Optical efficiency of Ag and Au nanoparticles
In this paper, we present the results of calculations aimed at the optical radiation efficiency of Ag and Au nanoparticles, which is defined by the ratio of the scattering cross-section to the extinction one. The calculations were performed using Mie theory formalism for surrounding medium of var...
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| Cite this: | Optical efficiency of Ag and Au nanoparticles / N.L. Dmitruk, S.Z. Malynych, I.E. Moroz, V.Yu. Kurlyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 369-373. — Бібліогр.: 14 назв. — англ. |
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Dmitruk, N.L. Malynych, S.Z. Moroz, I.E. Kurlyak, V.Yu. 2017-05-30T16:06:29Z 2017-05-30T16:06:29Z 2010 Optical efficiency of Ag and Au nanoparticles / N.L. Dmitruk, S.Z. Malynych, I.E. Moroz, V.Yu. Kurlyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 369-373. — Бібліогр.: 14 назв. — англ. 1560-8034 PACS 78.67.Bf, 81.07.Bc https://nasplib.isofts.kiev.ua/handle/123456789/118553 In this paper, we present the results of calculations aimed at the optical radiation efficiency of Ag and Au nanoparticles, which is defined by the ratio of the scattering cross-section to the extinction one. The calculations were performed using Mie theory formalism for surrounding medium of various refractive indexes. It has been shown that silver nanoparticles exhibit substantially larger optical efficiency in a broad spectral range as compared to gold nanoparticles. The optical efficiency for silver nanoparticles with diameters over 90 nm exceeds 90%. We thank Prof. G. Chumanov (Clemson University, USA) for collaboration and fruitful discussions. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Optical efficiency of Ag and Au nanoparticles Article published earlier |
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Optical efficiency of Ag and Au nanoparticles |
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Optical efficiency of Ag and Au nanoparticles Dmitruk, N.L. Malynych, S.Z. Moroz, I.E. Kurlyak, V.Yu. |
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Optical efficiency of Ag and Au nanoparticles |
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Optical efficiency of Ag and Au nanoparticles |
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Optical efficiency of Ag and Au nanoparticles |
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Dmitruk, N.L. Malynych, S.Z. Moroz, I.E. Kurlyak, V.Yu. |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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In this paper, we present the results of calculations aimed at the optical
radiation efficiency of Ag and Au nanoparticles, which is defined by the ratio of the
scattering cross-section to the extinction one. The calculations were performed using Mie
theory formalism for surrounding medium of various refractive indexes. It has been
shown that silver nanoparticles exhibit substantially larger optical efficiency in a broad
spectral range as compared to gold nanoparticles. The optical efficiency for silver
nanoparticles with diameters over 90 nm exceeds 90%.
|
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1560-8034 |
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https://nasplib.isofts.kiev.ua/handle/123456789/118553 |
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Optical efficiency of Ag and Au nanoparticles / N.L. Dmitruk, S.Z. Malynych, I.E. Moroz, V.Yu. Kurlyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 369-373. — Бібліогр.: 14 назв. — англ. |
| work_keys_str_mv |
AT dmitruknl opticalefficiencyofagandaunanoparticles AT malynychsz opticalefficiencyofagandaunanoparticles AT morozie opticalefficiencyofagandaunanoparticles AT kurlyakvyu opticalefficiencyofagandaunanoparticles |
| first_indexed |
2025-11-25T22:46:31Z |
| last_indexed |
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1850573077249785856 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 369-373.
PACS 78.67.Bf, 81.07.Bc
Optical efficiency of Ag and Au nanoparticles
N.L. Dmitruk1, S.Z. Malynych1, I.E. Moroz2, V.Yu. Kurlyak3
1V. Lashkaryov Institute of Semiconductors Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
Phone: +38(044) 525-64-86, e-mail: s.malynych@gmail.com, dmitruk@isp.kiev.ua
2National University “Lviv Polytechnica”, 12, S. Bandery str., 79013 Lviv, Ukraine
3Ivan Franko Lviv National University, 8, Kyryla & Methodiya str., 79005 Lviv, Ukraine
Abstract. In this paper, we present the results of calculations aimed at the optical
radiation efficiency of Ag and Au nanoparticles, which is defined by the ratio of the
scattering cross-section to the extinction one. The calculations were performed using Mie
theory formalism for surrounding medium of various refractive indexes. It has been
shown that silver nanoparticles exhibit substantially larger optical efficiency in a broad
spectral range as compared to gold nanoparticles. The optical efficiency for silver
nanoparticles with diameters over 90 nm exceeds 90%.
Keywords: metal nanoparticles, optical properties, light scattering.
Manuscript received 02.06.10; accepted for publication 02.12.10; published online 30.12.10.
