Calculation of Optical Properties of Nano ParticlePHYSICS 5535- .docx

Calculation of Optical Properties of Nano Particle
PHYSICS 5535- Optical Properties Matter-Spring 2017
Raznah Yami
Outline
1. Introduction: this part gives a precise overview of the whole
paper. It begins by illustrating a brief introduction and
importance of Nano Particles and the theoretical approaches
used for their calculation.
2. Main idea: this section provides a step-by-step in-depth
analysis of recently developed theories the calculation of
optical properties of nanoparticles. It also provides calculation
and equations employed these approaches.
2.1 Optical Properties of Nanoparticles: this section talks about
the basics principles and governing the optical behavior of Nano
particles and provides in-depth knowledge of different
phenomena observed while dealing with optical properties of
Nano particles.
2.2 Mie-Theory: the research provides exhaustive information
the study optical properties of nanoparticles using Mie theory.
This research focuses on Mie theory for the calculation of
optical properties of Nano particle according to which we can
calculate the place of surface Plasmon resonance in optical
spectra of metallic spherical nanoparticle.
2.3 Discrete Dipole Approximation method: this section
enumerates sufficient information about the calculation of
absorption and scattering efficiencies and optical resonance
wavelengths for three commonly used classes of nanoparticles:

gold Nano spheres, silica-gold Nano shells, and gold Nano rods
and we examine the magneto-optical scattering from nanometer-
scale structures using a discrete dipole approximation.
3. Conclusion: This section provides a summary of the most
important points, which presents an overview of the practical
application and calculation methods of optical properties of
Nano particles talking about core principles, which therefore
explain the behavior exhibited by nanoparticles.
List of figures:
Figure 1: Localized surface Plasmon resonance ,resulting from
the collective oscillations of delocalized electrons in response
to an external electric field
Figure 2: Absorption spectra of semiconductor nanoparticles of
different diameter. Right-nanoparticles suspended in solution.
Figure 3: Comparison of absorbance along increasing
wavelength between Nano GaAs (7-15 nm) and Bulk GaAs
showing an apparent blue shift
Figure 4: Showing the effect of blue shift because of quantum
confinement as the wavelength shifts from 1100 nm to 2000 nm
when we move from particle size of 9nm to parcile size of 3 nm.
Figure 5: Emission spectra of several sizes of (Cdse) Zns core-
shell quantum dots.
Figure 6: The optical spectra and transmission electron
micrographs for the particles in vials 1–5 are also shown. Scale
bars in micrographs are all 100 nm
Figure7: Shows the effect of varying relative core and shell
thickness of gold Nano Shells, there is an apparent blue shift as
the frequency increases

References:
1. . P. S. Pershan. ""Magneto-optical effects." J. Appl. Phys
(2009): 38. Document.
2. al, Dabbousi et. "J. Phys. Chem. B ." 9463-9475 (997): 101.
Paper.
3. al, J.Nayak et. "J. Nayak et al., Physica." (2004: 227–233.
Document.
4. Annual Review of Biomedical Engineering. "Annual Review
of Biomedical Engineering." 23 4 2014.
http://www.annualreviews.org. Document. 22 1 2017.
5. Bhardwaj, Achal. "Optical Properties of Nanoparticles."
(2016): 224.
6. Lin-Wang, Li J. and Wang. "Band-structure-corrected and
density approximation." International Science Congress
Association (2005): Phys.Rew. B, 72. Documnet.
7. Manna, Scher and Alivisats. "Cdse nanocrystals." Cluster Sci
13 (2002): 521. paper.
8. nanocomposix. http://nanocomposix.com. 12 2 2014.
electronic. 23 2 2017.
9. S. J. Oldenburg, R. D. Averitt, S. L. Westcott, N. J. Halas. "
Chem. Phys. Lett. 288." (1998): 288, 243.
6
Calculation of Optical Properties of Nano Particle

Summary
Nanoparticles are used in a variety of applications and their
usage is growing vastly because of their superior’s
characteristics among these properties optical properties play a
vital role in various applications. This paper presents an
overview of the practical application and calculation methods of
optical properties of Nano particles talking about core
principles which therefore explain the behavior exhibited by
nanoparticles. Introduction The optical properties of
nanoparticles are highly dependent on the particle size, shape,
chemical composition, and the local dielectric environment. it is
possible to selectively tune these properties to suit a given
application Many studies have explored the optical properties of
metal nanoparticles using simulations, that are useful in
applications including solar cell, imaging, sensing and
constructing nanostructures. This paper focuses on Mie theory
for the calculation of optical properties of Nano particle
according to which we can calculate the place of surface
Plasmon resonance in optical spectra of metallic spherical
nanoparticle Metal nanoparticles are widely used to construct
structures that possess unique electronic, photonic and catalytic
properties such as local surface Plasmon resonance (SPR).
Surface Plasmon resonance of metallic nanoparticles is one of
the reasons of their unique optical properties. (Bhardwaj)

