Abstract—The plasmonic effectss of gold nanostructures can be

tuned from the visible to the near infrared region by controlling the

size (diameter) and structure (nanorod vs. nanoshell). In this paper, we

numerically compared the difference of optical properties on the

surfaces of a gold nanorod and a gold nanoshell by means of the finite

element method in a three dimensional model. Results show that

near-field optical images present spatially oscillatory pattern on the

surface of a gold nanorod and nodal fields penetrates the central part of

a gold nanoshell, and these features of images are attributable to

plasmon-mode wave-functions. We discuss these phenomena which

involve electric field nodes on the surface of a gold nanorod and a gold

nanoshell. These potential results can be used for the field-enhanced

spectroscopy and other relating applications in nanoscale.

Keywords—Finite element method, plasmon-mode, nanorod,

nanoshell

I. INTRODUCTION

OLD nanorod and gold nanoshells are spherical particles

with diameters typically ranging in size from 10 to 2000 nm.

They are known for their ability to support surface plasmon

resonance (SPR), making them strong scatterers and absorbers

of visible light with resonance peak wavelengths that are highly

sensitive to the nanoparticle size, shape, and local environment.

[1]. These properties coupled with advances in nanoparticle

technologies, have stimulated interest in the use of both

scientific and technological perspective [2-4]. Some

advantages of nanorods are reported in Ref. [2-4]. These

studies are not only for the fundamental interests, but also for

possible applications to sensor technology, to characterize

molecules on the interface between metals and dielectric media

[5], to extremely sensitive surface enhanced Raman scattering

(SERS) [6], to plasmonic devices [7], and so on.

Recently, non-diffraction limited transport of surface

plasmons (SPs) was in fact demonstrated [8] and there has been

continuing intensive interests in the properties of SPs in

laterally confined metal structures. A number of experimental

works are focus on these fields [9-15]. As the electromagnetic

observed enhancements of scatterers within nanoscale which

size of diameter less than 100 nm, the explanations of

experimentally observed enhancement factors in SERs as well

Yuan-Fong Chau is with the Chien Hsin University of Science and

Technology, Taoyuan county,32097,Taiwan, R.O.C. (corresponding author’s

phone: +886-920146302 ; e-mail:yfc01@uch.edu.tw).

Chan You Li, was with the Chien Hsin University and Technology, Taoyuan

county,32097,Taiwan, R.O.C.

as the spatial distribution of the electric field near the metal

nanorod and how plasmon modes plays roles in the mental

nanorod are still not fully understood. In the observation of our

recent experiment [the experimental setup as shown in Fig.

1(a)], we found that the electric field intensity distribution is

not uniform on the surface of the gold nanorod with an

illumination of parallel polarized fluorescent light on it.

Fig. 1 Simulation models of a gold nanorod with length of L=1.5μ

m and SCS vs. wavelengths. (a) Simulation model for y-polarization,

(b) Simulation model for x-polarization, (c) SCS vs. wavelengths for

y-polarization and (d) ) SCS vs. wavelengths for x-polarization,

respectively.

Motivated by these previous works cites here and inspired by

these interesting issues, in this paper, we investigate

numerically on the interaction and imaging between incident

wave and a gold nanorod and a gold nanoshell surrounded by

air by using finite element method (FEM). The optical

properties, such as variations of aspect ratio (D/L), polarization

directions, the optical scattering cross sections as well as the

local electromagnetic and induced charge densities at the

surfaces of a gold nanorod are discussed in detail. This analysis

reveals several intriguing features of light propagation in a gold

nanorod and a gold nanoshell. In particular subwavelength

resolution can be achieved with the gold nanorod and a gold

nanoshell when the localization of the light wave is within areas

whose sizes are less than a wavelength. Simulation results

reveal characteristic features of plasmon modes in

photoluminescence (PL) images, which can enable us to obtain

knowledge of electric field distributions around a gold nanorod

Comparison Analysis of Plasmonic Effects on a

Gold Nanorod and a Gold Nanoshell

Yuan-Fong Chau, and Chuan You Lee

G

International conference on Innovative Engineering Technologies (ICIET’2014) Dec. 28-29, 2014 Bangkok (Thailand)

http://dx.doi.org/10.15242/IIE.E1214062 115

and a gold nanoshell.

