Simulation Effects on the Optical Response of Gold Nanoparticles

Tanaporn Leelawattananon

and Suphamit Chittayasothorn

Department of Physics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Department of Computer Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang,

Bangkok, Thailand

Keywords: Localized Surface Plasmon Resonances, Gold Nanoparticles, Optical Properties, Finite Element Method.

Abstract: In this research work, we use simulation models for the investigation of the sizes and shapes of gold

nanoparticles on BK-7 substrate base, which affect the optical characteristics in a large spectral range of the

gold nanoparticles. Linearly polarized light with wavelengths of 300 – 800 nm are specified as the impact

light on gold nanostructures. We try to find the suitable wavelength of the impact light when localized

surface plasmon resonance takes place. The gold nanoparticles are spherical, elliptical oval, and 10nm x 40

nm block-shape and have their aspect ratio similar to the nanorod shape nanoparticles used in other

experiments. The results are useful for the development of plasmonic complex nanostructure with tunable

surface plasmon resonances which generate heat and have potential applications in medical thermal

therapy.

1 INTRODUCTION

According to technological advancement, metals

which have structures at the nanometer level can be

manufactured. This advancement attracts attention

of physicists, chemists, material scientists, and

biologists which are interested in the surface

plasmon phenomenon. Surface Plasmon Resonance

(SPR) is the phenomenon which takes place when

there are excitations of free electrons at the interface

between an electrical conductor and a dielectric

layer thus create evanescent electromagnetic waves.

The excitation of Surface Plasmon waves leads to

the occurrence of other phenomena, including the

optical responses of materials. Plasmonics in the

material structures at the nanometer level find

applications in the surface-enhanced sensing and the

measuring of intra molecular distances in molecules.

The optical response of metallic nanoparticles

(NPs) can be adjusted by the controlling of the size

and shape of the particles and also the environment.

This knowledge initiates research areas such as

Surface Plasmon based Photonics or Plasmonics (G.

Alexandre Brolo, 2012). There have also been new

techniques in the synthesis of nano particles which

aim at the creation of nanoparticles, which have

adequate size and shape for excitation of the Surface

Plasmon waves (Z. Ying et.al., 2018). These surface

plasmon waves can be employed in magneto-optic

applications. They also help improve the efficiency

of surface-enhanced sensing and spectroscopy,

which find applications in bio detection and

chemical therapy (Z. Zhang et.al., 2014).

It has been recently found that the shape of the

nanoparticles affects the optical response of the

particles. Researches have been conducted to study

optical characteristics of nanoparticles and to find

out the effects of sizes and shapes of these

nanoparticles. Shapes include spherical, cube, and

other polyhedrons (Y. Wang et. Al., 2013) ( M.

Chen et.al., 2017). The more nanoparticle becomes

sphere-like, the more the main surface plasmon

resonance is red-shifted where the dependence of the

position of the resonances is analytically explained

in terms of their aspect ratio (Cecilia Noguez,

2007). The development of plasmonic complex

nanostructure with tunable surface plasmon

resonances results in a higher heat generation which

finds applications in medical thermal therapy (H.

Vahid et.al., 2018) (K. Jiang et.al., 2013).

In this project, we simulate the Surface Plasmon

Resonance phenomenon of gold nanoparticles which

have different shapes and sizes and have been

employed to align 1D structures. The finite element

method (FEM) is used in the analysis and

simulations. The simulation results show plasmon

wave electric fields when using these gold

360

Leelawattananon, T. and Chittayasothorn, S.

Simulation Effects on the Optical Response of Gold Nanoparticles.

DOI: 10.5220/0007959603600367

In Proceedings of the 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2019), pages 360-367

ISBN: 978-989-758-381-0

nanoparticles which are excited by the visible light

sorce. The goal of the project is to find suitable sizes

and shapes of gold nanoparticles for plasmonics

which can be applied in medical thermal therapy

including the killing of cancer cells. There has been

successful experiments in using such thermal

therapy using heats from the localized surface

plasmon resonances (LSPR) of gold nano particles

(Z. Qin et al., 2016). The simulation results will

also lead to the development of plasmonics complex

nanostructures with tunable surface plasmon

resonances and to compare heating between

increasing complex plasmonic nanostructures.

