Download Supplementary Information Manipulation and detection of single

Supplementary Information
Manipulation and detection of single nanoparticles and biomolecules
by a photonic nanojet
Yu-Chao Li1,2, Hong-Bao Xin1, Hong-Xiang Lei2, Lin-Lin Liu3, Yan-Ze Li4, Yao
Zhang1 & Bao-Jun Li1
1
Institute of Nanophotonics, Jinan University, Guangzhou 511443, China; 2State Key
Laboratory of Optoelectronic Materials and Technologies, School of Materials Science and
Engineering, Sun Yat-Sen University, Guangzhou 510275, China; 3State Key Laboratory of
Microbial Technology, School of Life Sciences, Shandong University, Jinan 250100, China
and 4National Engineering Research Centre for Beijing Biochip Technology, Beijing 102206,
China
Correspondence: Y Zhang, Email: [email protected]; BJ Li, Email: [email protected]
1. SEM images of the 3-μm PS and TiO2 microlenses
The SEM images confirmed that the 3-μm-diameter PS and TiO2 microlenses were in
spherical shapes with smooth surfaces, which benefits in generating the photonic
nanojets.
Figure S1 | SEM images of the dielectric microlenses. (a) 3-μm PS
microlenses. (b) A single 3-μm TiO2 microlens.
2. The full width at half maximum (FWHM) as a function of the input laser
wavelength
The FWHM of the photonic nanojets as a function of the input laser wavelength can
be obtained by a series of three dimensional simulations with a finite-element method
(COMSOL Multiphysics 4.4). The results indicate that the FWHM of the photonic
nanojets increases with the wavelength of the input laser beam (Fig. S2). For the 808
nm laser used in our experiments, the FWHMs were 389 and 208 nm for the PS and
TiO2 microlenses, respectively, while for the commonly used laser wavelength (1064
nm) for optical trapping, the FWHM were 520 and 292 nm of the PS and TiO2
microlens, respectively. The FWHM of the photonic nanojets at 808 nm was ~1.4
times smaller than that at 1,064 nm.
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Figure S2 | FWHM of photonic nanojets generated by the 3-μm PS
and TiO2 microlenses as a function of the input laser wavelength.
3. Simulations and calculations
The simulations for the trapping strength analysis were performed by a three
dimensional finite-element method (COMSOL Multiphysics 4.4) with perfectly
matched layer boundary conditions. The light source for exciting the optical fibre
probe was set as a Gaussian beam at a wavelength of 808 nm. The mesh sizes of the
regions of the fibre probe, microlens, water, and nanoparticle were set as 200, 80, 150,
and 5 nm, respectively. The simulations for the signal enhancement analysis were
performed by a three dimensional finite-difference time-domain method (Optiwave
Systems Inc., OptiFDTD 4.0) with perfectly matched layer boundary conditions. The
mesh sizes of the regions of fibre probe, microlens, water, and point source were set
as 210, 80, 160, and 15 nm, respectively. The refractive indices of the fibre probe, PS
microlens, TiO2 microlens, PS nanoparticle, and water were set as 1.44, 1.58, 1.99,
1.58, and 1.33, respectively.
4. Experimental set-up details
The experimental set up was schematically shown in Fig. S3. An optical microscope
(Union, HISOMET II-DH II) with a 100× objective (numerical aperture: 0.73) was
used for observation of the manipulation process. A computer-connected charge
coupled device (CCD, Sony iCY-SHOT, DXC-S500) camera was used for capturing
images and recording videos. The total magnification in the field of view is 1000×.
Fibres 1 and 2 were fixed by tunable six-axis microstages (SAM, Kohzu Precision Co.,
Ltd., resolution: 50 nm) in the opposite directions. The two tips of the fibres were
introduced into a microfluidic chamber which contained the solution and was placed
on a two-dimensional translation stage (resolution: 50 nm). Fibre 1 was connected to
the stem of a 1:9 fibre coupler. The 808 nm laser beam was connected to the 10% arm
of the coupler, while the 90% arm was connected with a photodetector or an optical
fibre spectrometer with a bandpass filter (for the photodetector: 790-1200 nm; for the
optical fibre spectrometer: 500-790 nm). The photodetector was used for monitoring
the reflected 808 nm signals while the spectrometer was used for measuring the
2
fluorescent spectrum of the fluorescent PS nanoparticle (with a 639 nm emission).
Fibre 2 was coupled with a 398 or 532 nm laser to excite the fluorescent nanoparticles
or illuminate the DNA molecules in the dark-field, respectively.
Figure S3 | Schematic of the experimental set-up. The red, purple and
green arrows indicate the propagation of the trapping light (808 nm),
detected signals (backscattering: 808 nm; fluorescent: 639 nm) and
exciting/illuminating light (398/532 nm), respectively.
