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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.

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