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OPTICAL PROPERTIES OF METALLIC NANOSTRUCTURES
Adam Wong Wei Ren
1, Wu Jiang
1, Koh Cheong Yang Henry
2, Li ShuZhou
3, Chen Chao
3
1Victoria Junior College, 20 Marine Vista, Singapore 449035
2DSO National Laboratories, 20 Science Park Drive Singapore 118230
3Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
ABSTRACT
The field regarding the optical properties of core shell structures remain new and
undeveloped. This project aims to provide a numerical analysis of two types of cylindrical
core shell structures – hollow gold shell structures and silver core gold shell structures1.
Using the Finite-Difference Time-Domain (FDTD) method, dimers of the aforementioned
structures was studied. The dimensions of the structures as well as the distance between the
dimers was varied to study how their optical properties changed. Results have shown that a
very sharp optical response was obtained when the dimers of silver cores with gold shells was
placed close together, at a distance of around 8nm and less. The optical properties of hollow
gold shell dimers when the distance between them changed was also surprising and unique,
showing a valley like pattern for the peaks of the absorption and extinction cross section.
INTRODUCTION
Noble metal nanostructures can show unique optical properties because of a phenomena
known as Surface Plasmon Resonance (SPR)1,2
. This occurs when the frequency of incident
light on the nanostructure matches the natural frequency of the electrons oscillating due to
charge interaction and electron damping, causing resonance3,4
.
Metal nanostructures can serve a wide range of practical applications. In the case of gold
nanostructures, the inert nature of gold enables it to be resistant to oxidation and corrosion
over time5. Through the study of how the geometry and configuration of metal nanoparticles
affects its ability to absorb and scatter light of certain wavelength range, many potential
applications can then be thought of5-7
.
One example is colouring. The traditional way of using dyes depend on using organic
compounds in the dye to give it a distinct colour. Overtime, as the compounds are exposed to
external stresses such as sunlight, the compounds may break down, causing the colour to
fade. By varying the size and shape of metal nanostructures, a similar colour to using organic
dyes can be obtained, but immune to fading issues. Furthermore, the synthesis of metal
nanostructures are thought to be more efficient and ecological as compared to the traditional
organic synthesis industry.
Another example is Raman detection8,9
, which is a way to detect explosives. When a metal
nanostructure is on its own, the frequency of light that causes resonance is fixed, giving it a
distinct colour. When brought close to an explosive, some of the molecules from the
explosive, such as TNT, can attach to the metal nanostructure, causing the resonance
frequency to change, as a result changing the colour of the metal nanostructure. These
changes in colour can be detected by electronics, or if in large quantities, by the human eye,
thus serving as an explosive detector10,11
.
The objective of this research is to investigate the absorption, scatter and extinction cross
section of gold nanostructures, in particular core shell structures, to expand human
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knowledge of this new and undeveloped field. Through computer simulations investigating
light interactions with such structures, it is hoped it will become clear how the absorption,
scatter and extinction cross section of these structures change as their dimension and
configuration change.
MATERIALS AND METHODS
Gold and Silver
The material used in all simulations is the refractive index of gold and silver by Johnson and
Christy. This set of experimental data by Johnson and Christy was chosen as it is a popular
experimental value set which is generally accepted as accurate. Figure 1 shows the real and
imaginary parts of the refractive index of gold and silver used by the software, Lumerical
FDTD solutions, and the experimental data12,13
.
Fig 1: Refractive index of gold and silver used by the software, Lumerical FDTD
solutions, and experimental values
Finite-Difference Time-Domain (FDTD) Method
The FDTD14
method was adopted for this research project. It uses a numerical analysis
technique to study how light interacts with matter. The software is based upon the time
dependent Maxwell’s equations, solving the electric field vector component within a small
cell in one instant, then solving the magnetic field vector component within the same cell in
the next instant, repeating the process until a desired end is acquired.