II. SIMULATION MODELS, RESULTS AND DISCUSSION

The structure under study are a gold nanorod and a gold

nanoshell with diameter D and length L surrounded by vacuum

(air=1) as shown in Figs. 1 (a) and (b). The rod diameter is

much shorter than the wavelength, while the length can be

longer than the wavelength. In our numerical simulation, we

use a three dimensional (3-D) calculation model which couples

the incident light into a gold nanorod and a gold nanoshell by

using the finite-element method (FEM) based on solving

Maxwell’s equations in the frequency domain [16] to calculate

the near field distribution and far field scattering cross section

(SCS). Throughout this paper, the gold permittivity data are

obtained from Johnson and Christy [17] and corrected by

Drude model, which is including size effect [18]. Here, two

different polarizations of incident light are considered, i.e., the

illumination are x-polarized (k along negative axis and electric

field E parallel to x axis, longitudinal mode) and y-polarized (k

along negative axis and E perpendicular to x axis, transverse

mode), respectively.

Fig. 2 The y-z cross sectional planes of the scattered near-field

amplitude |E| distribution for y-polarization (left side) and

x-polarization (right side) on the surface of a gold nanorod at SP

modes for different D (25, 50, 75 and 100 nm) while L is kept constant

(L=1500 nm).

To compare with the behavior of total SCS, an

electromagnetic wave was illuminated to a gold nanorod and a

gold nanoshell with length L = 1.5 μm and a varying diameter

D (25, 50, 75 and 100 nm, respectively). The far field SCS of

total face and reflection face as a function of wavelengths with

y-polarized [Fig. 1(c)] and x-polarized [Fig. 1(d)] incident light,

respectively, are shown in Fig. 1. As clearly seen in Fig. 1(c)

for y-polarization, the strong excitation of SPR peak occurs at

= 630 nm (red light region), and a second peak occurs at

=930 nm (infrared region). This indicates that the two

wavelengths could be used to excite the SPR for the

longitudinal mode. In addition, a local minimum peak of SCS is

at =496 nm, which can be assigned to the interband transition

(because the interband damping has less effect on the near-field

response). For the transverse mode case (x-polarization) as

shown in Fig. 1(d), only one SPR peak occurs at =521 nm, and

presents the same curve behavior of the total SCS and

backward SCS.

It is well-know that the physical mechanisms of

photoluminescence in a solid (for example, a gold nanorod) can

be attributed to the electron-hole pair excitation, relaxation of

the initially excited electron and hole to new energy states

occurs via a manifold of scattering processes in gold nanorod,

and emission radiated when the electron and hole recombine.

The incident light is scattered by the gold nanorod and couples

to the SP mode. This interaction is thus proportional to sfm,

where s is the SCS of gold nanorod and fm is the fraction of

scattered energy that couple to the SP mode. The guided mode

has a propagation length of L, and thus, the gold nanorod can

act as a channel for the energy transform by means of SP.

Finally, a fraction of this energy is scattered into air as fair. To

further understand the field pattern produced inside and on the

surface of the goldu nanorod, y-z cross sectional planes of the

scattered near-field amplitude |E| distribution at SP modes for

different D on the gold nanorod axis for longitudinal modes

(y-polarization), are displayed in the left side of Figs. 2. An

interesting result, some nodal fields, was found around the

surface of a gold nanorod. When L is kept constant L=1500 nm)

and D is increased from 25 nm to 100 nm [see Fig. 2], the nodal

field number and position will be changed for various SPR

wavelength of the incident light. In the observation of our

simulations, the zero-order mode, which does not have any

nodal field oscillation along the gold nanorod. This mode has

finite charge, which connected with infinitely long wavelength

oscillations, and cannot be excited by an external

electromagnetic wave. The first mode with physical meaning is

a dipolar mode, with a nodal field around the gold nanorod,

which piles up positive and negative charge at opposite ends of

the gold nanorod. This mode responds to a field polarized along

the y-axis and drives the response at longer wavelength.

Another mode can be identified by the number of nodal fields

around the gold nanorod. It is worthy to note that here only

even number of nodal field can be found on the surface of the

gold nanorod in our simulations. This result is much different

from those obtained by means of the boundary element method

(BEM) [19], which includes odd and even modes

simultaneously. The discrepancy between our 3D FEM

simulation model and Ref. [19] by BEM can be attributed to the

x-polarization incident field always piles up the positive and

negative charge pair along the propagation direction of the gold

nanorod and no net dipole in their charge distribution in our

simulation. Thus, only even number of nodal field can be found

on the surface of the gold nanorod. For even order modes, the

wavelengths decrease as additional longitudinal nodes (positive

and negative charge pair) are added. It can be seen in the left

side of Fig. 2 for fixing L=1500 nm cases, the numbers of nodal

fields around the gold nanorod for the longitudinal mode are

dependent on the aspect ratio (D/L), which corresponds to

different eigenmodes and frequencies (wavelengths). As the

aspect ratio (D/L) increases, the nodal field number increases as

D decreases. In order to understand the transverse modes (x-polarization)

of incident light acts on the gold nanorod, the right side of Fig.