Introduction
Many of the optical properties of Nano particle are closely
related to the electrical and electronic properties of the
material. But as we shall see other factors also come into
discussion when we deal with optical properties. Usually talking
about optical properties, we usually refer to the interaction of
electromagnetic radiation with matter. Simply put we may
consider it as a ray of an electromagnetic wave of a single
frequency entering a medium from vacations ray could be
reflected transmitted or may be absorbed. The reflection could
be specular or diffuse. When there is an interaction of a medium
with electromagnetic radiations first being the radiation my
exhibit scattering secondly being the ray may get absorbed i.e.
if one considers a wider range of frequencies then some part of
the spectrum could be absorbed while the other frequencies
could be scattered. Semiconductor and metallic nanomaterials
and nanocomposites possess interesting linear absorption,
photoluminescence emission, and nonlinear optical properties.
Nanomaterials having small particle sizes exhibit enhanced
optical emission as well as nonlinear optical properties due to
the quantum confinement effect. Synthesis, characterization,
and measurement of optical properties of nanomaterials with
different anisotropic shapes have also drawn significant
attention. The selection of nanoparticles for achieving efficient
contrast for biological and cell imaging applications, as well as
for photothermal therapeutic applications, is based on the
optical properties of the nanoparticles. We use Mie theory and
discrete dipole approximation method to calculate absorption
and scattering efficiencies and optical resonance wavelengths
for three commonly used classes of nanoparticles: gold Nano
spheres, silica-gold Nano shells, and gold nanorods. The
calculated spectra clearly reflect the well-known dependence of
nanoparticle optical properties viz. the resonance wavelength,
the extinction cross-section, and the ratio of scattering to
absorption, on the nanoparticle dimensions. A systematic

quantitative study of the various trends is presented in this
paper. In this research, a systematic study of recently developed
Mie theory and Discrete dipole approximation method DDA is
derived. Thereafter, a classical analysis of each method is
presented to get an understanding of how they are employed in
development of metamaterials. We also talk about size and
shape effect on the behavior of Nano particles while bringing
some light on the use of these theories and meta materials
applications in the field of super lenses.
Optical Properties of Nano particles
Discussing the optical behavior of nanomaterials, in order to do
that we must first look at the concepts of some various
phenomena in material like reflection, refraction, refractions
and absorptions these phenomena give rise to colors in materials
and they are also responsible for what we call the overall
optical response of the material. (The Physics Classroom)
Light can be considered as having waves and consisting of
particles called photons.
Energy of a photon
· h-Planck’s constant (6.62x J.sec)
· v-frequency
· c-speed of light
· -wavelenght
Absorption essentially involves activating some process in the
material to take it to an excited state. The material can
essentially get excited by the follow ways.
i. Electronics
ii. Vibrational

iii. Rotational excitation
Further part of the absorbed energy could be re-emitted or
absorbed dissipated as heat and is known as dissipative
absorption.
Plasmon
We may differentiate of metals on the basis of free electrons
which give rise to Plasmon’s. A Plasmon is a collective
excitation of the electronic "fluid" in a piece of conducting
material, like ripples on the surface of a pond are a collective
mode of the water molecules of the liquid These electronic
ripples can have a well-defined wavelength as light consists of
photons, the plasma oscillation consists of Plasmon’s. That is,
what makes the Plasmon waves we also have to discuss the
frequency regime where the wavelength of the incoming
radiation determines the response of the metal to the incoming
radiation i.e. the metal could itself could become somewhat
transparent or it could even reflect it depending on the
frequency of the incoming radiation we also know that in case
of semiconductors we have to keep in mind the band gap if we
plan to understand how the absorption of a semiconductor is
going to be when we impose an electromagnetic radiation.
(Zhang)
Keeping in view the above statement the important question we
now ask is that when we put a nanomaterial how is the behavior
as compared to bulk metal going to change or a bulk
semiconductor is going to change when we have a material in
the nanoscale. As we discuss the size effect on optical
properties the bulk metal absorbs electromagnetic radiation in
visible region.
Surface Plasmon’s
Thin films of metals may partially transmit just because there is
insufficient material to absorb the radiation (Au films few 10s
nanometers may become partially transparent) apart from the
insufficient material effect there are other phenomena’s which
become relevant in nanomaterials specially Nano free standing
and Nano crystalline particles and these include the phenomena

