SIMULATION OF THE OPTICAL PROPERTIES OF SILVER AND
SILICA/SILVER CORE/SHELL NANOSPHERES
Sara Mohammadi Bilankohi 1, Majid Ebrahimzadeh1*, Hossein
Ghaforyan1
1 Department
of Physics, Payame Noor University, Iran.
* pasiran@gmail.com
ABSTRACT. Optical properties of silver and silica/silver core/shell nanospheres
such as extinction, absorption and scattering cross section are studied based on
Mie theory. The numerical simulation results show that optical properties of silver
and silica/silver core/shell nanospheres are mainly dependent on their sizes and
refractive index of environment that’s are embedded. The wavelength
corresponding to maximum extinction shifts to longer wavelengths as the size of
the nanoparticle is increased. The influence of higher-order multipoles is evident
for large nanospheres, making the spectra more complex. When the shell thickness
of a core/shell particle is decreased, the plasmon resonance shifts to longer
wavelengths. This red shift is accompanied by an increase in peak intensity.
Keywords: Mie Theory, Nanospheres, Optical Properties
INTRODUCTION
Nanostructured materials are corroborating an expanding development and
used in a variety of applications. They exhibit a wideness of fundamental
properties that can be tailored extensively to design new and adapted
functionalities. This is typically because nanoparticles have a greater surface area
per weight than larger particles which causes them to be more reactive to some
other molecules [1]. The light scattering from nanoparticle surface due to the
oscillatory motion of nanoparticle electrons. These electrons produces radiation.
Also, if the light is absorbed by the nanoparticle, the energy of the incident light is
converted to another form e.g. heat. The optical properties is strongly dependent on
size, shape and composition of the particles and medium of nanoparticles are
embedded. By modifying these parameters, we can simulate the some optical
properties of nanoparticles like scattering, absorbing and extinction (sum of the
absorbed and scattered energy) over a wide range of wavelengths. These optical
properties of nanoparticles interesting as functional materials for many applications
such as electronic and optical devices [2], chemical and biological sensors [3],
optical energy transport [4] and thermal ablation[5].
1
In recent years, more attention has to silver nanoparticles due to the optical
properties and its application [6]. When silver nanoparticles interact with the light,
according to the fluctuation of the electron band on nanoparticle surface, a
phenomenon called surface plasmon occurs. Silver nanoparticles plasmon modes
have a high absorption in the ultraviolet and violet spectral region [7]. Also, when a
silica and silver core/shell nanosphere is used, a sharp plasmon frequency is
observed, that can be reduced by changing the diameter of the core and shell .
Recently, the strong photostimulated luminescence is obtained from silver and
silver iodide nanoclusters [8]. The main advantage of using spherical geometry of
nanoparticles is control of optical properties in a highly predictive state. Also, the
optical properties of a material with sphere geometry can be simulated by using the
solution of Maxwell’s Equations for arbitrary radius and dielectric constant.
Therefore, we uses the Mie theory solution for simulation of the optical properties
of silver and core/shell silica/silver nanospheres and discuss about their optical
properties.
SIMULATION METHOD
In 1908, Gustav Mie obtained the solution of Maxwell’s equations for
spherical particles [9]. These solutions, showed the extinction spectra of spherical
particles with arbitrary size. Researchers are also trying to find the Maxwell’s
Equations solution for other shapes like nonspherical particles, Au spheroidal
particles and Ag spheroidal particles that it was the result of Mie research [10].
Bohren and Huffman described the complete conclusion of Mie theory and in this
paper, we used it [11]. According to this theory, the cross section parameter can be
calculated. This parameter is a quantity that show the power of the scattered,
absorbed or extincted of the incident light waves. Since that the sum of the
scattered and absorbed cross section is extincted cross section, we can calculate the
absorption cross section.