5. Distances between the trapped nano-object and the microlens
In the trapping process, the distances between the trapped nanoparticle/DNA and
microlens, defined as D1 and D2 (or D3) in Fig. S4a,b, exhibited fluctuations due to
their Brownian motion in the solution. The origin of D1 and D2 (or D3) was defined as
the tangent point of the microlens and a black dashed line, as indicated in Fig. S4a,b.
Figure S4c shows the distance D1 between a trapped 85-nm nanoparticle and the
microlens with an optical power P1 of 3.2 mW as a function of time t1. The distance
D1 was above the critical distance Dr1 which was defined as the distance when the
nanoparticle touched the microlens, indicating that the nanoparticle did not touch the
microlens. By statistically analyzing the distances D1, the histogram of distance
distribution was obtained and presents a Gaussian distribution (Fig. S4d). The central
distance Dc1 of the Gaussian distribution, which denotes the distance between the
position of the trapped nanoparticle with the minimum potential (i.e., the focus of the
photonic nanojet) and the microlens, was calculated as ~480 nm. This Gaussian
distribution indicates that the nanoparticle was trapped in a harmonic potential well.
For this situation, the trapping stiffness κtrap can be obtained from the variance <x2> of
the Gaussian distribution. To get <x2>, a Gaussian fit was obtained in Fig. S4d. The
value of <x2> was 8.9 × 103 nm2. Then, κtrap can be calculated using the equipartition
theorem:1
1
1
k BT   trap x 2
2
2
,
(1)
where kB is Boltzmann’s constant and T is absolute temperature of the medium. The
calculated value of κtrap for the nanoparticle was 0.14 pN nm−1 W−1.
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For the trapping of the plasmid DNA with an optical power of 5 mW, the
Brownian motion of the plasmid DNA was stronger than that of the nanoparticle,
which caused a larger distance fluctuation (Fig. S4e). Thus the trapped plasmid DNA
touched the microlens at t2 = 4.1, 5.8, 10.8, and 16.1 s (marked by blue circles with
numbers 1−4 in Fig. S4e). The central distance Dc2 was also obtained as ~480 nm
from the histogram of distance D2 distribution (Fig. S4f). By increasing the optical
power to 7 mW, the Brownian motion of the plasmid DNA was efficiently suppressed
due to the stronger optical forces so that the trapped plasmid DNA did not touch the
microlens (Fig. S4g) and has a central distance Dc3 of ~480 nm (Fig. S4h).
Figure S4 | Distances between the trapped nano-object and the
microlens. (a) Schematic of the distance D1 between a nanoparticle and
the microlens. (b) Schematic of the distance D2 (or D3) between a
plasmid DNA and the microlens. (c) Distance D1 between an 85-nm
nanoparticle and the microlens in the trapping process with an optical
power P1 of 3.2 mW as a function of time t1. (d) Histogram of D1
distribution with a Gaussian fit. (e) Distance D2 between a plasmid DNA
and microlens in the trapping process with an optical power P2 of 5 mW
as a function of time t2. (f) Histogram of D2 distribution with a Gaussian
fit. (g) Distance D3 between a plasmid DNA and microlens in the
trapping process with an optical power P2 of 7 mW as a function of time
t3. (h) Histogram of D3 distribution with a Gaussian fit.
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6. Frequency-domain analysis of the trapping stiffness
To obtain the value of the trapping stiffness κtrap in our system, the power spectral
density was fitted to the Lorentzian model2,3 with the following form:
P( f ) 
k BT
  ( f 2  f c2 )
2
(2)
where P(f) is the power spectral density, kB is the Boltzmann’s constant, T is the
absolute temperature of the medium, fc is the corner frequency, and β is the Stokes
drag on a particle. The fitted result shows that the measured corner frequency is fc =
89.5 Hz. β can be expressed as:
β = 6πηr
(3)
−4
where η = 9.2 × 10 Pa s is the viscosity of the medium at room temperature and r the
radius of the particle. The trapping stiffness κtrap was then calculated by:
(4)
 trap  2 f c
In our experiment, the optical power was set as 3.2 mW. Accordingly, the calculated
κtrap was 0.13 pN nm−1 W−1.
7. Trapping of a plasmid DNA using a single fibre for both illuminating and
trapping.
By launching the 808 (for trapping) and 473 nm (for illuminating) laser beams with
optical powers of 7 mW and 10 μW into a single fibre probe (Fig. S5a), respectively,
the plasmid DNA was stably trapped by the photonic nanojet and illuminated in the
dark field, as shown in Fig. S5b. The trapped DNA was eventually released due to the
increased Brownian motion and the fluctuations of the environment (Fig. S5c).
Figure S5 | Optical trapping
of a plasmid DNA using a
single
fibre
for
both
illuminating and trapping.
Dark-field images (a) before
trapping, (b) during trapping
and (c) in the release of a
single plasmid DNA.