of surface Plasmon’s and quantum confinement effects. Surface
Plasmon’s (SPs) are coherent delocalized electron oscillations
that exist at the interface between any two materials where the
real part of the dielectric function changes sign across the
interface (e.g. a metal-dielectric interface, such as a metal sheet
in air). SPs have lower energy than bulk (or
volume) Plasmon’s which quantize the longitudinal electron
oscillations about positive ion cores within the bulk of
an electron gas (or plasma). (Zhao)
Figure 1 Localized surface Plasmon resonance (LSPR), resulting
from the collective oscillations of delocalized electrons in
response to an external electric field
Quantum Dots
A term that needs to be discussed in the this regard are the
Quantum dots that are very small semiconductor particles, only
several nanometers in size, so small that their optical and
electronic properties differ from those of larger particles. They
are a central theme in nanotechnology. Many types of quantum
dot will emit light of specific frequencies if electricity or light
is applied to them, and these frequencies can be precisely tuned
by changing the dots' size, shape and material, giving rise to
many applications.
Figure 2 Absorption spectra of semiconductor nanoparticles of
different diameter. Right-nanoparticles suspended in solution.
If we take quantum dots like this and we make them different
sizes they either emit different colors or they absorb different
colors, so if we take small cadmium selenide particle 5 nm in
diameter and another one 4 nm in diameter and we hit them with
ultra violet light we will experience luminance meaning they
will emit light corresponding to the energy levels one will emit

say blue light and one will emit green light (Manna)
As we know that in a Nano crystalline material, Nano materials
or free standing Nano particles there is a large surface to
volume ratio so surface dominant effects like surface Plasmon’s
come into play, in semiconductor quantum dots optical
absorption and emission shift to the blue higher energies which
implies that inherently there is something changing in
nanostructured materials regarding what we call the
electromagnetic structure or the band structure.
The size reduction is more prominent in the case of
semiconductors as compared to metal, now to see the
confinement effects in metals we have to go down to smaller
sizes as compared to semiconductor crystals this effects
becomes prominent in larger sizes in semiconducting crystals it
will also be seen that very small sizes metal nanoparticles can
develop a bandgap and can become semiconductors and
insulators.
Because of dimension confinement the density of state changes
between a bulk 3D semiconductor, normal conductor to 2D kind
of a system, further as we go to a 1D dimensional metal which
actually develops a band gap i.e. if we take a material like
copper which is a bulk metallic material and reduce its size and
it is seen that the density of state starts to actual develop an
energy gap and it starts to behave like a semiconductor or an
insulator in very small sizes. Now as we go down to a zero-
dimensional metal in the bulk then the material starts to behave
like an atom having discrete energy levels
Now in the case of semiconducting nanoparticles and films on
decreasing the size the electron gets confined to the particle and
confinement effect starts to dominate and this leads to two
important effects first being increasing the band gap energy and
the second being the band levels get quantizes, say you have a
bulk semiconductor we have a valance band and a conduction
band separated by a band gap now in accordance with the
Quantum size confinement effect the energy level spacing
increases with decreasing dimension. (Annual Review of

Biomedical Engineering)
Quantum Confinement
If the particle size is too small compared to the wavelength of
the electrons, the quantum confinement effect was observed. To
that end understand, we broke the word as quantum and
Mitigation word meant to the movement of electrons move
arbitrarily restrict their movement in a given energy level
(discrete) in the quantum realm of subatomic reflect limit. As
the particle size decreases until it reaches the limits reduction
nanoscale size makes discrete energy levels, and this increase or
add a wide band gap, and, ultimately, increases the band gap
energy. Since the bandgap wavelength and inversely
proportional to each other, decreases with decreasing
wavelength, it was found to emit blue radiation
Now on the other hand the band gap levels get quantize as in a
nanoparticle there are these discrete levels but since they are
places so closely we can consider them to be a continuous state
which we term as a band .But when the number of particles in
the system reduce obviously there are not enough particles to
make a continuous or semi-continuous level and therefore the
we observe discretization effect and these level start to become
discrete so there are two important factors that come into play
when you reduce the size of the particle namely being the
increase in bandgap and the band levels get quantized or start to
show the discreteness level of the band. (Lin-Wang)
·
·
·
·
·
·
In a case study of Bulk GaAs (Gallium arsenide) and Nano
GaAs we see that along the wavelength the bulk shows a

decrease in absorbance as the wavelength is increasing in the
right-hand direction the energy is increasing in the left-hand
direction. On the other hand, we have Nano-GaAs with a size
variation (7-15 nm) which means there isn’t a single but range
of band gaps so expect absorption to take place over a range of
energies and that is a reason that the peak is actually broadened
and is not a very short peak as one would expect. The broad
excitonic peak occurs at about a range of 526nm and
corresponds to an energy of about 2.36eV as compared to the
bulk Gallium arsenide energy gap which is 1.43eV which shows
that the band gap has effectively increased. Bulk Gallium
arsenide has a different absorption spectrum as compared to the
Nano gallium arsenide in Nano gallium arsenide a very strong
peak is observed which corresponds to a band gap of 2.36eV
which means that now the band has “BLUE SHIFTED” which
means it happens at higher frequencies or in other words at
lower wavelengths, the overall absorbance in higher in Nano
material as compared to its counterpart bulk material and this is
attributed to the enhanced oscillator strength (dimensionless
quantity to express the strength of the transition from the
valance band to the conductance band). (J. e. al)
Figure 3 Comparison of absorbance along increasing
showing an apparent blue shift
Now we take up an equivalent case of Pbse nanocrystals we
again observe the effect of blue shift, which is coming from
quantum confinement effect in these semiconductor
nanocrystals the density state becomes more quantized and the
band gap shifts to higher energies which is the root cause of this
blue shift In the case of Pbse Nano crystals again we are we are
again plotting the wavelength as the function of the absorbance
and the curves have been shifted vertically so a comparison can
be made there is a change in the absorption peak as we go from
9 nm particles of Pbse to 5.5 nm particles to 4.5 nm and then to