2 THEORY AND PRINCIPLES

2.1 Surface Plasmon Resonance (SPR)

Phenomenon

Surface plasmon waves take place at the surface of

the metal. The highest amplitude of the electric field

which is called the evanescent field is at the

interface between the metal surface and the

dielectric layer. The amplitude drops exponentially

when the distance from the metal surface increases.

The excitation of the SP waves is typically done

by using the Kretchmann configuration (T.A.

Leskova et. Al., 2000) which uses light from a light

source to impact a prism and the metal thin film on

the prism surface. The reflected light from the prism

is then detected and measured using a light detector.

Metal thin films which have the suitable

characteristics for the excitement of the SP waves

are noble metals such as gold, silver, and copper.

The typical thickness of the metal layer is 50

nanometers.

The evanescent field of the reflected light at the

dielectric-metal interface penetrates into the metal.

With the appropriate thickness of the metal layer, the

evanescent wave reaches the metal-dielectric

interface (or metal-air interface). In the case that the

phase of the incoming light matches the phase of the

surface plasmon waves, the surface plasmon

resonance is generated and surface plasmon waves

propagate along this metal-dielectric interface. They

are generated according to a certain condition which

depends on the incident angle and the incident

wavelength: (H. Bateman, 1915)



















(1)

is the wave vector of surface plasmon waves

is the wave vector of the incoming light

is the refractive index of the prism

θ is the resonance angle

According to the equation, the energy and

momentum of the incoming light which impact the

prism is transferred to the electrons group of the

metal thus excite surface plasma wave. The

dispersion relation of surface plasmon wave is

shown in the following equation: (H. Bateman,

1915)





























 



(2)

is the relative permittivity of the metal

is the relative permittivity of the dielectric

layer

The necessary condition for the surface plasmon

resonance to take place is the wave vector (k

) of

the incoming light must be the same as the wave

vector of the surface plasmon waves (k

). Surface

plasmon waves propagate along the metal-dielectric

interface as shown in Fig. 1a.

Figure 1a: Surface plasmon resonance at the interface

between the metal thin film layer and dielectric layer.

From Fig. 1b, when light impacts structure at the

nano level of the metal, electrons are excited to the

conduction band and oscillate with the impact light

thus creates plasmon polaritron which can be

transferred at the interface between metal and

dielectric layers. This phenomenon takes place at the

external shell of the metallic nanoparticle since the

external light cannot penetrate into the nanoparticle.

This phenomenon is therefore called the localized

surface plasmon resonance (LSPR ) phenomenon.

The impact light on the surface of the particle

has two kinds of interactions: absorption, and

scattering. The strong optical absorption and

scattering of noble metal nanoparticles is due to an

effect called localized surface plasmon resonance,

which enables the development of novel biomedical

applications. When plasmon resonance takes place,

the absorbed light generates enough heat which can

kill cancer cells. This phenomenon also find

Simulation Effects on the Optical Response of Gold Nanoparticles

361

applications in biosensing (R. M. Cabral et.al., 2014)

(X. Cao et.al., 2011).

Figure 1b: The excitation of localized surface plasmon

resonance of spherical nanoparticles.

2.2 Localized Surface Plasmon

Resonance (LSPR)

We can use the result of the Mie theory to explain

the scattering and absorption of impact light on

spherical particles (G. Mie, 1908). The extinction

cross section (σ

ext

) can be obtained from the

summation of the absorption cross section (σ

abs

) and

the scattering cross section (σ

sca

) of metal

nanoparticles: (σ

ext

= σ

abs

+ σ

sca

)

For very small particles, (d << λ) the Mie

equation for explaining σ

ext

for spherical

nanoparticles is:

























































(3)

where V

= (4π/3) R

ω is angular frequency

is dielectric function of metal nanoparticles

is real value of dielectric functions of metal

nanoparticle.

is imaginary value of dielectric functions of

metal nanoparticle.

