Download Quasi Phase Matching Devices for Optical

A Project Report on
“Quasi Phase Matching Devices for
Optical Frequency Conversion”
Submitted by
Pranav Vinod Kumar
(114004140)
Vignesh.S
(114004233)
Deepak Kumar.K
(114004039)
Mahadevan.V
(114004103)
In partial fulfillment for the award of the degree of
Bachelor of Technology
In
Electronics & Communication Engineering
School of Electrical and Electronics Engineering
SASTRA University
Thanjavur, India
April-2014
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BONAFIDE CERTIFICATE
Certified that the project work entitled “Quasi Phase Matching Devices for
Optical Frequency Conversion” submitted to SASTRA University,
Thanjavur by Pranav Vinod Kumar (Reg No: 114004140), Vignesh.S
(Reg No: 114004233), Deepak Kumar.K (Reg No: 114004039),
Mahadevan.V (Reg No: 114004103) in partial fulfillment for the award of
degree of Bachelor of Technology in Electronics & Communication
Engineering. The work is carried out independently under my guidance during
the period December 2012 - April 2013.
Project Guide
Dr. S.K. Pandiyan
AP III, ECE, SEEE
EXTERNAL EXAMINER
INTERNAL EXAMINER
Submitted for the University Exam held on
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DECLARATION
We submit this project work entitled “Quasi Phase Matching Devices for Optical
Frequency Conversion” to SASTRA University, Thanjavur in partial fulfillment
of the requirements for the award of the degree of Bachelor of Technology in
Electronics & Communication Engineering. We hereby declare that it was carried
out independently by us under the guidance of Dr. S.K. Pandiyan.
Pranav Vinod Kumar
Vignesh.S
Deepak Kumar.K
Mahadevan.V
(114004140)
(114004233)
(114004039)
(114004103)
Date:
Place:
Signature: 1.
2.
3.
4.
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ACKNOWLEDGEMENTS
I would like to take this opportunity to thank all the people who gave me their
support and guidance for the successful completion of this project work.
I express my sincere thanks to Prof. R. Sethuraman, Vice Chancellor, SASTRA
University for providing the necessary facilities for the completion of my project.
I express my thanks to Dr. K. Thenmozhi, Associate Dean, School of SEEE,
SASTRA University, for the constant inspiration.
I extend my sincere thanks to the Project Coordinators Prof.Raju.N, AP-III, SEEE,
SASTRA University & Prof.Susan.D, Senior Assistant Professor, SEEE, SASTRA
University who has been inspiring and supporting during the project.
My heartfelt thanks to my project guide, Dr. S.K. Pandiyan, Assistant Professor III,
SEEE, SASTRA University, for his guidance, encouragement and timely support
which has motivated me for completing this project successfully.
I express my thanks to each one of teaching, non-teaching staffs and my friends for
their moral support and acceptance of my endeavor. Above all my deepest
gratitude to the almighty, for his guides, immeasurable blessings and throughout
the project.
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TABLE OF CONTENTS
List of Figures ……………………………………………………………... 8
Notations and Abbreviations ……………………………………………… 10
Abstract …………………………………………………………………….. 11
Chapter 1:
1. Introduction
1.1 Introduction to Optics
12
1.2 Linear Optics
12
1.3 Nonlinear optics
13
1.4 Phase matching
15
1.5 Second harmonic generation
16
1.6 Quasi-Phase Matching
17
1.7 QPM Applications in WDM
18
1.8 Periodic and Aperiodic QPM devices
19
1.9 Multiple Peaks in QPM
20
1.10 Significance of Multiple Peaks
20
Chapter 2:
2. Review on related Literature
2.1 Multiple QPM Devices using CPM
22
2.2 Bandwidth and tunability enhancement in QPM by SHG
23
2.3 Non-Periodic distributed Pi-phase shifting domain
23
2.4 Periodic distributed Pi-phase shifting domain
25
5
2.5 Broadband and visible laser generation by segmented QPM
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2.6 Tunable all optical wavelength broadcasting
28
Chapter 3:
3. Methods and Procedures
3.1 Wave Equations
30
3.2 Nonlinear coupled wave equations for SHG
33
3.3 Fourier Optics of QPM SHG
34
3.4 Aperiodic QPM Structures
36
3.5 Periodic and Aperiodic QPM Devices
37
3.6 Mathematica
38
Chapter 4:
4. Results and Interpretations
4.1 Analysis
39
4.2 Results
40
4.3 Single cycle sinusoidal Profile
40
4.3.1 Three aperiodic domains
4.3.2 Five aperiodic domains
4.3.3 Seven aperiodic domains
4.4 Three cycle sinusoidal Profile
4.4.1 Three aperiodic domains per cycle
6
44
4.4.2 Five aperiodic domains per cycle
4.4.3 Seven aperiodic domains per cycle
Chapter 5:
5. Summary and References:
50
5.1 Summary
5.2 Future extension
5.3 References
Appendix-A
52
7
LIST OF FIGURES
1.1.1 Linear and nonlinear interaction of waves.
1.1.2 Energy band diagram of linear and nonlinear optics.
1.1.3 Second harmonic generation.
1.1.4 Quasi Phase Matching.
1.1.5 Dual Peak Second Harmonic Spectrum.
2.2.1 QPM grating with ∏ phase shifting domains.
2.2.2 Tuning curves of relative conversion efficiency against pump
wavelength.
2.2.3 QPM grating with periodically distributed ∏ phase shifting domains.
2.2.4 Segmented QPM grating.
2.2.5 SHG conversion response against fundamental wavelength.
2.2.6 Difference in peak intensity of SHG phase reversal structure.
3.3.1 Phase mismatch for Second harmonic generation.
3.3.2 Quasi-phase matching in ferroelectrics.
3.3.3 First order SHG spectrum of an aperiodic spectrum
3.3.4 Periodic QPM device-Type-0 phase matching condition.
3.3.5 Schematic of the phase reversal QPM device.
3.3.6 Schematic of the phase reversal QPM device (multiple aperiodic
domains).
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4.4.1 Grating profile for three aperiodic domains.
4.4.2 Grating structure for three aperiodic domains.
4.4.3 Wave mismatch vector vs intensity output for three aperiodic domains.
4.4.4 Grating profile for five aperiodic domains.
4.4.5 Grating structure for five aperiodic domains.
4.4.6 Wave mismatch vector vs intensity output for five aperiodic domains.
4.4.7 Grating profile for seven aperiodic domains.
4.4.8 Grating structure for seven aperiodic domains.
4.4.9 Wave mismatch vector vs intensity output for seven aperiodic domains.
4.4.10 Grating profile for three aperiodic domains per cycle.
4.4.11 Grating structure for three aperiodic domains per cycle.
4.4.12 Wave mismatch vector vs intensity output for three aperiodic domains
per cycle.
4.4.13 Grating profile for five aperiodic domains per cycle.
4.4.14 Grating structure for five aperiodic domains per cycle.
4.4.15 Wave mismatch vector vs intensity output for five aperiodic domains
per cycle.
4.4.16 Grating profile for seven aperiodic domains per cycle.
4.4.17 Grating structure for seven aperiodic domains per cycle.