the 3 nm particles. So, as it is clearly visible that there is a blue
shift in the peaks and the peak shifts towards higher frequencies
or in other words lower wavelengths and the energy of the
transition becomes high and therefore the material absorbs at
higher energies when we actually reduce the particle size from 9
nm to 3 nm and the wavelength shifts from 1100 nm to greater
than 2000 nm which demonstrates a clear quantum confinement
effect in these nanoparticles that effects its optical properties.
(D. e. al)
Figure 4 Showing the effect of blue shift because of quantum
when we move from particle size of 9nm to parcile size of 3 nm.
Photoluminescence
The counterpart or other side of the absorbance is called photo
luminance which can be defined as the phenomena when a
material is put into an excited state then it is going to relax to
its ground state and in the process, is going to emit a photon. If
the energy of the emitted photon lies in the range of 1.8 - 3.1
eV the radiation will be in the visible range, by changing the
size of the nanoparticles the frequency of emission can be
tailored the decrease in size of Nano particles accompanies a
blue shift.
Core Shell nanostructures
A semiconductor acts like a core while being enveloped by
another semiconductor that behaves like a shell some prominent
examples of these are CdS coated with MoS4, ZnSe coated with
CdSe, Cdse coated with CdS where the bandgaps are tunable
near the I-R which can be used as IR biological luminescent
markers. In luminescent properties are characteristics of the

core and the shell actually leads to an enhancement of the
properties of the core where the shell could be performing many
roles like acting as a permeable layer where it may be
protecting the core from the environment. Deposition of a
semiconductor with a larger bandgap than the core typically
results in ‘luminescence enhancement’ due to radiation less
recombination mediated by the surface states the transition
between these layers may not always result in a luminescence
effect and therefore the shell enhances the luminescence
properties of the semiconductor.
Now in the case of ZnS Shell on Cdse core we will first observe
the luminescence properties with the shell and then in the
absence of the shell, there is a shell of ZnS and we will compare
it with a case where there is no shell of ZnS and the trend
observed due to this change in size is the change in color. There
is an enhancement in the luminescence properties in the
presence of the shell which an important effect of putting a
shell around the core, as change in particle size occurs the
frequency exhibit a blue shift. In each of the in each one of
these cases the core shell structure has a higher emission as
compared to the bare core (only the core).
Figure 5 Emission spectra of several sizes of (Cdse)Zns core-
shell quantum dots.
Metallic Nano Particles
Gold nanoparticles used as a pigment of ruby-colored stained
glass dating back to the 17th century. 1-10 nm sized particles
give rise to this color and this color is due to surface Plasmon’s
resonance. Thin film of Au ~100nm or less will transmit blue-
violet light, the color of metallic particles depends on size in
the nanoscale regime as bulk Au can is golden yellow color
while nanoparticles of gold can have red, purple, or blue color.
The color depends on the size and shape of the particle and

dielectric properties of the medium as the surface Plasmon’s are
excited by incident electromagnetic radiation.
For Ag or Au particles of about 50nm and smaller than this
there will be no scattering within the particle and all the
interaction will be with the surface in other words in small
particle we have to consider the effect of the surface more
meaning we have to consider the surface Plasmon more as
compared to the bulk Plasmon’s and these surface Plasmon’s are
going to be the key factors that are going to determine the
optical properties of the nanoparticles.
The optical properties of gold and silver nanoparticles change
drastically with nanoparticle shape. The photograph shows
aqueous solutions of 4 nm gold Nano spheres (vial 0) and
progressively higher aspect ratio gold nanorods (1–5). The
optical spectra and transmission electron micrographs for the
particles in vials 1–5 are also shown. Scale bars in micrographs
are all 100 nm. (nanocomposix)
Figure 6 The optical spectra and transmission electron
bars in micrographs are all 100 nm
The optical response of gold Nano shells depends dramatically
on the relative size of the core nanoparticles as well as the
thickness of gold shell.
By varying the relative core and shell thickness, the color of
such gold Nano shells can be varied across a board range of
optical spectrum spanning the visible and the near-infrared
spectral regions. Semiconductors Core/Shell Nanoparticles are
used for medical or bioimaging purposes enhancement of optical
properties, light-emitting devices, nonlinear optics, biological
labeling, improving the efficiency of either solar cells or the
storage capacity of electronics devices. (S. J. Oldenburg)

