0 = 1 cm. The GVD is fixed at β2 = −0.034 s2 m−2 and γr P = 0.1m−1 . .
4.3
The anti-Stokes spectrum for different pump power: 0.1P0 , P0 and 10P0 , where
P0 = 0.1 W . The GVD is fixed at 0.1β2 = −0.0034 ps2 m−1 and γr = 1m−1 W−1 . .
4.4
42
43
The anti-Stokes spectrum for different injected Stokes flux: 0.1fStokes , fStokes
and 10fStokes , where fStokes = 107 photons/Hz/s. The GVD is fixed at 0.1β2 =
−0.0034 ps2 m−1 and γr = 1m−1 W−1 , P = 0.1W. . . . . . . . . . . . . . . . . . .
4.5
44
The anti-Stokes spectrum of CARS signal with Stokes flux of fStokes = 107 photons/Hz/s
(up) and Spontaneous Raman signal with fStokes = 0 (below) The GVD is fixed
at 0.1β2 = −0.0034 ps2 m−1 and γr = 1m−1 W−1 , P = 0.1W. . . . . . . . . . . . .
45
5.1
A sketch to demonstrate the staggered electric and magnetic field in Yee’s cells. .
51
5.2
A SEM picture of Ag-CaCO3 micro-beads. . . . . . . . . . . . . . . . . . . . . . .
52
5.3
The structure of Ag-CaCO3 bead in the simulation . . . . . . . . . . . . . . . . .
53
5.4
The cross-section of the Ag-CaCO3 bead resting on the silicon nitride waveguide.
54
LIST OF FIGURES
5.5
87
Field enhancement in the cross-section 1 nm away from the lower surface of
CaCO3 cuboid. The area corresponds to the NTP monolayer is covered by the
rings.
5.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Structure for the simulation and calculation of the coupling efficiency. The dipole
is put above the waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7
55
56
Power of SECARS signal that coupled into the fundamental TE mode of the
waveguide is calculated for varying gap distance between the two hemispheres
with different radius. The dash line marks the required power level that is decided
by the collecting efficiency and detection limits. . . . . . . . . . . . . . . . . . . .
6.1
Waveguide cross-section (within the yellow contour) pictured by SEM. Outside
the waveguide is the materials deposited for FIB to create this cross-section . . .
7.1
59
63
Schematic plot of Raman setup in alignment configuration. Ti:saf is the short of
the Ti:sapphire laser. BS1 is a 50:50 beamsplitter. BS2 is actually a dichronic
mirror reflecting wavelengths shorter than 790 nm. PH: pinhole; L, lens; M,
mirror; ASPL, aspheric lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2
67
Schematic plot of Raman setup in measurement configuration. SC stands for
supercontinuum source. D1 is a spectrometer to detect the Stokes signal and D2
is for anti-Stokes signal. The filter is a short pass one transmitting wavelengths
shorter than 755 nm. DM is a short pass dichronic mirror with cut-off frequency
of 775 nm. BS1 is a 50:50 beamsplitter. BS2 is actually a long pass dichronic
mirror reflecting wavelengths shorter than 790 nm. PH: pinhole; L, lens; M,
mirror; ASPL, aspheric lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3
Spectrum obtained with the chip when both the Ti-sapphire laser and Supercontinuum source are switched on. The integration time is 1 s. . . . . . . . . . . . .
7.4
70
Spectrum obtained without the chip when both the Ti-sapphire laser and Supercontinuum source are switched on. The integration time is 1 s. . . . . . . . . . .
7.5
69
71
Spectrum obtained with the chip when only the Supercontinuum source is switched
on. The integration time is 1 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
LIST OF FIGURES
7.6
88
SERS spectra measured after we apply Ag-CaCO3 beads onto the waveguide. The
black spectrum, SERS8, is the reference obtained before the beads are applied.
7.7
The integration time is 10 s for all the spectra. . . . . . . . . . . . . . . . . . . .
73
Normalized SERS spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
LIST OF TABLES
89
List of Tables
4.1
Parameters for the estimation of γr . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.2
Parameters of CARS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
5.1
Parameters of the structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
5.2
Parameters of the structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
7.1
The peaks measured in our experiment are listed in the first column. The corresponding wavenumbers are in the second column. NTP peaks measured under a
confocal Raman microscope are shown in the third column. . . . . . . . . . . . .
74