So, we considered a spherical particle with radius r0 and complex electric
permittivity ɛ=n2 embedded in a dielectric medium of permittivity ɛm=nm2. This
particle is illuminated by a plane wave of angular frequency. Within the Mie
solution, the cross-sections for scattering, extinction and absorption can be
expressed by following formulas:
2 
2l  1 al 2  bl 2
2 
q l 1
2 
Qextinction  2   2l  1 Re  al  bl 
q l 1
Qabsorption  Qextinction  QScattering
Qscattering 


(1)
 2
3
The scattering parameters al and bl are defined as follows:
2
al 
Fae  l 
Fbm  l 
and
b

l
Fae  l   iGae  l 
Fbm  l   iGbm  l 
 4
Where Fae  l  , Fae  l  Gae  l  , and Gbm  l  are related to the Bessel and Neumann
functions.
RESULTS AND DISCUSSION
Johnson and Christy determined the dielectric functions of copper, silver and
gold [12] and due to the small correction below R~5 nm, in this work, these
dielectric functions used to described the optical properties of silver nanoparticles.
According to these data, we can provide the absorption, scattering and extinction
cross section of a nanosphere as functions of the particle radius and the medium
refractive index nm.
The optical properties of silver nanospheres are highly dependent on the
nanosphere diameter. The extinction cross section area spectra of 10 sizes of silver
nanospheres are displayed in the Figure. 1. The identical mass concentrations for
these nanospheres is 0.05 mg/mL. Smaller silver nanospheres primarily absorb
light and have peaks near 404 nm (Figure.2). All spectra have a high resonance at
visible spectrum (Table 1), caused by the collective oscillations of the electron on
silver nanoparticles surface. The wavelength corresponding to maximum extinction
shifts to longer wavelengths (red shift) as the particle radius increases (Figure.3),
while larger spheres exhibit increased scattering and have peaks that broaden
significantly and shift towards longer wavelengths (known as red-shifting) and
generally lies to the near infra-red (Figure.4). High light scattering of the larger
spheres due to have larger optical cross sections.
3
Extinction Cross Section Area(m2)
6.0x10-14
d=10nm
d=20nm
d=30nm
d=40nm
d=50nm
d=60nm
d=70nm
d=80nm
d=90nm
d=100nm
5.5x10-14
5.0x10-14
4.5x10-14
4.0x10-14
3.5x10-14
3.0x10-14
2.5x10-14
2.0x10-14
1.5x10-14
1.0x10-14
5.0x10-15
0.0
350
400
450
500
550
600
650
700
750
800
Wavelength(nm)
Figure 1. Extinction cross section area for silver nanopheres of varying diameter.
Refractive index of medium is 1.33.
Absorption Cross Section Area(m2)
2.0x10-14
d=10nm
d=20nm
d=30nm
d=40nm
d=50nm
d=60nm
d=70nm
d=80nm
d=90nm
d=100nm
1.8x10-14
-14
1.6x10
1.4x10-14
1.2x10-14
1.0x10-14
8.0x10-15
6.0x10-15
4.0x10-15
2.0x10-15
0.0
350
400
450
500
550
600
650
700
750
800
Wavelength(nm)
Figure 2. Absorption cross section area for 10 sizes silver nanospheres of varying
diameter. Refractive index of medium is 1.33.
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Scattering Cross Section(m2)
1.6x10-12
1.4x10-12
R=100nm
R=200nm
R=300nm
R=400nm
1.2x10-12
1.0x10-12
8.0x10-13
6.0x10-13
4.0x10-13
2.0x10-13
0.0
350
400
450
500
550
600
650
700
750
800
Wavelength(nm)
Figure 3. Absorption cross section area for spherical silver nanoparticles of varying
radii. Refractive index of medium is 1.33.
Scattering Cross Section Area(m2)
5.5x10-14
d=10nm
d=20nm
d=30nm
d=40nm
d=50nm
d=60nm
d=70nm
d=80nm
d=90nm
d=100nm
5.0x10-14
4.5x10-14
4.0x10-14
3.5x10-14
3.0x10-14
2.5x10-14
2.0x10-14
1.5x10-14
1.0x10-14
5.0x10-15
0.0
350
400
450
500
550
600
650
700
750
800
Wavelength(nm)
Figure. 4. Scattering cross section area for large silver nanopheres of varying
diameter. Refractive index of medium is 1.33.
The optical properties of silver nanopheres also depend on the refractive index
near the nanoparticle surface. As the refractive index near the nanoparticle surface
increases, the nanoparticle extinction spectrum shifts to longer wavelengths.