Figure 7 Shows the effect of varying relative core and shell
the frequency increases
Recently Developed LMTO Methods
Mie Theory:Mie theory describes the light scattering particles.
"Particles" as used herein refers to an aggregate of, the
surrounding region (NMED), a refractive index (NP) of the
material. In dipole radiation pattern of such particles of
molecular electronic superposition oscillation strong net
radiation. In addition, the re-radiation pattern of all the dipoles
is not in the forward direction of the incident light are shifted,
homogeneous media is correct, but is long and destructively
interfere in the radiation pattern. For example, particles with
different efficiencies "scattering" light in all directions.
Gustav Mie in 1908 published a solution to the problem of light
scattering by homogeneous spherical particles of any size. Mie's
classical solution is described in terms of two
parameters, nr and x:
the magnitude of refractive index mismatch between particle
and medium expressed as the ratio of the n for particle and
medium,
nr = np/nmed
The sizes of the surface of refractive index mismatch which is
the "antenna" for retardation of electromagnetic energy,
expressed as a size parameter (x) which is the ratio of the
meridional circumference of the sphere (2a, where radius = a) to
the wavelength (/nmed) of light in the medium,
x = 2a/(/nmed)
A Mie theory calculation will yield the efficiency of
scattering which relates the cross-sectional area of
scattering, s [cm2], to the true geometrical cross-sectional area
of the particle, A = a2[cm2]:

s = QsA
Finally, the scattering coefficient is related to the product of
scattered number density, s [cm-3], and the cross-sectional area
of scattering, s [cm2], (see definition of scattering coefficient):
µs = s
Theoretically, the particles by Mie theory generally spherical,
but, in fact, particles are generally manufactured as a cubic or
cylindrical ease of manufacturing. To the uniform criteria,
which are much smaller than can satisfy in the form of a lattice
constant, said operating wavelength, the relative dielectric
constant of the dielectric particles is significantly higher than
the 1
Consider the source, the spherical scattering particles and the
observer, whose three positions define a plane called the
scattering plane. The incident and scattered light can be reduced
to its parallel or perpendicular to the scattering plane.
Figure 8 shows in the following figure, the parallel and vertical
components can be experimentally selected by a linearly
polarizing filter oriented parallel or perpendicular to the
scattering plane. (Sun)
The scattering matrix describes the relationship between the
vertical and parallel incident and scattered electric field
components observed in the "far field”.
For practical scattering measurements, the above equation
simplifies to the following:
Consider the scattering pattern from a 0.304-µm-dia.
nonadsorbing polystyrene sphere in water irradiated by HeNe
laser beam:

Table 1 Nonadsorbing polystyrene spheres in water at a
concentration of 0.1% volume fraction
np = 1.5721
particle refractive index
nmed = 1.3316
medium refractive index
a = 0.152 µm,
particle radius
= 0.6328 µm
wavelength in vacuum
nr = np/nmed = 1.5721/1.3316 = 1.1806
relative refractive index
x = 2a/(/nmed) = (2)(3.1415)(0.152)/(0.6328/1.3316) = 2.0097
size parameter
Mie theory algorithm:
Mie (nr, x) ---> S1(), S1() as complex numbers
Mie (1.1806, 2.0097) ---> S1.re + jS1.im, S2.re + jS2.im as
functions of
To view the results, calculate the intensities of scattering for
parallel and perpendicular orientations of polarized
source/detector pairs:
Ipar =S2S2* =Re{(S2.re +jS2.im)(S2.re -jS2.im)}
Iper = S1S1* = Re{(S1.re + jS1.im)(S1.re - jS1.im)}
which are shown in the following figures, and can be
experimentally measured as described below.
The following figures describe the experimental measurements
that illustrate the angular dependence of the scattered intensities
Ipar and Iper:Iper
Irradiate dilute solution of spheres in water with laser beam
polarization oriented perpendicular to the table. Collect
scattered light as a function of angle in plane parallel to table.
Place linear polarization filter in front of
detector perpendicular to the table.

Figure 9 Cylindrical cuvette holding sphere solution
Ipar
Irradiate dilute solution of spheres in water with laser beam
polarization oriented parallel to the table. Collect scattered light
as a function of angle in plane parallel to table. Place linear
polarization filter in front of detector parallel to the table.
Figure 10 Cylindrical cuvette holding sphere solution with
polarization filter in front of detector
For a randomly polarized light source, the total scattered light
intensity is given by the term S11:
S11 is the first element of the so-called Mueller Matrix, a 4x4
matrix which relates an input vector of Stokes parameters (Ii,
Qi, Ui, Vi) describing a complex light source and the output
vector (Is, Qs, Us, Vs) describing the nature of the transmitted
light. For randomly polarized light, S11 describes the transport
of total intensity:
Is = S11Ii
Mie scattering" suggests situations where the size of the
scattering particles is comparable to the wavelength of the light,
rather than much smaller or much larger. Mie scattering
(sometimes referred to as a non-molecular or aerosol particle
scattering) takes place in the lower 4.5 km of the atmosphere,
where there may be many essentially spherical particles present
with diameters approximately equal to the size of the
wavelength of the incident energy.
Double Discrete Dipole Approximation
Electromagnetic scattering from nanometer-scale objects is
currently being investigated both experimentally and