4.4.18 Wave mismatch vector vs intensity output for seven aperiodic domains
per cycle.
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NOTATIONS AND ABBREVIATIONS
WDM
-
Wavelength Division Multiplexing.
QPM
-
Quasi Phase Matching.
OPO
-
Optical Parametric Oscillation.
OPA
-
Optical Parametric Amplification.
CPM
-
Continuous Phase Modulation.
DFG
-
Difference Frequency Generation.
SFG
-
Sum Frequency Generation.
SHG
-
Second Harmonic Generation.
NLO
-
Nonlinear Optics.
LO
-
Linear Optics.
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ABSTRACT
Quasi phase matching (QPM) is a method for achieving efficient energy transfer between
interacting waves in a nonlinear process. It is most efficient and practical form of this technique is
based on a spatial modulation of the nonlinear properties along the interaction path in the material.
Such a spatial modulation can be obtained in ferroelectric crystals by periodically altering the
crystal orientation so that the effective nonlinearity changes according to the orientation.
In fiber optic communication WDM is a technology which multiplexes a number of optical
carrier signals onto a single optical fiber by using different wavelengths of laser light generally.
Since WDM requires tunable wavelength to accommodate flexible routing, switching and dynamic
reconfiguration of channels, the phase reversal QPM paves the way to enhance it. We are using
QPM phase reversal structures to act as channel sources which serves to accommodate various
wavelength channels that helps in enhancing the speed and eradication of ISI when the QPM phase
reversal structure is error free.
Periodic QPM devices, having uniformly spaced domains with altered polarization for
every coherence length lc, are widely used for most of the frequency conversion processes as they
provide large conversion efficiency. Aperiodic QPM devices are the ones generally used for
rendering broadband frequency conversion process. Depending on the applications, their
periodicity and duty ratio are varied.
The analysis done in the paper on Multiple Quasi-Phase-Matched Device Using
Continuous Phase Modulation of Grating and Its Application to Variable Wavelength Conversion
used Periodic QPM devices where the periodicity and duty ratio of the domains are varied to get
multiple peak output.
For our analysis, we use aperiodic QPM devices where we vary the frequency of positions
of aperiodic domains as per our pre-defined sinusoidal profile to obtain the similar multiple peaks
with high conversion efficiency. Our analysis proves that this method is more economical and
easier to fabricate when compared to the preexisting method which varies the periodicity and duty
ratio to obtain the same results.
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CHAPTER 1
PROLOGUE
Our project is mainly based on constructing a Quasi Phase Matched device using
Continuous Phase Modulation, with equal Duty Cycle between the domains, varying the number
of aperiodic domains. The spacing between the aperiodic domains is gradually increased or
decreased with respect to total number of domains to get a proper response similar to that of the
ideal phase reversal device but with multiple peaks leading to multiple channels. It mainly deals
with their operations, advantages and its efficiency when satisfying several needs of WDM
Applications such as variable wavelength converters.
1.1 INTRODUCTION TO OPTICS:
Optics plays a major role in development of technology from the time science started
evolving. In future optics will have a major impact in the growth of science and its applications.
We know that it a branch of science which deals with light and its properties. It can be further
divided into two types. They are
1. Linear Optics
2. Non-Linear Optics.
Linear and Non-linear optics mainly covers the interaction of light with various matter.
The use of optics in fields such as telecommunication and medicine has resulted in detailed
theoretical explanation of various theories. This has resulted in the field of theoretical study of
linear and non-linear waves.
1.2 LINEAR OPTICS:
It is also called as ‘Optics of weak light’. The main property of linear
optics is that the electric field is less than the intra-atomic field (Efield << Intra-Atomic field). In
linear optics the light gets delayed and deflected but its frequency is never changed, thus resulting
in same characteristics of source. Though it is used in linear optical quantum computing as beam
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splitters, phase shifters and mirrors, it is non-linear optics which stand apart in terms of its usage
and its support to evolvement of better technological advancements in the field of medicine and
telecommunication.
1.3 NONLINEAR OPTICS:
It is also called as ‘Optics of intense light’. Here the electric field is always greater than the intraatomic field (Efield >> Intra-Atomic field). Nonlinear optics mainly deals about the behavior of
light in the non-linear media. In this medium the polarization P responds non-linearly to the electric
field E of the light. This type of non-linearity is observed in high intensity light such as Lasers.
Non-linear optics remain unexplored until they discovered Second Harmonic Generation (SHG).
Induced polarization field in the material is generated when there is interaction between
electromagnetic field and a dielectric material. Normally, the response of the material is linear, so
that several electro-magnetic waves can penetrate and propagate through the material without
modifying the optical properties. But, when illuminated with sufficiently intense electro-magnetic
fields, the induced polarization will exhibit nonlinear properties.
(a)
(b)
Fig. 1.1.1. (a) Linear and (b) Non Linear interaction of waves
To explain how the linear and non-linear interaction of waves occur it is necessary to know the
energy level diagram of them. The figure 1.2. (a) and 1.2. (b) Clearly explains the energy level
diagram of linear and non-linear wave of light.
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(a)
(b)
Fig. 1.1.2. Energy band diagram of linear (a) and nonlinear optics (b)
For the better explanation of Fig 1.1 the energy level diagram 1.2 is absolute necessary. In linear
optics we obtain the same waves which has same energy as the input light under the weak beam.
But when using high intensity beam of light, the excited photons can be excited to higher energy
levels. Here the emitted light has higher energy when compared to the input beam. These waves
which are newly created brings out the concept of Non-Linear Optics. Series expansion of the
polarization will include higher order terms of the electromagnetic field,