To test the reliability of the software, two methods were used. First, various simulations were
made to find the absorption, scatter and extinction cross section of gold nanospheres. The
results were then compared with results from the existing Mie Theory. It was found that the
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calculations from the software matches those from the Mie Theory closely (Annex A),
showing that the software is accurate.
Next, it is known that the absorption cross section and scatter cross section is directly
proportional to the volume of an object and the volume of an object squared respectively2,4,15
.
This is true when the object is very small compared to the wavelength of light used, so that
diffraction does not take place. When the curves of the absorption and scatter cross section
produced by the software was normalised, it was found that the curves became extremely
similar to one another (Annex B), thus showing that the calculations made by software is
accurate.
RESULTS AND DISCUSSION
Finding the Trend for the Absorption, Scatter and Extinction Cross Section
a. Gold Nanosphere
As the radius of a gold nanosphere increases, the peak wavelength of the absorption cross
section is blue shifted, while the peak wavelength of the scatter and extinction cross
section is red shifted. (Annex C)
b. Gold Nanorod (Light injection perpendicular to rod’s long axis)
As the length of the gold nanorod changed, there is no trend in the absorption, scatter and
extinction cross section. As the radius of the gold nanorod increases, there is a gradual red
shift in the peak wavelength of the absorption, scatter and extinction cross section.
(Annex D)
c. Gold Nanorod (Light injection parallel to rod’s long axis)
As the length of the gold nanorod changed, there is no trend in the absorption, scatter and
extinction cross section. As the radius of the gold nanorod increases, there is a gradual red
shift in the peak wavelength of the absorption, scatter and extinction cross section.
(Annex E)
d. Gold Nanorod Dimer (Light injection perpendicular to rod’s long axis)
As the distance between the two gold nanorod increases16,17
, there is a blue shift in both
peak wavelengths of the absorption, scatter and extinction cross section. The electric field
around the gold nanorod dimers was also studied to gain insights on the phenomena of
electric field enhancement18
. It was found that the enhancement of the electric field was
greater when the gap between the two gold nanorods is small, and the enhancement of the
electric field is also greater near corners and edges. (Annex F)
CORE SHELL STRUCTURES
The previous findings were a start for the numerical analysis of the optical properties of basic
metallic nanostructures. Today, the field concerning the optical properties of core shell
structures remains new and undeveloped. This project aims to bridge the gap of knowledge
and find out more about these structures. Core shell structures are structures containing a core
made up of a particular material surrounded by a shell made of another material. This project
focuses on core shell dimers, in particular hollow gold shells and gold shells surrounding a
silver core. Figure 2 shows an example of the simulations done.
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Fig 2: Example of the simulations done in FDTD. Left: hollow gold shells. Right: gold
shells surrounding a silver core
HOLLOW GOLD SHELLS
Effects of Changing the Inner Radius
Simulations were run with two hollow gold shells, each of length 200nm, separated by a
distance of 10nm. The outer radius of the shells were fixed at 50nm, while the inner radius
was varied to study how the inner radius affected its optical properties. As the inner radius
increased, there is a red shift in the peak wavelength of the absorption, scatter and extinction
cross section. However, this trend for the absorption cross section only held true for smaller
values of the inner radius. This means that as the shell grew thinner, the peak wavelength no
longer followed a simple trend. Figure 3 shows the results obtained from the simulations.
Fig 3: Graphs showing the absorption, scatter and extinction cross section of dimers of
hollow gold shells with varying inner radius
Effects of Changing the Gap Distance
Simulations were run with two hollow gold shells, each of length 200nm, inner radius 45nm
and outer radius 50nm. The distance between the two gold shells was varied to study how the
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separation between two gold shells affected their combined optical properties. As the distance
changed from 5nm to 25nm, the peak wavelengths for the absorption cross section appears to
follow a valley like pattern, with the lowest peak being at a distance of 23nm for the range
600nm – 660nm and a distance of 15nm for the range 660nm – 750nm. There was no obvious
trend for the scatter cross section and the extinction cross section showed similar trends as the
absorption cross section. Figure 4 shows the results from the simulations.