Practically, this means that the nanoparticle extinction peak location will shift to
shorter wavelengths (blue-shift) if the particles are transferred from water (n=1.33)
5
to air (n=1.00), or shift to longer wavelengths if the particles are transferred to oil
(n=1.5). The Figure.5 displays the calculated extinction spectrum of a 50 nm silver
nanosphere as the local refractive index is increased. Increasing the refractive index
from 1 to 1.33 results in an extinction peak shift of over 75 nm, moving the peak
from the ultraviolet to the visible region of the spectrum. When embedded in high
index materials, the extinction cross section is substantially increased.
Extinction Cross Section Area(m2)
2.97E-014
n=1
n=1.33
n=1.51
n=1.923
2.64E-014
2.31E-014
1.98E-014
1.65E-014
1.32E-014
9.90E-015
6.60E-015
3.30E-015
0.00E+000
350
400
450
500
550
600
650
700
750
800
Wavelength(nm)
1.06
104
990
3.96×103
1.02×104
1.84×104
2.71×104
3.62×104
4.42×104
5.11×104
400
400
404
409
422
431
449
463
481
499
260
1.99×103
5.58×103
9.43×103
1.18×104
1.19×104
1.10×104
1.11×104
1.47×104
1.85×104
395
40
404
409
418
427
440
454
395
400
Waveleng
th(nm)
10
20
30
40
50
60
70
80
90
100
Waveleng
th(nm)
Table 1. Resonance peak of the optical properties of silver nanospheres
Scattering
Absorption
Extinction
Atomic
Particle
Cross
Cross
Cross
Molarity Concentration
Section
Section
Section
(mmol/L) (particle/ml)
Peak(nm2)
Peak(nm2)
Peak(nm2)
Waveleng
th(nm)
Diameter
Figure. 5. Extinction cross section area for 50 nm silver nanospheres of varying
refractive index
261
2.09×103
6.57×103
1.34×104
2.17×104
3.04×104
3.79×104
4.50×104
5.16×104
5.75×104
395
400
404
409
418
431
445
458
476
494
0.464
0.464
0.464
0.464
0.464
0.464
0.464
0.464
0.464
0.464
9.103×1012
1.138×1012
3.372×1011
1.422×1011
7.283×1010
4.214×1010
2.65×1010
1.778×1010
1.249×1010
9.103×109
Figure. 6 shows the extinction for silica\silver core\shell nanospheres with different
sizes. The total nanospheres radius is kept constant at 50 nm. The spectrum with a
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peak at 498 nm is the extinction from a silver sphere with a radius of 50 nm (no
silica core). As the shell thickness is decreased, the peaks shift to the red and
become more intense. Increasing the ratio of core radius to total radius causes the
peak to shift red. Thinning the shell layer produces a large increase in polarization
at the sphere boundary, which yields the more intense extinction peaks. The same
general trends are observed when the nanoparticle size is increased.
1056nm
Shell thickness : 3nm
-13
750nm
2
Extinction Cross Section Area(m )
1.2x10
Shell thickness : 7nm
-13
1.0x10
660nm
Shell thickness : 10nm
-14
8.0x10
543nm
Shell thickness : 20nm
-14
6.0x10
Shell thickness : 50nm
498nm
-14
4.0x10
-14
2.0x10
0.0
400
600
800
1000
1200
Wavelength(nm)
Figure. 6. Extinction cross section area of core/shell nanoparticles. The core is
silica and the shell is silver. The total nanoparticle radius is 50 nm.
CONCLUSIONS
The optical properties of spherical silver and silica/silver core/shell
nanospheres can be find by modifying the physical dimensions. The thickness and
radius of the nanospheres are extremely important and play a important role in the
intensity and placement of the plasmon resonances. If silver spherical nanospheres
get larger, the peaks broaden and shift to longer wavelengths. Higher-order modes
also become important, making the extinction spectrum more complex. The
silica/silver core/shell nanospheres display a red shift and an increase in intensity
of extinction as the shell size is decreased. The magnitude of the shift is highly
dependent on the shell thickness.
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