P   0  (1) E   (2) E E   (3) E E E 
P
L
 PNL
𝑃𝐿 = 𝜀0 𝜒 (1) 𝐸 is the linear part and PNL the nonlinear part of the polarization, and 0 is the
permittivity of free space . The second and third-order nonlinear optical susceptibilities are
known as χ(2) and χ(3) respectively. Second-order nonlinear interactions can occur only in nonCentro symmetric crystals, that is, in crystals that do not display inversion symmetry. But, thirdorder nonlinear optical interactions can occur both for Centro symmetric and non-Centro
symmetric media.
The main outcome of non-linear properties is that the various electromagnetic waves of different
frequency can interact with each other in the material. With the help of this phenomenon we can
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obtain frequency conversion. There are two important types of frequency conversion. Firstly, the
process requires two photons which can be added or subtracted into one photon or even higher or
lower energy. This process includes SHG, SFG and DFG. Secondly, it requires parametric downconversion which includes OPO and OPA. It mainly starts from one input photon and results in
two photons of lower energies.
1.4 PHASE MATCHING:
There are many parametric processes such as frequency doubling, sum and difference
frequency generation, parametric amplification and oscillation involved in phase-sensitive nonlinear process. These processes in common requires phase matching to be highly efficient.
Basically, this ensures a proper phase relationship between the interacting waves which is for
optimum nonlinear frequency conversion is maintained along the propagation direction. This
maintains proper amplitude distribution from different locations and thus ensures that waves are
all in phase. This condition states that there should be some phase mismatch that should be close
to zero.
For example, the type I phase matching of frequency doubling with collinear beams, the phase
mismatch is given by,
k = k2 – 2k1
Where k1 and k2 are the wave vectors of the fundamental and second-harmonic beam,
respectively.
The usual technique for achieving the phase matching condition is called as birefringent phase
matching. Here the method of cancellation of phase mismatch is done by exploitation of
birefringence. It comes in many types.
Type-I phase matching means that i.e. in sum frequency generation the two beams have the same
polarization which is perpendicular to that of the sum frequency wave. But in Type-II phase
matching technique, the two fundamental beams have different polarization directions. This is
comparatively appropriate when the birefringence is really strong or the phase velocity mismatch
is small.
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The distinction between type I and type II similarly applies to frequency doubling, and to
processes such as degenerate or non-degenerate parametric amplification. The different
polarization arrangements can have various practical implications, for example for the
combination of several nonlinear conversion stages, or for intra-cavity frequency doubling.
Critical phase matching is a technique where we can make angular adjustment to the crystal in
order to find out the phase matching configuration. But in non-critical phase matching the
polarization directions are along the crystal axes, so in this case angular adjustment is not a case
sensitive parameter.
Wave vectors which are involved may have the same direction (collinear phase
matching) or different directions (non-collinear phase matching). However, the vector sum of the
generating beams equals the wave vector of the product beam. Achromatic phase matching is a
special technique where at least one of the interacting beams is angularly dispersed so that each
frequency component of the signal is properly phase-matched.
QPM is a very special technique where the real phase matching never occurs, due to high
conversion efficiencies which are nevertheless obtained in a crystal in which there is varying sign
of non-linearity periodically. Such a variation technique of nonlinearity can be achieved by
periodic polling.
1.5 SECOND HARMONIC GENERATION:
In this phenomena, an input wave in a nonlinear material can generate a wave with twice
the optical frequency (i.e., half the wavelength). This process is also called second harmonic
generation represented in Fig. 1.3. When a beam of monochromatic light impinges on a surface,
the lack of symmetry at the surface (or a buried interface), it can lead to the generation of light at
a frequency twice that of the incident light (i.e. the second harmonic). But in most of the cases, the
pump waves are delivered in the form of laser beam which is frequency doubled (Second
Harmonic). This is generated in the form of a beam which is propagating in the similar direction.
This phenomenon helps us to study Surface phenomena such as molecular adsorption,
aggregation and orientation. The detected second harmonic light is of particular interest in studying
buried interfaces as most surface science techniques cannot access such structures. The
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information on the electric field at an interface can be provided by. Related techniques are SFG
and DFG.
(a)
(b)
(c)
Fig 1.1.3 (a) A wave of frequency  incident on a NLO crystal generates a wave of frequency
2. (b) As the photon flux density 1(z) of the fundamental wave decreases the photon flux
density 3(z) of the SH wave increases. Since photon numbers are conserved, the sum 1(z) +
23(z) = 1(0) is a constant. (c) Two photons of frequency  combine to make one photon of
frequency 2
1.6 QUASI PHASE MATCHING:
It was first proposed by Armstrong et al in the year 1962. It is the most efficient
method for achieving efficient energy transfer between the interacting waves in the nonlinear
process. It is most efficient and practical form of this technique is based on a spatial modulation
of the nonlinear properties along the interaction path in the material. Spatial modulation can be
obtained in ferroelectric crystals by periodically altering the crystal orientation so that the effective
nonlinearity changes according to the orientation. The phase mismatch accumulates and  is
reached when the interacting waves propagate with different phase velocities, the sign of the
driving nonlinear susceptibility is also reversed so that the phase difference is “reset” to zero. In
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Fig 1.1.4 step-wise growth in the output power along the crystal length can be seen. The highest
conversion efficiency is obtained when the periodicity of the modulation corresponds to 2lc, where,
lc is the coherence length, which represents first-order QPM.
The involvement of ferroelectric crystal such as LiNbO3 involves forming regions of
periodically reversed spontaneous polarization domains. Quasi-Phase matching has lower
efficiency than the perfect phase matching. In fig 1.1.4 it brings out the useful flexibility into
optical parametric processes. The main advantages of QPM is that it allows use of any convenient
combination of polarization in the non-linear interactions. It includes the case which is called as
Co-polarized too. Co-polarized interactions are the ones which have largest nonlinear
susceptibility in many materials. These are necessary in cases when only optical waves of
polarization are supported in a QPM device.
I2
(a)
(b)
Ps
Ps
(c)
0
lc
2lc
3lc
4lc
5lc
6lc
Fig.1.1.4. Effect of phase matching on the growth of second harmonic intensity with distance in a
nonlinear crystal. (a) Perfect phase-matched; (b) first order QPM by flipping the sign of the
spontaneous polarization every coherence length of the interaction; (c) nonphase-matched
interaction.
1.7 QPM APPLICATIONS IN WDM:
Generally in Fiber Optic Communication, QPM is widely used. WDM is a technology which
multiplexes a number of optical carrier signals into a single optical fiber by using different
wavelengths of laser. This normally increases the multiplication capacity of the channels and also
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enables the bidirectional communications over one strand of fiber. The WDM (Wavelength
division multiplexing) is mainly applied to optical carrier which is described by its wavelength.
WDM is different from other technologies because of it capability of being compatible to the
existing hardware, being modular and also having the ability of saving a lot costly equipment if
designed properly. WDM requires tunable wavelength to accommodate flexible routing, switching
and dynamic reconfiguration of channels, the phase reversal QPM paves the way to enhance it.
We used the QPM phase reversal structures to act as channel sources which serves to accommodate
various wavelength channels that helps in enhancing the speed and eradication of ISI when the
QPM phase reversal structure is error free. This led to various Experiments upon which it resulted
in creating 40 WDM channels which are used for multiple idlers broadcasting.
1.8 PERIODIC AND APERIODIC QPM DEVICES:
Periodic QPM devices, having uniformly spaced domains with altered polarization for
every coherence length lc, are widely used for most of the frequency conversion processes as they
provide large conversion efficiency. In periodic QPM devices there are equal number of original
and reversed domain in the crystal. The direction of polarization is periodically inverted for every
lc. It is often referred to as a binary variation of the nonlinear coefficient and producing the largest,
d33.
The Aperiodic QPM devices are the ones generally used for rendering broadband frequency
conversion process. Depending on the applications, their periodicity and duty ratio are varied. We
consider a periodic device except that it has an aperiodic domain in the middle of width  (twice
the domain width). This is typically called as the phase reversal QPM device. In an ideal phase
reversal device, the size of the aperiodic domain is to be twice as that of the other domains i.e., 
and located exactly at the middle of the device. By keeping the aperiodic domain in the middle of
the domains yields a dual peak second harmonic (SH) spectrum where the intensity corresponding
to the phase matching point is zero. The peak intensities are identical to each other with no SHG
for the position satisfying the phase matching condition.
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q = k/2
SH Intensity, I2
(b)
1/
q
Fig 1.1.5. Dual Peak Second Harmonic Spectrum.
1.9 MULTIPLE PEAKS IN QPM:
Periodically polled devices give rise to single peak output. To convert this single
peak output to multiple peaks, we insert aperiodic domains in between the periodic domains. The
number of peaks depend on the number of aperiodic domains inserted as well as the profile in
accordance to which the aperiodic domains are inserted. Multiple peaks are obtained only when
odd number of phase reversal/aperiodic domains are added. These results are not obtained when
even number of phase reversal/aperiodic domains are added. When even number of phase
reversal/aperiodic domains are added, we obtain only a single peak output. This single peak output
has innumerable applications in innumerable fields, but has very limited applications in the
fabrication of optical frequency converters.
1.10 SIGNIFICANCE OF MULTIPLE PEAKS:
Optical frequency converters have the basic need to convert a monochromatic single
wavelength laser beam input into multiple wavelength output to enable multiple channels. Hence,