Fig 4: Graphs showing the absorption, scatter and extinction cross section of dimers of
hollow gold shells with varying gap distances
GOLD SHELL SURROUNDING A SILVER CORE
Effects of Changing the Core Radius
Fig 5: Graphs showing the absorption, scatter and extinction cross section of dimers of
gold shells surrounding silver cores of varying radius
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Simulations were run with two gold shells surrounding a silver core, each of length 200nm,
separated by a distance of 10nm. The outer radius was fixed at 50nm, while the radius of the
silver core was varied to study how this variation affected the optical properties of the core
shell structure. As the radius of the silver core increases, the peak wavelength of the
absorption cross section is blue shifted. For the scatter cross section, there were two peak
wavelengths, one within the 500nm – 600nm range and the other within the 600nm – 700nm
range. As the radius of the silver core increases, both peak wavelengths are blue shifted. The
extinction cross section showed similar trends as the scatter cross section. Figure 5 shows the
results from the simulations.
Effects of Changing the Gap Distance
Simulations were run with two gold shells surrounding a silver core, each of length 200nm,
with a core radius of 45nm and shell thickness of 5nm. The gap distance between the two
core shell structures was varied to study how the optical properties changed as the distance
between them changed. It was found that when the gap distance is small (about 4nm – 7nm),
there was a sharp peak in the absorption cross section. This peak was blue shifted as the gap
between the two structures increased, and eventually disappeared as the gap distance
continued to increase. For the scatter cross section, there were two peak wavelengths, and
both showed a blue shift trend as the gap distance increased. As the distance is increased
further, the two peaks became a single peak that is blue shifted as the gap distance increases.
The extinction cross section showed similar trends as the scatter cross section. Figure 6
shows the results from the simulation.
Fig 6: Graphs showing the absorption, scatter and extinction cross section of dimers of
gold shells surrounding silver cores with varying gap distances
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Based on the above result, it can be seen that the effects of changing the distance between the
two core shell structures are more significant that changing the geometry of the structure.
Hence, if there is a need to alter the optical properties significantly, one should consider
altering the distance between structures rather than it’s geometry, while if there is a need to
alter the optical properties slightly, the geometry should be changed. The sharp peaks
obtained in the dimers of the silver-gold structures can considered for application in the field
of raman detection, since the addition of extra explosive molecules to the metal nanostructure
might cause a more drastic change its optical properties, thus being easier to detect.
CONCLUSION
This paper covers the simulation of two types of core shell structures, hollow gold shells and
gold shells with a silver core, providing a numerical analysis to their optical properties. It was
found that changing the distance between dimers of the core shell structure resulted in a more
significant change in its absorption, scatter and extinction cross section as compared to
changing its core radius. In the case of the core shell structure with a gold shell and silver
core, the sharp spike in the absorption cross section proves to be interesting, and may open
doors for further research. Similarly, the valley-like trend in the absorption cross section for
hollow gold shell dimers can also be looked into further. Based on the simulation results and
analysis, opportunities to incorporate core shell nanostructures in practical applications have
been opened. In the future, the optical properties of other types of core shell structures can be
studied, along with other types of configurations, such as an array of core shell structures.
This way, a more complete understand of these structures can be obtained, and practical
applications based on other types of core shell structures can be made reality.
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ANNEXES
Annex A – Comparison of FDTD simulations of a gold nanosphere and the Mie Theory
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Annex B – Graphs showing the normalised curves for the absorption and scatter cross section
of gold nanospheres
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Annex C – Graphs showing the absorption, scatter and extinction cross section of gold
nanospheres
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Annex D – Graphs showing the absorption, scatter and extinction cross section of gold
nanorods with light injection perpendicular to the rod’s long axis
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Annex E – Graphs showing the absorption, scatter and extinction cross section of gold
nanorods with light injection parallel to the rod’s long axis
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Annex F – Graphs showing the absorption, scatter and extinction cross section of gold
nanorod dimers (length of 150nm, radius of 20nm) and the strength of the electric field near
the dimers.