From equation (3) the absorption of plasmon

takes place when ε

(ω) ≈ -2ε

and from the detection

of LSPR signals, it has been found that the shape of

the nanoparticles influences the LSPR signals. These

nanoparticals have several possible shapes such as

nanospheres, nanodiscs, nanopyramids, and

nanorods.

3 THE SIMULATED

EXPERIMENTS

In this research project we simulate the optical

excitation of the localized surface plasmon

resonance (LSPR). We specify that linearly

polarized light impacts on metal nanoparticles and

substrate base. The nanoparticles are gold in

spherical, block, and oval shapes. For each shape,

the size, height, width, and distance between

particles are varied. The substrate base is BK7 Cover

glass. Both the gold nanoparticles and the substrate

base are contained in a spherical PML surface as

shown in Fig. 2.

Figure 2: The simulation model of gold nanoparticles and

BK-7 substrate in the internal PML surface.

Fig 3 is a simulation model of the optical

excitation. The gold nano particles are in block

shape with the size 10x40 nm. The distance between

adjacent particles is 10 nm. The impact light is

specified to be the linearly polarized plane wave and

the light impact angle is π/4 rad. The finite element

method (FEM) is used to analyze the resultant

electric field at the interface between the gold

nanoparticles and dielectric (air) layer. Parameters

used in the simulation are shown in Table 1.

Figure 3: The simulation model of the optical excitation of

10x40 nm block-shape gold nanoparticles.

We change the wavelength of the impact light

from 300 nm to 800 nm by 50 nm increment to

observe the wavelengths which are suitable for the

excitation of the localized surface resonance waves.

The light source is the linearly polarized plane wave

and the gold nanoparticles are as shown in Fig. 4.

SIMULTECH 2019 - 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

362

Table 1: Parameters used in the simulation.

Parameter name

Value

Refractive index of Air

Refractive index of

substrate BK-7

1.5151

Relative permitivity of gold

nanoparticle ( real part)

-4.6810

Relative permitivity of gold

nanoparticle ( imaginary part)

2.4266

r_pml

11*radius

t_pml

3*radius

radius

20 nm

Figure 4a: Sphere shape.

Figure 4b: Rectangular shape. Figure 4c: Ellipsoid shape.

Electromagnetic wave propagation as explained

by Maxwell’s wave equation in the frequency

domain is as follows:

 









  



 



















(4)

where 



is the relative permittivity of material

E is the

electric field equation





is the

wave vector in free space

This is an equation in differential form for the

analysis of the size of electric field at the interface

between gold nanoparticles and air dielectric. We

also specify the scattering boundary condition so

that the scattering of the light is within the PML

surface only. We partition subdomain in triangular

mesh elements with extrafine details.

4 SIMULATION RESULTS

In the first simulation experiment using the finite

element method (FEM), we use linearly polarized

incident light which has wavelength range from 300

to 800 nm and increment by 50 nm impact on

spherical gold nanoparticles with BK-7 substrate

base. The results surface plasmon resonance at the

interface between the nanoparticles and air dielectric

differ when the size of the nanoparticles varies.

When the size of the spherical gold nano particle

is 10 nm, the electric field at the interface between

the gold nanoparticles layer and the air has

maximum amplitude is equal to 4.6x10

V/m when

the wavelength is 550 nm as shown in Fig. 5. The

graph which shows relationships between the

wavelength of the impact light and the electric field

at the interface is shown in Fig. 6.

Figure 5: Electric field at the interface between 10 nm

spherical gold nanoparticles and air dielectric.

Figure 6: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between 10 nm gold nanoparticles and ir

dielectric.