as multiple channels are essential, multiple peaks are required as multiple peaks give rise to
multiple channels.
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The number of channels as well as bandwidth are determined by the number of
peaks and separation between the peaks respectively. Hence, suitable profiles are designed
depending on the number of channels required as well as the bandwidth of each channel.
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CHAPTER 2
REVIEW ON RELATED LITERATURE
2.1 MULTIPLE QPM DEVICES USING CPM:
QPM using a periodically modulated grating is a versatile technique for wavelength
conversion. The QPM technique allows us to satisfy the phase-matching condition by setting an
appropriate modulation period, and enables the highly efficient wavelength conversion of arbitrary
wavelength combinations in the wavelength region where the material is transparent. Wavelength
conversion based on difference frequency generation is attractive for applications in the
communication wavelength band because it has several distinct advantages including the
simultaneous conversion of wavelength division multiplexed channels, a large signal bandwidth
and independence of the modulation format. Efficient QPM-based wavelength conversion has
been demonstrated using a periodically poled LiNbO3 waveguide. Another feature of the QPM
technique is that we can extend the functionality of the wavelength converter by using an
engineered grating. Several grating structures and their applications have been proposed including
modulated gratings for broad-band phase matching a chirped grating for pulse compression, and
modulated gratings for multiple QPM. Multiple QPM devices using continuous phase modulation
have robust fabrication tolerance and very high efficiency when compared to the traditional
methods. Fast wavelength switching of a four channel device can be obtained with a maximum
speed of 40 GB/second. The only drawback is that the pump frequency is so narrow and hence
only single wavelength can be used as a result of which the output wavelength can be easily
predicted. To overcome this, three approaches has been proposed. The first approach is the
broadband phase matching technique which uses a type-I interaction using d31 non-linear
coefficient. The main advantage is that there is a large bandwidth for pump. The only disadvantage
is that the conversion efficiency is less because of small d31 coefficient of LiNbO3. The next
approach is to broaden or tune the phase matching curve by use of temperature gradient wherein
re-configurability is achieved by changing temperature but switching speed is reduced. The next
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approach is by using engineered domain structure allowing multiple QPM. It is more advantageous
than the other two approaches. It provides better efficiency than broad band phase matching
devices and is extremely suitable for WDM. Here only discrete wavelength switch is required and
fast wavelength switching is switching pump frequency.
2.2 BANDWIDTH AND TUNABILITY ENHANCEMENT IN QPM BY DFG:
All optical wavelength conversion is an important technique in future wavelength division
multiplexed optical networks. Among several demonstrated wavelength conversion approaches,
difference frequency generation is very attractive and promising with some advantages such as
strict transparency and simultaneous multichannel conversion ability. DFG has been realized in
LiNbO3.However, it is not yet very practical for WDM networks due to narrow pump bandwidth.
Several methods for relaxing the phase-matching condition in QPM second-harmonic-generation
and DFG have been proposed. An effective method to broaden and flatten both signal and pump
bandwidth is to introduce various patterns of π-shifting domains into QPM gratings.
2.3 NON- PERIODICALLY DISTRIBUTED Pi - PHASE SHIFTING DOMAIN:
In this type, we introduce non-periodically distributed domains along the grating. These
domains are placed in random positions inside the grating crystal. After introducing these nonperiodical domains across the crystal when we send a laser source inside this setup and analyze
the resultant wave we notice broaden and flattening of pump and signal bandwidth of the wave.
For example when we introduce 4 π-phase shifting domains at random positions we get a resultant
wave’s bandwidth 4 times larger than that of a normal grating’s wave.
Fig. 2.2.1 Model of QPM gratings with some π-phase shifting domains. [Wei Liu et. al.]
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Fig 2.2.2 Calculated tuning curves of relative conversion efficiency ηrel against pump wavelength
λpump for a 10 mm long grating with different numbers of p-phase shifting domains, respectively.
Signal is fixed at 1545 nm. The distributing parameters are curve (1): m = 0 (uniform grating),
L1 =L; curve (2): m =1, L1 =0.821L, L2 =0.179L; curve (3): m= 2, L1 =L3 =0.115L, L2
=0.770L; curve (4): m =3, L1=0.051L, L2 = 0.149L, L3 = 0.685L, L4 = 0.115L; curve (5): m =
4, L1 = L5 = 0.051L, L2 = L4 = 0.149L, L3 = 0.600L; where m denotes the numbers of p-phase
shifting domains. [Wei Liu et. al.]
24
2.4 PERIODICALLY DISTRIBUTED Pi- PHASE SHIFTING DOMAIN:
Although the pump bandwidth can be enhanced in some degrees using non-periodically
distributed pi-phase shifting domains larger continuous bandwidth (more than 2nm for the 10 mm
long grating) with acceptable conversion efficiency is almost impossible due to the trade-off
between the conversion efficiency and bandwidth. If the pump bandwidth is so narrow, the DFGbased wavelength converters can only provide very limited tunability. Although it is possible to
change the phase matching wavelength through controlling the temperature of waveguide devices,
this method is inadvisable due to the slow response speed and complicated operation. We consider
that since the wavelength channels of WDM systems are discrete, the broad pump tunability can
also be achieved by making a broadband comb like pump–wavelength tuning curve to avoid too
serious decrease of conversion efficiency.
Fig 2.2.3 Model of the QPM grating with periodically distributedp-phase shifting domains. (a)
Single-period pattern; (b) segmented multi-period pattern [Wei Liu et. al.].
Although DFG based wavelength converters have many attractive qualities its weak pump
tunability seriously limits their practical applications. As a solution we demonstrate that by
introducing various formats of pi-phase shifting domains into QPM grating is an effective and
simple method to enhance both signal and pump bandwidth.
25
2.5 BROADBAND AND MULTIPLE CHANNEL VISIBLE LASER GENERATION BY
USE OF SEGMENTED QPM GRATINGS:
In recent years, QPM optical frequency conversion becomes important for generating new
laser frequencies with development of domain inversion technologies. Many methods like second
harmonic generation, difference frequency generation and third harmonic generation have been
suggested to achieve this. Using SHG pumped by a near-infrared laser in a QPM structure is a
feasible scheme to obtain a visible laser source. In this method, the largest nonlinear coefficient of
the crystal is used, which is beneficial for increasing the intensity of the frequency-doubled laser
source. Although the periodically QPM structure is easy to be manufactured,the conversion
bandwidth is quite narrow, that is, very high quality laser sources are required and the processes
are difficult to be operated and controlled. In general, the wavelength bandwidth and temperature
tolerance can be enhanced in aperiodic QPM gratings, even multichannel generation is realized.
Here we concentrate on investigation of SHG in segmented QPM gratings to broaden the
conversion bandwidth and temperature tolerance, and the temperature tolerance, and realize
multiple channel generation.
Fig 2.2.4 Segmented representation of QPM grating [Shiming Gao et. al.]
For segmented gratings, the QPM conditions are easy to be satisfied in relatively wider
laser wavelengths and larger temperature region because of the enhancement of bandwidth and
temperaturetolerance. The requirement to laser source stability and environment temperature
accuracy is greatly reduced. The more segments, the broader the conversion bandwidth and
temperature tolerance, however, the lower the conversion efficiency. As shown below figures, the
26
efficiencies of the segmented gratings are less than that of the periodic grating. Fortunately, the
power of the solid-state lasers in the near-infrared region can reach even several tens of watts.
27
Fig 2.2.5 SHG conversion response versus fundamental wavelength for: (a) the periodic grating:
(b) the 2-segment grating; (c) the 3-segment grating [Shiming Gao et. al.].
We have investigated frequency conversion from the near-infrared region to the visible
region by SHG in segmented QPM gratings. The segmented gratings show much broader
conversion bandwidth and temperature tolerance. They are about four and eight times as large as
those of the periodic grating for the 2-segment and 3-segment gratings. Segmented gratings make
it possible to realize multiple-channel laser sources in the visible region with near-infrared
broadband laser sources.
2.6 TUNABLE ALL-OPTICAL WAVELENGTH BROADCASTING:
With ever-increasing data transmission capacity, WDM networks require tunable
wavelength broadcasting by replicating a signal to several channels to facilitate flexible routing,
switching and dynamic reconfiguration of the information carried by different channels. Owing to
their high speed, large bandwidth, large signal-to-noise ratio, transparency to signal format and
so on, all-optical quasi-phase-matched wavelength converters based on second-order nonlinearity
in periodically poled lithium niobate have attracted increasing attention. Over the past decade,
research on cascaded second-order nonlinear interactions in QPM-PPLN has been growing fast to
satisfy the needs of high speed and large capacity optical networks. Achieving wavelength
28
broadcasting in these QPM devices is also useful for several applications such as video distribution
and teleconferencing.
Fig 2.2.6 Difference in peak intensities between the theoretical and proposed
experimental setup [Meenu et. al.]
The difference in the peak intensities can be clearly inferred in fig 2.6. When the
experimental curve is clearly analysed, the left peak intensity is fairly low when compared with
the right peak. This deviation from the ideal theoretical value is due to various parameters in the
device setup. Alsotunable wavelength broadcasting has been achieved in a 10-mm long multipleQPM PPLN. One signal has been broadcasted into three idlers based on cascaded SHG-SFG/DFG
in the novel PPLN device for which three SH-SF peaks were achieved. The mutual spacing of
idlers and their position in the WDM grid was adjusted by tuning of the two pump wavelengths
assisted by temperature adjustment of the PPLN. The temperature tunability of the multiple-QPM
PPLN device assists in the choice of suitable pump wavelengths for tunable wavelength
broadcasting by positioning the idlers at desired destination channels in WDM networks. Channel
selective multiple broadcasting achieved by this scheme proves its crucial function in signal path
routing enabling the effective usage of WDM bandwidth and flexible network construction.
29
CHAPTER 3
METHODS & PROCEDURES
3.1 WAVE EQUATIONS:
The wave equation for the propagation of light through a nonlinear optical medium
begins with Maxwell’s equations,
 