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8. Characteristics, optical forces and potentials of the photonic nanojets with
different illuminating conditions
To demonstrate the effects on the characteristics, optical forces and potentials of the
photonic nanojets with different illuminating conditions, simulations and calculations
were performed for the photonic nanojets generated by the TiO2 microlenses as an
example. Figure S6a−c shows the simulated electric (E) field intensity distributions of
the TiO2 microlenses illuminated by a plane wave without fibre (Fig. S6a) and
Gaussian beams with an aligned fibre (Fig. S6b) and a misaligned fibre (Fig. S6c). In
the simulations, the misalignment between the optical axis of the fibre and the
microlens was set as 250 nm, which was the maximal misalignment in the
experiments. Because the presence of the microlenses, the outputted laser beams were
highly focused and formed into photonic nanojets with different characteristics. Line
scans were performed through the focal planes of the photonic nanojets in the y
direction. The results show that the FWHM of the photonic nanojets generated by the
microlenses without fibre, with the misaligned fibre and aligned fibre were 298, 235,
and 208 nm, respectively, and the corresponding peaks of the intensity were 0.35,
0.46, and 0.51, respectively (Fig. S6d). The optical forces and potential profiles were
obtained for an 85-nm nanoparticle positioned in the photonic nanojets in the x and y
directions (Fig. S6e−h). The trapping stiffness was estimated from the optical force
profiles (Fig. S6e,g) as 0.02, 0.05, and 0.06 pN nm−1 W−1 in the x direction, while it
was 0.11, 0.23, and 0.29 pN nm−1 W−1 in the y direction for the nanoparticle trapped
by the microlenses without the fibre, with the misaligned fibre and aligned fibre,
respectively. The corresponding potential differences ∆Ux1, ∆Ux2 and ∆Ux3 between
the maximal and minimal points were 1.8, 2.2, and 2.4 × 105 kBT/W in the x direction
(Fig. S6f), while ∆Uy1, ∆Uy2 and ∆Uy3 were 4.0, 4.6, and 5.0 × 105 kBT/W in the y
direction (Fig. S6h), respectively.
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Figure S6 | Simulated characteristics, optical forces and potentials of
the photonic nanojets generated by different illuminating conditions.
(a−c) E field distributions of the microlenses illuminated by (a) a plane
wave without fibre, and Gaussian beams with (b) aligned fibre and (c)
misaligned fibre. The red solid lines and arrows indicated the inputted
ports and 808-nm laser beams with an optical power of 1 W, respectively.
(d) E field intensity at the focal planes of the outputted light in the y
direction. (e) Optical force and (f) potential profiles of the nanoparticle as
a function of the distance X between the nanoparticle and the focus in the
x direction. (g) Optical force and (h) potential profiles of the nanoparticle
as a function of the distance Y between the nanoparticle and the focus in
the y direction.
9. Simulation and calculation of backscattering enhancement inside the
photonic nanojet.
The simulation and calculation of the backscattering enhancement factor was
performed with a finite-element method by COMSOL Multiphysics. As shown in Fig.
S7a, the E field intensity (I0) of the incident 808-nm laser and the reflected light of the
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fibre probe was obtained in the detected plane (indicated as yellow line). After an
isolated 85 nm nanoparticle was added in the focus of the outputted light (Fig. S7b),
the E field intensity in the detected plane was denoted as Iμ, which consists of the I0
and the backscattering signal intensity of the nanoparticle. Therefore, the
backscattering signal intensity (ΔI1) of the isolated nanoparticle can be expressed as
the difference of the Iμ and I0,
ΔI1 = Iμ – I0,
(5)
Then, a microlens was placed at the extreme of the fibre probe to generate a photonic
nanojet, as shown in Fig. S7c, and the E field intensity in the detected plane was
calculated as Iν. When a nanoparticle was introduced in the focus of the photonic
nanojet (Fig. S7d), the total intensity was calculated as Iμ+ν. Thus, the backscattering
signal intensity (ΔI2) of the nanoparticle inside the photonic nanojet can be expressed
as
ΔI2 = Iμ+ν – Iν,
(6)
Therefore, the enhancement factor (EF), which was defined as the ratio of the
backscattering signal intensity of the nanoparticle inside the photonic nanojet to that
of the isolated nanoparticle, can be expressed as
EF = ΔI2/ΔI1.
(7)
As a result, the calculated enhancement factors for the 85 nm nanoparticle were 1.5
and 5.3 × 103 inside the photonic nanojets generated by PS and TiO2 microlenses,
respectively.
Figure S7 | Simulation and calculation of the backscattering
enhancement factor of the photonic nanojet for a nanoparticle. (a) E
field intensity distribution of the bare fibre probe with the absence of
nanoparticle and microlens. (b) E field intensity distribution of the bare
fibre probe with an isolated 85 nm nanoparticle positioned in the focus of
the outputted light. (c) E field intensity distribution of a microlens placed
at the extreme of the fibre probe. (d) E field intensity distribution of an
85 nm nanoparticle positioned in the focus of the photonic nanojet.
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