When the size of the spherical gold nano particle

is 20 nm, the electric field at the interface between

the gold nanoparticles layer and the air has

maximum amplitude equal to 4.4x10

V/m when

the wavelength is 550 nm as shown in Fig. 7. The

graph which shows the relationships between the

wavelength of the impact light and the electric field

at the interface is shown in Fig. 8.

Simulation Effects on the Optical Response of Gold Nanoparticles

363

Figure 7: Electric field at the interface between 20 nm

spherical gold nanoparticles and air dielectric.

Figure 8: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between 20 nm gold nanoparticles and air

dielectric.

When the size of the spherical gold nano particle

is 30 nm, the electric field at the interface between

the gold nanoparticles layer and the air has

maximum amplitude equal to 6.3x10

V/m when

the wavelength is 550 nm as shown in Fig. 9. The

graph which shows relationships between the

wavelength of the impact light and the electric field

at the interface is shown in Fig. 10.

From the results of the first set of simulation

experiments, when the nanoparticles have spherical

shape, it has been noticed that the localized surface

plasmon resonance (LSPR) phenomenon takes place

with highest electric field magnitude when the

impact wavelength is 550 nm, for all the size of the

gold nanoparticles tested. These results correspond

with the results of the physical experiments. (Z. Qin

et al., 2016)

The second set of simulation experiments are

then conducted using the same light source with the

wavelength range from 300 nm to 800 nm,

increment by 50 nm on oval-shape gold

nanoparticles with the aspect ratio (b/a) >1. The a

axis is 10 nm and the b axis is 40 nm, the localized

Figure 9: Electric field at the interface between 30 nm

spherical gold nanoparticles and air dielectric.

Figure 10: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between 30 nm gold nanoparticles and air

dielectric.

surface plasmon resonance electric field at the

interface between the gold nanoparticles layer and

the air has maximum amplitude is equal to 8.5x10

V/m when the wavelength is 650 nm as shown in

Fig. 11. The graph which shows the relationships

between the wavelength of the impact light and the

electric field at the interface is shown in Fig. 12.

The third set of simulation experiments are then

conducted using the same light source with the

wavelength range from 300 nm to 800 nm,

increment by 50 nm on 10 nm x 40 nm block-shape

gold nanoparticles. The localized surface plasmon

resonance electric field at the interface between the

gold nanoparticles layer and the air has maximum

amplitude is equal to 1.8x10

V/m when the

wavelength is 700 nm as shown in Fig. 13. The

graph which shows the relationships between the

wavelength of the impact light and the electric field

at the interface is shown in Fig. 14.

SIMULTECH 2019 - 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

364

Figure 11: Electric field at the interface between elliptical

oval gold nanoparticles and air dielectric with the 10 nm

distance between particles.

Figure 12: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between elliptical oval gold nanoparticles and

air dielectric with the 10 nm distance between particles.

Figure 13: Electric field at the interface between block-

shape gold nanoparticles and air dielectric with the 10 nm

distance between particles.

We then try the fourth set of experiments using the

finite element method on the same software. The

impact light is the linearly polarized light with the

wavelength range from 300 nm to 800 nm

and increase the wavelength 50 nm at a time.

Figure 14: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between block-shape gold nanoparticles and air

dielectric with the 10 nm distance between particles.

The nanoparticle is the elliptical oval shape with a

axis = 10 nm and b axis = 40 nm. The distance

between nanoparticles is now reduced to 5 nm. The

simulation result shows that when the localized

surface plasmon resonance takes place at the

interface between the air dielectric and the elliptical

oval nanoparticles, the highest amplitude of the

electric field is 6.3x10

V/m. The wavelength of the

impact light is 650 nm as shown in Fig. 15. The

graph which show relationships between wavelength

of the impact light and the electric field at the

interface is shown in Fig 16.