  D  ext ,
(3.1)
 
 B 0 ,
(3.2)

 
B
 E   ,
t

  
D
  H  J ext 
.
t
(3.3)
(3.4)
We are primarily interested in the solutions of these equations in regions of space that
contain no free charges, so that
 ext  0 ,
(3.5)
and that contain no free currents, so that

J ext  0 .
(3.6)
If the material is nonmagnetic, so that


B  0 H
(3.7)


However, we allow the material to be nonlinear in the sense that the fields D and E are
related by
30

 
D 0E  P ,
(3.8)


in general the polarization vector P depends on the local electric field E .
To derive the optical wave equation in the usual manner, we take the curl of the 3rd
Maxwell’s Eq. (3.3), and interchange the order of space and time derivatives on the right-
 
hand side of the resulting equation. Using Eq. (3.4), (3.6), and (3.7) to replace   B by

D
0
, we obtain
t


2D
    E  0 2  0
t
(3.9a)
Substituting Eq. (3.8) in the above equation, we obtain,


 1 2E
2P
    E  2 2   0 2 .
c t
t
(3.9b)
This is the most general form of the wave equation in nonlinear optics. Under certain
conditions it can be simplified. For example, by using an identity from vector calculus, we
can rewrite the first term on the left-hand side of Eq. (3.9b) as



    E  (  E )   2 E .
(3.10)
In linear optics of isotropic and homogeneous source-free media, the first term on the
right-hand side of this equation vanishes because, the Maxwell’s equation
 
  E  0 . However, in
  E  0
results in
nonlinear optics this term is generally nonvanishing even for isotropic


materials, owing to the more general relation (3.8) between D and E . Fortunately, in
nonlinear optics the first term on the right-hand side of Eq. (3.10) can usually be dropped

for cases of interest. For example, if E is of the form of a transverse, infinite plane wave,
 
  E vanishes identically.

