Supplementary Information
Controllable orientation of single silver nanowire using two fiber probes
Xiaohao Xu, Chang Cheng, Hongbao Xin, Hongxiang Lei, and Baojun Li*
State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and
Engineering, Sun Yat-Sen University, Guangzhou 510275, China
*stslbj@outlook.com
1. Figures
Fig. S1. Silver nanowires synthesized via a polyol process. (a) SEM image of the silver
nanowires. (b) Diameter distribution of the silver nanowires. (c) Length distribution of the
silver nanowires.
Fig. S2. Scattering spectrum of a single silver nanowire measured by dark field illumination.
The spectrum exhibits peaks at about 400, 470, 620, and 730 nm. The inset shows the dark
field image of the silver nanowire used in the experiment. Scale bar is 2 μm.
1
Fig. S3. Simulated time-averaged intensity distribution of normalized electric field (|EA|2)
outputted from fiber probes FP1 and FP2. The refractive indices of the fiber probe and
surrounding (water) are set to be 1.45 and 1.33, respectively. (a) Simulated |EA|2 for FP1 in
x-y(z) plane. (b) Normalized |EA|2 along the optic axis for FP1. (c) Normalized |EA|2 at x = 2.5
μm for FP1. It shows the converged field with a full width at half maximum (FWHM) of 2.3
μm. (d) Simulated |EA|2 for FP2 in x-y(z) plane. (e) Normalized |EA|2 along the optic axis for
FP2. (f) Normalized |EA|2 at x = 2.5 μm for FP2. It shows the converged field with a FWHM
of 2.0 μm.
2
Fig. S4. An overview of geometric models used in the simulation. The insets I and II depict
details of FP1 and FP2, respectively.
Fig. S5. Simulated distribution of Poynting vector on the surface of silver nanowire with a
diameter of 600 nm and a length of 6.5 μm for s = 0 and θ = 0°, 45°, and −45° in x-y plane at z
= 0. The trends of the silver nanowire rotation was estimated from the distribution of the
radiation pressure, which is proportional to the Poynting vector: Fpres  <P> (Ref. 1). The red
arrows denote Poynting vector proportional to the magnitude. The dashed blue line labels the
middle transverse section of the nanowire. It can be seen, when θ  0°, the distribution of
Poynting vector is symmetric to the middle transverse section (labeled by blue dashed line),
indicating no rotation at this orientation (Fig. S5a). When θ  45°, the distribution is
asymmetric and a torque will be generated to rotate the nanowire clockwise (Fig. S5b). When
θ  −45°, the nanowire tends to rotate anticlockwise (Fig. S5c).
3
Fig. S6. Calculated optical torque M and rotational potential U as a functions of θ at s  −0.5
μm for ZnO nanowire with a diameter of 0.6 and a length of 6.5 μm. The nanowire is always
rotated towards θ = 75° where U reaches the minimum. Although the orientation with θ = 0°
and θ = 180° are equivalent states, the value of U at these two states are not equal with a
difference ∆U = 0.110−16 J. This is because the optical torque is nonconservative. Insets I
and II show the simulated time averaged energy density distribution around the nanowire with
θ  0° and 90°, respectively.
Fig. S7. Calculated trapping force F  iˆ   TM  n̂dA versus displacement ∆i (i = x, y, z)
near the equilibrium state for s  0 and θ  0°. The top panels describe the simulation model,
including a translucent nanowire showing the position of silver nanowire in Fig. 4a. The
bottom panels show the corresponding calculated forces. (a) The nanowire moves along the x
direction. (b) The nanowire moves along y direction. (c) The nanowire moves along z
direction.
4
Fig. S8. Simulated optical induced thermal effects for silver nanowire. (a) Equilibrium
temperature distribution in x-y plane. The inset shows a view in x-z plane. (b) Temperature T
versus x along middle section. Temperature is symmetric with respect to the nanowire,
because of the uniform distribution inside the wire. (c) Temperature gradient G (x component)
versus x. In calculation, the thermal conductivity of water and silver are set to κwater = 0.6
Wm−1K−1 and κmetal = 420 Wm−1K−1, respectively.
2. Table
FP1
FP2
Table S1. Geometric parameters of FP1 and FP2 for simulation.
Cone
parabolic body
Bottom radius (μm) Top radius (μm)
Parameters
Expression (μm)
3.0
2.1
a, b  (0,1)
x = 2.3b(a2-1)
y = 2.1a, z = 0
2.5
1.9
a, b  (0,1)
x = 3.3b(a2-1)
y = 1.9a, z = 0
3. Thermal effect
Heat spread much faster in silver than that in water for thermal conductivity κwater/κmetal << 1.
Therefore, temperature increment in silver nanowire can be regarded as uniform. The total
heat produced in silver nanowire by optical field P can be expressed as2
P 
2
ω
Imε  E dr ,
2π
(1)
where ω is the frequency of light, ε is the permittivity of silver, Im denotes the imaginary part,
E is the electric field. From the simulation results, the calculated P = 111 μW.
For silver nanowire, the temperature increment under steady-state can be expressed as2
ΔT 
P
,
4πReq βκ water
5
(2)
where Req is the radius of a sphere with the same volume as the nanowire, β is a dimensionless
thermal capacitance coefficient, κwater is the thermal conductivity of water (0.6 Wm−1K−1). Req
and β can be expressed as
Req = (3D2L/16)1/3
(3)
β = 1+0.96587ln2(L/D),
(4)
and
where L is the length of silver nanowire, D is the nanowire diameter. For a silver nanowire
with D = 600 nm and L = 6.5 μm, the calculated Req = 0.76 μm and β = 6.48316. According to
Eqs. (14), the calculated temperature increment ∆T  3 K. The fluctuation-dissipation
theorem of Einstein points out that the Brownian force is directly proportional to the
temperature of water3. For ∆T/T << 1, the increment of Brownian force arising from the
temperature increment in the work can be negligible.
References
1. Dienerowitz, M., Mazilu, M. & Dholakia K. Optical manipulation of nanoparticles: a
review. J. Nanophoton. 2, 021875 (2008).
2. Baffou, G., Quidant, R. & Abajo, F. J. G. Nanoscale control of optical heating in complex
plasmonic systems. ACS Nano 4, 709−716 (2010).
3. Okamoto, K. & Kawata, S. Radiation force exerted on subwavelength particles near a
nanoaperture. Phys. Rev. Lett. 83, 4534−4537 (1999).
6