International conference on Innovative Engineering Technologies (ICIET’2014) Dec. 28-29, 2014 Bangkok (Thailand)

http://dx.doi.org/10.15242/IIE.E1214062 116

2 shows the far-field SCS and reveals quite different results

from those of obtained from y-polarization, showing weaker

field intensity on the surface of a gold nanorod.

Fig. 3. Simulation models for gold nanoshell (with shell thickness t=10

nm) with length of L=1.5μm and SCS vs. wavelengths. (a) simulation

model for y-polarization, (b) simulation model for x-polarization, (c)

SCS vs. wavelengths for y-polarization and (d) SCS vs. wavelengths

for x-polarization, respectively.

Gold nanoshells are composed of a dielectric core (or hollow)

covered by a thin gold shell. As novel nanostructures, they

possess a remarkable set of physical, chemical and optical

properties, which make them ideal candidates for enhancing

cancer treatment, cancer detection, cellular imaging and

medical biosensing. As a direct result of nanoscale resonance

phenomena, gold nanoshells have very large optical absorption

and scattering cross - sections, which render them highly

suitable as contrast agents for imaging. They can be tuned to

preferentially absorb or scatter light at specific wavelengths in

the visible and near - infrared ( NIR ) regions of the spectrum.

Fig. 3 shows the simulation models for a gold nanoshell (with

shell thickness t=10 nm) with length of L=1.5μm and SCS vs.

wavelengths, where (a) simulation model for y-polarization, (b)

simulation model for x-polarization, (c) SCS vs. wavelengths

for y-polarization and (d) SCS vs. wavelengths for

x-polarization, respectively. These results are quite different

from those obtained from the gold nanorod. As clearly seen in

Fig. 3(c) for y-polarization, the strong excitation of SPR peak

occurs at = 630 nm (for D=50 nm), = 690 nm (for D=75 nm)

and = 790 nm (for D=100 nm), and the SCS is increased as the

value of D is increased. Tuning to the x-polarization case as

shown in Fig. 3(d), there is a dip of SCS value occurred around

= 790 nm and the value of SCS is increased as the wavelength

of incident light is increased.

The y-z cross sectional planes of the scattered near-field

amplitude |E| distribution for y-polarization (left side) and

x-polarization (right side) on the surface of a gold nanoshell

with thickness of t=10 nm at SP modes for different D (25, 50,

75 and 100 nm) while L is kept constant (L=1500 nm) are also

shown in Fig. 4. An intriguing result of the electric field pattern

penetrates the gold nanoshell can be found. As can be seen the

y-polarization case shown in Fig. 4(a), the electric field

distribution can be found on the surface and inside the gold

nanoshell, while the electric field distribution penetrates inside

the gold nanoshell and presents a node field pattern for the

x-polarization.

Fig. 4. The y-z cross sectional planes of the scattered near-field

amplitude |E| distribution for y-polarization (left side) and

x-polarization (right side) on the surface of a gold nanoshell with

thickness of t=10 nm at SP modes for different D (25, 50, 75 and 100

nm) while L is kept constant (L=1500 nm).

III. CONCLUSION

In conclusion, we have studied numerically the optical

response of a gold nanorod and a gold nanoshell by using FEM

to investigate their potential for the use of field-enhanced

spectroscopy. The response of the single Au nanorod is

sensitivity to the polarization of the incident light and rod

aspect ratio (D/L). Polarization parallel to the rod axis

(y-polarization) provides the maximum enhancement, whereas

polarization perpendicular to rod axis (x-polarization)

generates weaker near fields. The nodal field number on the

surface of a gold nanorod and a gold nanoshell can be carefully

controlled for the use of this kind of structure in field-enhanced

spectroscopy. The tunable plasmon resonant scattering of a

gold nanorod and a gold nanoshell provides an additional

“tools” for the coupling of light into and out of optical

waveguide structures. This property should lead to further

applications in optical waveguide structures, waveguide-base

photonic devices and other nano-photonic applications. The

phenomena of nano metal are still not understood very well.

Investigations are currently underway to explore further the

near-field of optical properties in coupled a gold nanorod and a

gold nanoshell by experiments and simulations analysis.

ACKNOWLEDGMENT

The authors acknowledge the financial support from the

National Science Council of the Republic of China (Taiwan)

under Contracts MOST 103-2112- M-231-001-.

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http://dx.doi.org/10.15242/IIE.E1214062 117

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