It is often convenient to split P into its linear and nonlinear part as
31
P  PL  PNL ,
(3.11)


Here PL is the part of P that depends linearly on the electric field E . The

displacement field D can be decomposed into two parts such as linear and nonlinear. The
nonlinear term can be written as,
D  D(1)  PNL ,
(3.12a)
Where the linear part is given by
D(1)   0 E  PL
(3.12b)
In terms of this quantity, the wave Eq. (3.9) becomes
 2 PNL
 2 D(1)
 E  0
  0
. (3.13)
t 2
t 2


In the case of a lossless, non-dispersive medium, the relation between D (1) and E
is real. The frequency-independent dielectric tensor  (1) can be expressed as
D(1)   (1)  E
(3.14a)
For the case of an isotropic material, this relation reduces simply to


D (1)   (1) E
(3.14b)
Where  (1) is now a scalar quantity, the wave Eq. (3.13) becomes
 2 PNL
n2  2 E
 E  2 2   0
c t
t 2
(3.15)
This equation has the form of a driven (i.e., inhomogeneous) wave equation; the
nonlinear response of the medium acts as a source term which appears on the right-hand side
of this equation. In the absence of this source term, Eq. (3.15) admits solutions of the form
32
of free waves propagating with phase velocity c / n , where  0 (1)   0 0
 (1) n 2
 , n is the
 0 c2
(linear) refractive index.
3.2 NON LINEAR COUPLED WAVE EQUATIONS FOR SHG:
d eff 2
dA2
i
A1 exp( ikz)
dz
c n2
(Up-conversion process)
d eff
dA1
i
A2 A1 exp( ikz) (Down-conversion process)
dz
c n1
(3.16a)
(3.16b)
Where n1 and n2 are the refractive indices of the fundamental (FM) and the second harmonic
(SH), respectively. Eqs. (3.16a) and (3.16b) represent the frequency up-conversion
(+2) and the down-conversion process (2), respectively. It should be noted
that diffraction effect was not considered for simplicity. These equations are coupled
through the nonlinear optical coefficient deff, describing the changes in the amplitude and
the phase of the fundamental and the second harmonic.
The wave vector mismatch k is defined as
k  k 2  2k1 
4

(n2  n1 ) .
(3.17)
Fig. 3.3.1 Phase mismatch for second-harmonic generation
Solving the Eqs. (3.16) under low depletion limit of the FM (A1 ~ constant). Eq. (3.16a) is
directly integrated to give the amplitude of the SH,
33
A2 
 d A12 (0) ikL
e  1 ,
n2 c
k
(3.18)
Where A1(0) is the input FM amplitude, and L is the sample length. The intensity of a light
wave with amplitude A can be written as
I
1
2
c o n A .
2
(3.19)
Substituting Eq. (3.18) into the Eq. (3.19), which gives
 kL 
sin 2 

2 d
2 
2 2

 kL  ,
I2 
L I1 (0)
 sinc 2
2

cnn
 kL 
 2 


 2 
2
2
eff
3 2
o
1 2
Where we define
sinc x 
(3.20)
sin x
.
x
3.3 FOURIER OPTICS OF QPM SHG:
Previously we have briefly treated the perfect phase matching SHG. In order to
enhance the efficiency, all the interacting beams must be phase matched at the desired
wavelength. In such cases, QPM is very attractive and powerful method to enhance the
efficiency of optical parametric process. From Eqs. (3.16) the SH becomes,
dA2
 i A12 exp( ikQ z )
dz
Where  
 d ( z)
c n2
(3.21)
, and d(z) is the periodically modulated nonlinear coefficient
represented by Fig. 3.2. The wave vector mismatch for the QPM interaction,
by
 kQ   k  m K  k2  2 k1 
m
,
lc
(3.22)
34
 kQ , is defined
where k ,k1, k2 are same as in Eq. (3.17), and lc 

4 (n2  n1 )


2
is the coherence
length for SHG.
L = 2 lc
lc
d(z )= deff -deff deff
deff -d
deff
eff deff
Ps

Fig. 3.3.2 Quasi-phase matching in ferroelectrics.
The up-conversion equation for SHG ( +  = 2) propagating in the z-direction is given
in Eq. (3.21),
dA2
 i A12 exp( ikz )
dz
(3.23)
Where A1(2) is the electric field amplitude of the fundamental (second-harmonic) wave,  is
proportional to the effective nonlinear optical coefficient, and k = k2 – 2k1 = 4(n2-n)/
is the wave vector mismatch. In the case of negligible depletion of the fundamental, Eq.
(3.23) can be directly integrated to give a sinc-form spectrum in k . In the case of QPM,
however  = (z) has modulation along z. Letting k = 2q, SHG amplitude can be
expressed as Fourier transform of (z),
A2 (q )  iA12   ( z )e i 2 qz  iA1 [ ( z )] .
2
(3.24)
Taking only the 1st order QPM, (z) can be expressed as
35
L

 z  z   2 z 
 ( z )  D rect 
 sin 
,
L

   


(3.25)
Where D is a constant proportional to the effective nonlinear optical coefficient, and L is the
device (poled) length. Applying Fourier Transform of the above Eq. (3.25),
1
𝜋
1
ℱ[𝜅(𝑧)] = 2𝑖 𝐿 𝐷 𝐺 (𝑞 ± Λ) ∗ [𝑠𝑖𝑛𝑐(𝐿𝑞)𝑒 𝑖 2 𝐿𝑞 ]
(3.26)
Then, the second harmonic amplitude is,
 1
 
D 
1   i L q    
A2 (q)  A
L sinc  L  q    e

2 
 
 

2
1
(3.27)
3.4 APERIODIC QPM STRUCTURE:
The structure of a phase reversal or aperiodic QPM device is similar to the grating structure
as periodic one with a domain reversed exactly at the centre. The length of the grating device
is L, an aperiodic domain has been introduced in the middle (L/2) of the device. Sellmeier
equation gives the relation between refractive index and wavelength for a particular
transparent medium. The effective nonlinear coefficient term can be written as,

L
3L  


z 
z



 2 z 
4
4 
 ( z )  D sin 
  rect  L   rect  L  
  





 2 
 2  
(3.28)
The Fourier transform of (z) can be written as,
𝜋
3𝜋
1
1
𝐿𝑞
𝐿𝑞
ℱ[𝜅(𝑧)] = 𝐿 𝐷 𝐺 (𝑞 ± ) ∗ [𝑠𝑖𝑛𝑐 ( ) 𝑒 𝑖 2 𝐿𝑞 − 𝑠𝑖𝑛𝑐 ( ) 𝑒 𝑖 2 𝐿𝑞 ]
2
Λ
2
2
1
= 𝐿 𝐷 𝑒 𝑖𝜋𝐿(𝑞±Λ)
𝜋
2
1
Λ
𝑠𝑖𝑛2 ( 𝐿(𝑞± ))
(3.29)
𝜋
1
𝐿(𝑞± )
2
Λ
Then, the second harmonic amplitude of the aperiodic QPM device Eq. (3.25) is
𝐴2 (𝑞) =
𝑖𝐴12
𝐿𝐷𝑒
1
Λ
𝑖𝜋𝐿(𝑞± )
𝜋
2
1
Λ
𝑠𝑖𝑛2 ( 𝐿(𝑞± ))
(3.30)
𝜋
1
𝐿(𝑞± )
2
Λ
36
The intensity spectrum of the second harmonic for this specific aperiodic structure is given
in Fig. 3.3.
q
0
-1/
1/
Fig. 3.3.3. First order SHG spectrum of an aperiodic QPM device.
3.5 PERIODIC AND APERIODIC QPM DEVICES:
Periodic QPM devices are those which have uniformly spaced domains with reversed polarization
as shown in the Fig. 3.4,
z
x
Fig. 3.3.4 Periodic QPM device of Type – 0 phase matching condition
Aperiodic QPM devices have unequal domains the size of those domains can be varied vary as
per our need. Here, we discuss an aperiodic device called as phase reversal QPM as shown in Fig.
3.5. The phase reversal QPM structure is similar to the ideal periodic one but it has an aperiodic
domain of width  at the middle of the device.
37
L