theoretically for the understanding and prediction of novel near-
field effects. Typically, near-field optical studies are performed
on noble-metal nanostructures where resonances from surface
Plasmon’s play an important role in near-field coupling and
propagation effects in this paper, we examine the magneto-
optical scattering from nanometer-scale structures using a
discrete dipole approximation (DDA). In the simplest form, the
approximation replaces individual nanoparticles with a single,
electromagnetic dipole radiator. The optical response of a
collection of particles is calculated self consistently by
calculating the response of each dipole to the incident field plus
the scattered field from all the other dipoles
In the DDA approximation, either the spherical nanoparticle,
with diameter , or a similarly small element of an extended
structure with dimensions on the order λ is represented by an
oscillating dipole with polarizability tensor α j which is
determined by the material properties. The dipole moment of the
element located at is , where the local field j is the incident
field , j plus the field radiated by all the other dipoles,
The incident field is given by where ω is the frequency of
radiation and κ is the wave vector with magnitude κ = ω/c.
Substituting the expression for the dipole moment and
rearranging yields,
where the radiation from a dipole has been written , = . Using
the well-known expression for radiation of a dipole located at
position evaluated at point
The optical interactions with a material which exhibits
magneto-optical effects (a gyrotropic material)
are described by its dielectric tensor,
(. P. S. Pershan)
where the magneto-optical Voigt parameter and , and mx m m y
z are the direction cosines of the magnetization vector. The

induced (uniform) polarization of a dielectric sphere valid for
arbitrary anisotropy is given by
where 1 is the 3×3 identity matrix and a is the radius of the
sphere This allows the identification of the polarizability as
where 1 ( 2)− ε + 1 is understood as matrix inversion. The
connection between magnetic field and optical field is through
the magnetization-dependent dielectric tensor. In fact, at optical
frequencies, the magnetic permeability is equal to unity and the
effects of the magnetic field are characterized by the dielectric
tensor through its dependence on the magnetization
Optical properties are manifestations of absorption and
reradiation of light from individual elements of the material.
For this reason, a slightly different definition is needed for
magneto-optical effects arising from materials whose
dimensions are on the order of or smaller than an optical
wavelength. We define the complex Faraday rotation angle as
the difference in the scattering extinction coefficients for left
and right circularly polarized light. The Faraday rotation, θ and
ellipticity, η (per unit length), are given by
In general, the calculation of the extinction coefficients requires
the calculation of dipole moments for two orthogonal
polarizations of incident electric field. In this case, we take the
both the incident and scattered fields to be the zˆ direction
(forward scattering), which matches our experimental geometry.
The scattering matrix elements are
where eˆ is a unit vector for the polarization and m and m′
denote the incident and scattered fields, respectively. is the
calculated dipole moment of the jth particle for incident
polarization ˆ. Since both the incident and scattered fields are in
the zˆ direction, the polarization unit vectors are simply xˆ and
yˆ. The Faraday rotation is calculated from the matrix element.

We now transform into the left-right circular polarization basis
to show that this is indeed equivalent to Eq. (8). The usual
transformation from (x,y,z) to (r,l,z), where r and l stand for
right and left respectively, is given by
In this basis, the x polarization is written
which is equivalent to difference in extinction coefficients for
left and right circularly polarized light, . The calculation
proceeds as follows. For a, given geometry, a lattice is
established with individual polarizabilities; values of the
dielectric tensor are taken from the literature. Equation (4) is
solved with incident x-polarized electric field which yields
We first apply the DDA calculations to magnetite nanowires.
The model for the nanowires is similar to that used in Ref. [10]
and is shown in Fig 1, showing the diagonal and off diagonal
components of the dielectric tensor. The Faraday rotation is
calculated for nanowires with 2 nm × 2 nm cross section and
lengths from 2 nm to 100 nm.
Figure 11 Model for the magnetite nanowires. The sphere
represents the individual discrete dipole elements. The cross
section is 2X2 elements with a length L varied from 2 to 100
elements. In all cases the element grid spacing d = 1.0nm
The results of these calculations are shown in Fig. 2 for incident
x polarization and nanowires aligned on the x axis and z axis.
The magneto-optics calculations assume that the externally
applied magnetic field is large enough to saturate the
magnetization of the material. In order to highlight differences
in nanowire orientation, we assume that the magnetization is in
the z direction in both Fig. 2 (a) and (b). The absolute Faraday
rotation is dependent on the volume of each scatterer as well as
the number density of scatterers and thickness of the sample.
We have normalized the calculations in Fig. 2 so that the