Figure 15: Electric field at the interface between elliptical

oval gold nanoparticles and air dielectric with the 5 nm

distance between particles.

We then try the fifth set of experiments using the

finite element method on the same software. The

impact light is the linearly polarized light with the

wavelength range from 300 nm to 800 nm and

increase the wavelength 50 nm at a time. The

nanoparticle is the block shape with the size 10 nm x

40 nm. The distance between nanoparticles is now

reduced to 5 nm. The simulation result shows that

Simulation Effects on the Optical Response of Gold Nanoparticles

365

Figure 16: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between elliptical oval gold nanoparticles and

air dielectric with the 5 nm distance between particles.

when the localized surface plasmon resonance takes

place at the interface between the air dielectric and

the elliptical oval nanoparticles, the highest

amplitude of the electric field is 1.15x10

V/m. The

wavelength of the impact light is 700 nm as shown

in Fig. 17. The graph which show relationships

between wavelength of the impact light and the

electric field at the interface is shown in Fig 18.

Figure 17: Electric field at the interface between block-

shape gold nanoparticles and air dielectric with the 5 nm

distance between particles.

From the second and the third set of simulation

experiments, it is noticed that the wavelengths of the

impact light which produce the LSPR phenomenon

on non-symmetrical nanoparticles such as elliptical

oval and block shape are higher red-shifted than the

ones on spherical nanoparticles. These correspond

with the physical experimental results as de-

scribed in [9]. From the fourth and fifth simulation

results, it has been noticed that the amplitude of the

electric field is higher when the distance between

nanoparticles is 10 nm than when the distance is 5

nm when the LSPR phenomenon takes place.

Figure 18: Graph which shows relationships between

wavelength of the impact light and electric field at the

interface between block-shape gold nanoparticles and air

dielectric with the 5 nm distance between particles.

5 CONCLUSIONS

According to the advances in material synthesis,

nanostructures for medical applications are

available. They can be applied in useful biomedical

applications such as thermal therapy, drug nano-

carriers, photothermal agents for tumor ablation. The

understanding of the effects of nanoparticles sizes

and shapes will lead to the wider and more precise

applications. This is due to the fact that the size and

the shape of nanoparticles can determine the optical

properties and interactions with biological systems.

In the case of gold spherical nanoparticle, which is

symmetric, the change in the size of the nanoparticle

results in color changes. Color can be tuned within

the visible spectrum to dark red when plasmon

resonances occur. In the case that the shape of the

gold nanoparticles are not symmetrical such as gold

nanorod the change of their aspect ratio causes

plasmon resonance to be tunable in the visible to

near-infrared spectrum range. Heat generations from

plasmonic nanostructure when plasmon resonances

can be used in thermal therapy.

In this research work, we analyze by simulation,

gold nanostructures which have a block-shaped

aspect ratio (b/a) = 4 which is similar to the aspect

ratio of gold nanorod to find electric fields at the

interface between the gold nanoparticles and the air

dielectric. With the applications of linearly polarized

light to gold nanoparticles on BK-7 base substrate,

we simulate and measure the electric fields at the

interface between the nanoparticles, with different

shapes and sizes, and the air dielectric. Linearly

polarized light with the wavelengths between 300

nm – 800 nm are employed for excitation. From the

simulation results, it has been found that gold

SIMULTECH 2019 - 9th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

366

nanoparticles with elliptical oval shapes with a axis

10 nm and b axis 40 nm, and block-shape gold

nanoparticles 10nm x40 nm, which have the same

aspect ratio, are suitable for producing plasmon

resonance which can be tuned in the visible to near-

infrared spectrum. The elliptical oval shape gold

nanoparticle with a axis 10 nm and b axis 40 nm

gives higher electrical field amplitude than the 10nm

x40 nm block-shape nanoparticle which has the

same aspect ratio. The amplitude of the electric field

is higher when the distance between nanoparticle is

10 nm than when the distance is 5 nm when the

LSPR phenomenon takes place.

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