Fig. 3.3.5 Schematic of the phase reversal QPM device.
This type of QPM devices are the recent development in WDM networks as the peak intensity and
the separation between the peaks can be engineered by modifying the domain size.
Fig. 3.3.6 Schematic of the phase reversal QPM device (multiple aperiodic domains).
The above QPM device consists of multiple aperiodic domains. The domains are arranged in a
particular manner in order to suit a pre-defined profile. This profile is used to obtain the required
output based on number of channels and width of each channel. To obtain dual/multiple peaks,
odd number of aperiodic domains are inserted (i.e. n is an odd number).
3.6 MATHEMATICA:
Wolfram Mathematica is a powerful tool for mathematical analysis. As our analysis
of aperiodic domains is very complex, Mathematica served as an ideal tool to plot the responses
for the various cases.
38
CHAPTER 4
RESULTS AND INTERPRETATIONS
4.1 Analysis:
For our theoretical model, we assume low conversion efficiency, CW or long-pulse
interaction and no losses for the fundamental or second harmonic waves. The basic slowly varying
amplitude equation governing the growth of the second harmonic field under these conditions,
dA2
 iA12 e ikz
dz
(4.1)
Where  is proportional to the effective nonlinear optical coefficient deff, and
k  k 2  2k1 
4

n2  n1  , for negligible depletion of the fundamental wave, the above Eq. (4.1)
can be directly integrated to give a sinc-form of spectrum if  is constant in the medium. In case
of QPM,  is not a constant, but  = (z). Even in this case, the above equation can be integrated.
Let k = 2q, then
𝐴2 (𝑞) = 𝑖𝐴12 ∫ 𝐾(𝑧)𝑒 −𝑖Δ𝑘𝑧 𝑑𝑧
(4.2)
The above equation is used in the case of single aperiodic domain. For the case of multiple
aperiodic domains, summation of 𝐴2 needs to be implemented.
𝑡2
𝑡3
𝐴2 (𝑞) = 𝑖𝐴12 {∫ 𝐾(𝑧)𝑒 −𝑖Δ𝑘𝑧 𝑑𝑧 − ∫ 𝐾(𝑧)𝑒 −𝑖Δ𝑘𝑧 𝑑𝑧
𝑡1
𝑡2
𝑡4
+ ∫ 𝐾(𝑧)𝑒
𝑡𝑛
−𝑖Δ𝑘𝑧
𝑑𝑧 … … … … . − ∫
𝑡3
𝐾(𝑧)𝑒 −𝑖Δ𝑘𝑧 𝑑𝑧}
𝑡 𝑛−1
(4.3)
t1, t2, t3….tn are the respective domain widths. The number of domains varies based on the
profile. The value of n is always an odd number.
In our analysis t1=t2=t3=…. tn=8.
39
4.2 Results:
For the continuous sinusoidal profile, the results obtained for different number of
aperiodic domains are shown below.
4.3 Single cycle sinusoidal Profile:
In the single sinusoidal profile, the following assumptions are considered.
Total number of domains=128.
Domain width=8.
4.3.1 Three Aperiodic Domains:
A
Distance between aperiodic domains
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
Length
Fig. 4.4.1. Grating profile for 3 aperiodic Domains
Fig. 4.4.2 Grating structure for 3 aperiodic Domains
The locations of the aperiodic domains are {32, 64, 96}.
40
B
200000
intensity
150000
100000
50000
0
0.30
0.35
0.40
0.45
0.50
wave mismatch vector
Fig. 4.4.3 Wave mismatch vector vs Intensity output for 3 aperiodic Domains.
Fig 4.4.1 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.2
represents the grating structure and Fig 4.4.3 represents the multiple peak output for the respective
profile structure.
4.3.2 Five Aperiodic domains:
Distance between aperiodic domains
A
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
20
40
60
80
100
120
Length
Fig. 4.4.4 Grating Profile for 5 aperiodic domains.
41
Fig. 4.4.5 Grating structure for 5 aperiodic domains.
The locations of the aperiodic domains are {32, 48, 64, 80, 96}.
B
100000
intensity
80000
60000
40000
20000
0
0.30
0.35
0.40
0.45
0.50
wave vector mismatch
Fig. 4.4.6 Wave mismatch vector vs Intensity output for 5 aperiodic Domains
Fig 4.4.4 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.5
represents the grating structure and Fig 4.4.6 represents the multiple peak output for the respective
profile structure.
42
4.3.3 Seven Aperiodic domains:
A
Distance between aperiodic domains
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
Length
Fig. 4.4.7 Grating Profile for 7 aperiodic domains.
Fig. 4.4.8 Grating Structure for 7 aperiodic domains.
The locations of the aperiodic domains are {32, 48, 56, 64, 72, 80, 96}.
43
B
100000
80000
intensity
60000
40000
20000
0
0.30
0.35
0.40
0.45
0.50
wave vector mismatch
Fig. 4.4.9 Wave mismatch vector vs Intensity output for 7 aperiodic Domains.
Fig 4.4.7 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.8
represents the grating structure and Fig 4.4.9 represents the multiple peak output for the respective
profile structure.
4.4 Three cycle sinusoidal profile:
In the three cycle sinusoidal profile, the following assumptions are considered.
Total number of domains=384.
Domain width=8.
44
4.4.1 Three aperiodic domains per cycle:
B
Distance between aperiodic domains
65
60
55
50
45
40
35
30
0
50
100
150
200
250
300
350
400
Length
Fig. 4.4.10 Grating Profile for three aperiodic domains per cycle.
Fig. 4.4.11 Grating Structure for three aperiodic domains per cycle.
The locations of the aperiodic domains are {32,64,96,160,192,224,288,320,352}
45
B
1400000
1200000
1000000
intensity
800000
600000
400000
200000
0
0.35
0.40
wave mismatch vector
Fig. 4.4.12 Wave mismatch vector vs intensity output for three aperiodic domains per cycle.
Fig 4.4.10 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.11
represents the grating structure and Fig 4.4.12 represents the multiple peak output for the
respective profile structure.
4.4.2 Five aperiodic domains per cycle:
B
Distance between aperiodic domains
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
350
400
Length
Fig. 4.4.13 Grating Profile for 5 aperiodic domains per cycle.
46
Fig. 4.4.14 Grating Structure for 5 aperiodic domains per cycle.
The locations of the aperiodic domains
are {32,48,64,80,96,160,176,192,208,224,288,304,320,336,352}.
B
800000
700000
600000
intensity
500000
400000
300000
200000
100000
0
-100000
0.35
0.40
0.45
wave vector mismatch
