Enhancement of Second-Harmonic Generation through Plasmon
Resonances in Silver Nanorods
Nicholas Wang1, Patrick McAvoy2, Isaak Mayergoyz2, Oded Rabin1,3
1. Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742
2. Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742
3. Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742
Abstract
Results
Goal
Determine cylinder geometries suitable for the enhancement of
second-harmonic generation
No Smoothing
2λ2
2λ2
λ1
λ2
λ1
Bevel Smoothing
3-D view
λ2
2-D view
 Aspect Ratio = cylinder length:diameter
 The above plots show the calculated values of resonance wavelength for the 1st
axial mode, 2nd axial mode, and twice the 2nd axial mode vs. cylinder aspect
ratio for a solid nanorod (left) and a nanotube (right).
 We observe that the criteria for enhanced second-harmonic generation
(λ1/λ2 = 2) is met for cylinder aspect ratio value of 8 for solid rods and 7 for
tubes.
Plasmonic Spectra for Cylinders with Concentric Holes
λ1/ λ2
ε* and λ
of plasmon
resonances
Eigenvalue
algorithm in
MATLAB®
Charge distribution
 The above plots show the shift in wavelength due to edge
rounding for cylinders of aspect ratio 1 (left) and 9 (right). Edge
rounding affects small aspect ratio structures more prominently.
In these structures, evanescent electric fields are more
concentrated along the edges.
λ1/ λ2
Blender® model
Methods
We studied the effects of cylinder edge rounding on the resonance
wavelength for the 1st and 2nd axial dipole plasmon modes.
Δλ
We report a theoretical study of enhanced second-harmonic generation
through the calculation of plasmon resonances for 3-D nano-objects
with cylindrical symmetry. Our algorithms calculate the resonant
wavelengths characteristic to silver nanostructures in vacuum. Focusing
on axial dipole plasmon modes, the criteria for enhanced secondharmonic generation are met when the wavelength of the first
resonance mode is twice that of the second resonance mode.
Enhanced second-harmonic generation is predicted in nanorods of
aspect ratios of 7, 8, and 9 with varying concentric hole depths and
various degrees of edge rounding. The enhancement is most effective
when the excitation is at 980 nm.
Plasmonic Spectra for Cylinders – Varying Aspect Ratio (AR)
Δλ
Second-Harmonic Generation (SHG) is an optical process in which
incident radiation interacts with a nonlinear medium, producing
photons with twice the energy. SHG can be useful for PV and IR
imaging. Enhanced SHG may be achieved by coupling the radiation to
surface plasmons in metallic nano-objects.
Effects of Cylinder Edge Rounding
Conclusions
1st mode
 For cylinders of aspect ratio 7, 8, and 9 with varying concentric
hole depths, we observe ratios of λ1stmode/λ2ndmode close to 2,
which meet the criteria of enhancement of second-harmonic
generation.
2nd mode
1. Create cylinder model using Blender® 3-D software and export
mesh coordinates
2. Run eigenvalue algorithms (MATLAB®) to identify the axial dipole
plasmon resonances of the input geometry using the metal
dielectric function. The outputs for each resonance mode are: ε* –
resonance permittivity, λ – resonance wavelength, and a surface
charge density distribution.
3. Reiterate the process with a new cylinder geometry until
λ1stmode/ λ2ndmode = 2.
 Hole depth is defined to be the length of a concentric hole introduced both
in the top and bottom faces of the cylinder, as seen in the wire view above.
The unit (hole depth*2)/cylinder length is used for normalization among
different AR cylinders.
 Above is a plot of the ratio of resonance wavelengths of the
and
modes for cylinders of various aspect ratios vs. concentric hole depth. The
values vary monotonically with aspect ratio but not with hole depth.
1st
2nd
 The criteria of enhanced second-harmonic generation can be met only by
cylinders of aspect ratio 7 ≤ AR ≤ 9.
 The effects of rounding are negligible at high aspect ratios.
Future Work
 Calculate the electric field around the cylinders for the 1st and 2nd
axial dipole modes at resonance to determine the extent of
electric field overlap between the two modes.
 Calculate plasmon resonances for Au nanorods