Faraday rotation at the positive peak (~500 nm) is unity. The
spectrum of the 2×2×2 element particle is the same as a single
nanoparticle. Little change in the spectral Faraday rotation is
noted for nanowires when the nanowire is aligned with
polarization of the incident field. However, the Faraday rotation
spectrum changes dramatically when the nanowire is aligned in
the direction of light propagation (z direction). The overall
effect is a blue shift of the spectrum with increasing nanowire
length.
Figure 12 Calculation of the Faraday rotation of a magnetic
nanowire. The long axis of the nanowire is aligned with the (a)
x axis and (b) z axis. In both cases, the magnetic field is applied
in the z direction
The model can be used as finite element method for the
calculation of the magneto-optical response of non-spherical
nanostructures with dimensions approaching the wavelength of
light. The model can also be used to calculate magneto-optical
scattering from collections of nanoparticles, where each
nanoparticle is represented by a radiating dipole. The particle
collections need not be homogeneous; in fact, we apply the
model to binary nanoparticle systems which consist of a noble-
metal and magnetic oxide nanoparticles. We calculate
enhancements of the Faraday rotation near the plasmin
resonances of the metal nanoparticles. These enhancements are
evident for interparticle spacing’s on the order of 20 nm or less.
(Stokes)
Conclusion
The optical properties of nanomaterials are the most attractive

and useful properties, and have been extensively studied by
means of different optical spectroscopic techniques.
Semiconductor and metallic nanomaterials and nanocomposites
possess interesting linear absorption, photoluminescence
emission, and nonlinear optical properties. Nanomaterials
having small particle sizes exhibit enhanced optical emission as
well as nonlinear optical properties due to the quantum
confinement effect. Synthesis, characterization, and
measurement of optical properties of nanomaterials with
different anisotropic shapes have also drawn significant
attention. Optical properties and correlation spectroscopy basic
understanding of nanomaterials for anyone interested in
understanding of semiconductors, insulators or metal required.
This is partly because the optical properties, and other
properties are closely related functions. Chemistry and physics
advances extended to a unique and powerful set of optical
properties of nanostructured materials. These nanomaterials
provide a new tool for biomedical engineers, biologists and
medical scientists to explore new instruments such as
biosensors and biological fluids, searching cells and tissues and
chemical characteristics. Nanomaterials are also used for
applications such as the development of drug delivery
adjustment optical test equipment and optical treatment
applications. And control the various components of the optical
properties of Nano-scale integration remains one of the most
difficult challenges. These calculations provide a tool for
modeling the magneto-optical scattering from no spherical
structures as well as provide a framework for the basic,
qualitative understanding of the near-field coupling effects on
magneto-optical scattering. Incidentally, none of these effects
are predicted by any effective-medium type model or any mean-
field theory which does not include near-field interactions The
study shows a model for magneto-optical scattering from
nanometer-scale structures based on a modification of the
discrete dipole approximation. The model can be used as finite
element method for the calculation of the magneto-optical

response of non-spherical nanostructures with dimensions
approaching the wavelength of light. The model can also be
used to calculate magneto-optical scattering from collections of
nanoparticles, where each nanoparticle is represented by a
radiating dipole. The particle collections need not be
homogeneous; in fact, we apply the model to binary
nanoparticle systems which consist of a noble-metal and
magnetic oxide nanoparticles. We calculate enhancements of the
Faraday rotation near the plasmon resonances of the metal
nanoparticles. These enhancements are evident for interparticle
spacings on the order of 20 nm or less. However, progress in a
relatively short time internal meta-material is made remarkable.
Different disciplines to the full potential of this new material
will include electronics, communications, medical diagnostics,
healthcare and manufacturing, including a far-reaching impact.
List of Table and Figures
Figure 1 Localized surface Plasmon resonance (LSPR), resulting
from the collective oscillations of delocalized electrons in
response to an external electric field5
Figure 2 Absorption spectra of semiconductor nanoparticles of
different diameter. Right-nanoparticles suspended in solution.5
Figure 3 Comparison of absorbance along increasing
showing an apparent blue shift7
Figure 4 Showing the effect of blue shift because of quantum
when we move from particle size of 9nm to parcile size of 3
nm.8
Figure 5 Emission spectra of several sizes of (Cdse)Zns core-
shell quantum dots.9
Figure 6 The optical spectra and transmission electron
bars in micrographs are all 100 nm10

Figure 7 Shows the effect of varying relative core and shell
the frequency increases11
Figure 8 shows in the following figure, the parallel and vertical
components can be experimentally selected by a linearly
polarizing filter oriented parallel or perpendicular to the
scattering plane. (Sun)12
Figure 9 Cylindrical cuvette holding sphere solution14
Figure 10 Cylindrical cuvette holding sphere solution with
polarization filter in front of detector14
Figure 11 Model for the magnetite nanowires. The sphere
represents the individual discrete dipole elements. The cross
section is 2X2 elements with a length L varied from 2 to 100
elements. In all cases the element grid spacing d = 1.0nm17
Figure 12 Calculation of the Faraday rotation of a magnetic
nanowire. The long axis of the nanowire is aligned with the (a)
x axis and (b) z axis. In both cases, the magnetic field is applied
in the z direction18
Works Cited
. P. S. Pershan. ""Magneto-optical effects." J. Appl. Phys
(2009): 38. Document.
al, Dabbousi et. "J. Phys. Chem. B ." 9463-9475 (997): 101.
Paper.
al, J.Nayak et. "J. Nayak et al., Physica." (2004: 227–233.
Document.
Annual Review of Biomedical Engineering. "Annual Review of
Biomedical Engineering." 23 4 2014.