Fig. 4.4.15 Wave vector mismatch vs intensity output for 5 aperiodic domains per cycle.\
Fig 4.4.13 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.14
represents the grating structure and Fig 4.4.15 represents the multiple peak output for the
respective profile structure.
47
4.4.3 Seven aperiodic domains per cycle:
B
Distance between aperiodic domains
70
60
50
40
30
20
10
0
0
50
100
150
200
250
300
350
400
Length
Fig. 4.4.16 Grating Profile for 7 aperiodic domains per cycle.
Fig. 4.4.17 Grating Structure for 5 aperiodic domains per cycle.
The locations of the aperiodic domains
are{32,48,56,64,72,80,96,160,176,184,192,200,208,224,288,304,312,320,328,336,352}.
B
600000
500000
intensity
400000
300000
200000
100000
0
0.30
0.35
0.40
0.45
wave vector mismatch
Fig. 4.4.18 Wave vector mismatch vs intensity for 7 aperiodic domains per cycle.
48
Fig 4.4.16 represents the profile of the placements of aperiodic domains in the structure. Fig 4.4.17
represents the grating structure and Fig 4.4.18 represents the multiple peak output for the
respective profile structure.
49
CHAPTER 5
SUMMARY AND REFERENCES
5.1 SUMMARY:
The dual peak spectral response in phase reversal QPM has attributed to the phase reversal
of the second harmonic wave arising from the aperiodic domain in the centre of the crystal can be
used widely in WDM operations. . The second harmonic generation has attributed to tremendous
research in field of optical networks, mainly QPM devices and in opto-electronics etc. Thus QPM
proved to be an efficient source in WDM networks. Further, it can be used in the optic fiber
communications as well.
We have also analyzed the dual peak spectral response by placing the aperiodic
domains throughout the crystal and increasing its number to 3, 5, 7 etc and keeping the domain
width () constant where in the response we observed that spacing between the peaks get enhanced
when the number of aperiodic domains are increased. Hence by which the overlapping between
the peaks can be eliminated. Then we modified the distance between aperiodic domains (increased
or decreased) in order to obtain the second harmonic dual peak response for that profile. Then we
stressed the sine wave profile (one cycle) and calculated the dual peak response with 3, 5, 7
aperiodic domains and then we have done the same with three cycle sinusoidal profile to get dual
peak response.
5.2 FUTURE EXTENSION:
1. To increase the number of aperiodic domains in sinusoidal profile and determine the
response since it will bring more efficiency.
2. To increase the domain length to 1 centimeter and determine the response.
3. Evaluate the obtained response using Fourier analysis.
50
5.3 REFERENCES:
[1] R. W. Boyd, Nonlinear Optics, Academic Press, San Diego, USA (1992).
[2] A. Yariv, Quantum Electronics, 3rd ed, John Wiley & Sons Inc, New York (1988).
[3] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918
(1962).
[4] K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, M. Cha, Optics Express 17, 17862 (2009).
[5] M. Ahlawat, A. Tehranchi, K. Pandiyan, M. Cha, and R. Kashyap, Optics Express 20, 2742527433 (2012).
[6] M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, H.Suzuki, IEEE Journal of Quantum
Electronics, Vol. 41 (2005).
[7] Wie Liu, J. Sun, J. Kurz, Optics Communications 216 (2003).
[8] M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE Journal of Quantum Electronics 28 ,
2631 (1992).
[9] L.N. Zhao, Y. Yuan, X.J. Lv, C.D. Chen, X.P. Hu, G. Zhao, S.N. Zhu, Optics Communications
285, 4537 (2012).
[10] C.A. Brackett, IEEE Journal on Selected Areas in Communications 8, 948 (1990).
[11] S.J.B. Yoo, Journal of Lightwave Technology 14, 995 (1996).
[12] A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, B. Mukherjee, Journal
of Optical Networking 4 ,737 (2005).
[13] S. Hari Hara Subramani, K. Karthikeyan, A. Mirunalini, R. K. Prasath, S. Boomadevi and
K. Pandiyan, Journal of Optics (IOP), (article in press).
[14] D.Simeonov, S.Saltiel , Department of Quantum Electronics, Faculty of Physics, Sofia
University, Sofia 1126, 5 J.Bourchier Blvd
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APPENDIX A
Types of Phase Matching
(a) Type-I QPM SHG
Fig. A.1 shows the configuration of Type-I QPM SHG. Type-I interaction uses d31 or d32 in
LiNbO3 crystal. The polarization notation for the interaction is o  o e .
Second Harmonic
z
Output
x
Fundamental
Input
Fig. A.1 Schematic diagram of Type-I QPM SHG.
The wave vector mismatch for type-I QPM SHG is
 n2e
 kQI  k2e  2 ko  K m  2  
 2

2no


m
,
 
(1)
Where n2e is the extraordinary refractive index for the SH (wavelength 2 ), no is the
ordinary refractive index for the FW (wavelength  ), and m is the order number of QPM. From
the Sellmeier’s equations of LiNbO3 crystal, the QPM period (), was calculated versus FW
wavelength  for type-I QPM SHG as shown in Fig. A.2.
52
QPM Period (m)
29
28
27
26
25
24
Type-I QPM SHG
o
T = 20 C
o
T = 100 C
23
22
21
20
800
1000
1200
1400
1600
1800
2000
Fundamental Wavelength (nm)
Fig. A.2 The 1st order QPM periods for type-I QPM SHG.
(b) Type-0 QPM SHG
Fig. A.3 shows the configuration of type-0 QPM SHG. Type-0 interaction uses d33 in
LiNbO3 crystal. The polarization notation for the interaction is e  e e .
Second Harmonic
z
Output
x
Fundamental
Input
Fig. A.3 Schematic diagram of Type-0 QPM SHG.
53
The wave vector mismatch for type-0 QPM SHG is
k  k
0
Q
e
2
 n2e 2ne m 
 2 k  K m  2  

  .
 2   
e
(2)
From the Sellmeier’s equation for the extraordinary wave of LiNbO3 crystal, the QPM
periods for type-0 QPM SHG are shown in Fig. B.4. Here we chose the first order QPM of
m=1.
QPM Period (m)
30
25
20
15
Type-0 QPM SHG
o
T = 20 C
o
T = 100 C
10
5
0
800
1000
1200
1400
1600
1800
2000
Fundamental Wavelength (nm)
Fig. A.4 The 1st order QPM periods for type-0 QPM SHG.
54