http://www.annualreviews.org. Document. 22 1 2017.
Bhardwaj, Achal. "Optical Properties of Nanoparticles." (2016):
224.
Lin-Wang, Li J. and Wang. "Band-structure-corrected and
density approximation." International Science Congress
Association (2005): Phys.Rew. B, 72. Documnet.
Manna, Scher and Alivisats. "Cdse nanocrystals." Cluster Sci 13
(2002): 521. paper.
nanocomposix. http://nanocomposix.com. 12 2 2014. electronic.
23 2 2017.
S. J. Oldenburg, R. D. Averitt, S. L. Westcott, N. J. Halas. "
Chem. Phys. Lett. 288." (1998): 288, 243.
Sir Jhon Pendry imperial College of London. Physics World
(2000). Lecture.
Stokes, Damon A. Smith and Kevin L. "Discrete dipole
approximation for magnetooptical." Dept. of Physics and
Advanced Materials Research Institute, University of New
Orleans, New Orleans, (2006). Documnet.
Sun, Qiang Fu and Wenbo. "Mie theory for light scattering by a
spherical particle in an absorbing medium." Applied Optics Vol.
40, Issue 9 (2001): 1354-1361. Paper.
The Physics Classroom. he Physics Classroom. 3 January 1996-
2016. Document. 27 2 2017.
Zhang, Jin Zhong. "Optical Properties and Spectroscopy of
Nanomaterials." World Scientific, Singapore, 2009. (2009).
Documnet.
Zhao, Jing et al. "Resonance Localized Surface Plasmon
Spectroscopy." J. Phys. Chem. 112: (2008): 58:267–97.
Document.

What we have learned
In this study, we have learned that nanoparticles are used in a
variety of applications and their usage is growing vastly
because of their superior’s characteristics among these
properties optical properties play a vital role in various
applications and with further research became familiar with the
core principles with control the behavior of these nanoparticles
under different circumstances. The optical properties of
nanoparticles are highly dependent on the particle size, shape,
chemical composition, and the local dielectric environment. We
got valuable insight of how the behavior of the material changes
when it is in its nano state as compared to its bulk form and the
influence of the surface Plasmon’s in deciding their properties.
The use of high extinction coefficient of quantum dots and its
role in deciding the optical properties of nanoparticles is an
important factor in nanotechnology. The case of enchantment of
optical properties of nanoparticles e.g. luminescence by using
shell core arrangements provides us with valuable insight which
helps us in varying the properties of these nano particles to suit
our situations and demands. This research also provides us
information about the effect of size and shape of the particle
and dielectric properties of the medium as the surface
Plasmon’s are excited by incident electromagnetic radiation.
This paper gives us some of the prominent methods used for
calculation of optical properties of Nano particles regarding the
problem of light scattering by homogeneous spherical particles
of any size in the light of Mie theory which is further used to
calculate the model for tissue optical properties followed by an
example for shows us how to calculate angular scattering
pattern which includes the calculation of scattering cross
section and coefficient. As we go towards particle that are much
larger than the wavelength of the incident light source we
discuss discrete dipole approximation for simulation of light
scattering by particles much larger than the wavelength. A near-

field calculation of light electric field intensity inside and in the
vicinity of a scattering particle is discussed in the discrete
dipole approximation. A fast algorithm is presented for gridded
data. This algorithm is based on one matrix times vector
multiplication performed with the three-dimensional fast
Fourier transform. The approximation is used as a finite-
element method for non-spherical particles whose dimensions
are on the order of or smaller than the incident light
wavelength, λ. Also, we use the approximation to calculate
scattering from arrangements of spherical nanoparticles with
diameters ≪λ. We propose that for scattering from
subwavelength magnetic particles, the specific Faraday rotation
should be defined as the difference in optical extinction for left-
and right-circularly polarized light. We apply the model to
calculations of Faraday rotation from magnetite nanowires as
well as a binary (two-component) nanoparticle arrangement.
Enhancements in Faraday rotation are predicted for composites
containing both noble metal and ferrite nanoparticles. These
theoretical methods have vast applications and are used for
medical or bioimaging purposes enhancement of optical
properties, light-emitting devices, nonlinear optics, biological
labeling, improving the efficiency of either solar cells or the
storage capacity of electronics devices
Optical Properties of Nano particles and their Calculations

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