1. Introduction
Tendency towards miniaturization of various electronic
devices as well as the development of experimental
methods for manufacturing and characterization of
nanoscale systems instigate growing interest to studying
their physical properties. Metal nanoparticles, especially
gold and silver are the most promising for practical
applications. It is well known that visible light excites
collective oscillations of free electrons inside metal
particles, which are Localized Surface Plasmon
Resonances (LSPR). In other words, LSPR are coupled
oscillations of the electron density and electromagnetic
waves. The excitation of LSPR in metal nanoparticles
represents the most efficient process by which light
interacts with matter and defines optical properties of
nanoparticles. It is also very important that LSPR
frequency could be successfully tuned within a broad
spectral range by varying the refractive index of
surrounding medium or by using the nanoparticles of
different size and shape [1]. For gold and silver
nanoparticles, the resonance falls into the visible region
of electromagnetic spectrum. A striking consequence of
this fact is bright colors exhibited by particles immersed
into transparent matrix (e.g., aqueous suspensions or
glass) both in transmitted and reflected light.
Up to date, it has been proposed a number of
practical applications of gold and silver nanoparticles
and nanoparticle arrays for needs of photonics [2],
nonlinear spectroscopy [3], submicron visualization [4],
surface-enhanced Raman and infrared spectroscopy
[5, 6], photovoltaics [7], and various sensors [8]. The
fundamental background of all the mentioned processes
is a resonant enhancement of light interaction with metal
nanoparticles, and it is crucial to minimize the losses
caused by absorption of incident light, wasted as heat, by
the metal nanoparticles for efficient energy transfer into
the active materials. It is proposed to use the ratio of the
scattering cross-section to the extinction cross-section as
a quantitative parameter that describes efficiency of
energy transfer [9]. This ratio or optical radiation
efficiency represents the fraction of the energy reradiated
from the particle out from the energy of the incident
light.
2. Localized surface resonances in metal
nanoparticles
As opposed to the surface plasmon-polaritons that are
actually electromagnetic waves coupled to the electron
plasma of a conductor and propagating along the metal–
dielectric interface plasmons in the subwavelength metal
nanoparticles are localized collective oscillations of
conducting electrons. The curved surface of the particle
exerts an effective restoring force on the driven
electrons, so that a resonance can arise, leading to field
amplification both inside and in the near-field zone
outside the particle. As a consequence, there is an
effective scattering of incident light by metal
nanoparticles just at the LSPR frequency. It also means
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
369
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 369-373.
that LSPR could be excited directly by incident light
without any phase matching techniques, as it is required
in the case of surface plasmon-polaritons.
Light extinction by small metal nanoparticles of the
spherical shape can be described using simple quasi-
static approximation provided that R << λ. In that case
polarizability defined as
m
mR
ε+ε
ε−ε
πε=α
2
4 3
0 ,
where ε0 is the vacuum permittivity, α is the
polarizability of particles, R – radius of the particle, ε
and εm are the permittivities of the particle and
surrounding medium, respectively, λ is the wavelength
in vacuum. It is apparent that the polarizability
experiences a resonant enhancement under the condition
that the denominator is minimal, i.e. Re[ε(ω)] = –2εm
(Fröhlich condition). Again, this expression is valid for
very small (R << λ) particles. In this case, the phase of
the harmonically oscillating electromagnetic field is
practically constant over the particle volume, so that one
can calculate the spatial field distribution by assuming
the simplified problem of a particle in an electrostatic
field. Then, the harmonic time dependence can be added
to the solution, once the field distributions are known.
This oscillation mode is exactly the dipole surface
plasmon of metal nanoparticle. Tanabe [9] used quasi-
static approximation to calculate the optical radiation
efficiency of nanoparticles for a number of metals at
fixed wavelengths.
However, for larger particles quasi-static
approximation is no longer valid due to retardation
effects, so a rigorous electrodynamic approach is
required. Such a theory was firstly developed by G. Mie
as early as in 1908. Nowadays, that theory is widely
used and is treated in a variety of books [10]. According
to the Mie theory, extinction, scattering, and absorption
cross-sections can be calculated by series expansion of
the internal and scattered fields into a set of partial
waves described by vector harmonics:
( ) ( LL
L
ext baL
k
C ++
π
= ∑
∞
=
Re122
1
2
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
) ,
( )( )22
1
2 122
LL
L
sca baL
k
C ++
π
= ∑
∞
=
,
scaextabs CCC −= ,
with
( ) ( ) ( ) ( )
( ) ( ) ( )mxxmxm
mxxxmxma
LLLL
LLLL
L ψ′ξ−ξ′ψ
ψ′ψ−ψ′ψ′ψ
=
( ) ( ) ( ) ( )
( ) ( ) ( )mxxmmx
mxxmxmxb
LLLL
LLLL
L ψ′ξ−ξ′ψ
ψ′ψ−ψ′ψ
= ,
where m = n/nm, n and nm – are he complex refractive
index of the nanoparticle and real refractive index of the
surrounding medium, respectively, k is the wave vector,
x = ⏐k⏐R – size parameter, ψL, ξL are Riccati-Bessel
cylindrical functions. The prime indicates differentiation
with respect to the argument. The summation index L
gives the order of the partial wave, L = 1 corresponds to
dipole fields, L = 2 – to quadrupole, L = 3 – to octupole
fields, and so on.
Thus, by calculating the values of the extinction
and scattering cross-sections one can obtain the optical
radiation efficiency of nanoparticles:
abssca
sca
ext
sca
opt CC
C
C
C
+
==η .
3. Results and discussion
The calculations of the extinction and scattering cross-
sections by Ag and Au nanoparticles where performed
using the modified version of Mie solution code [11].
For many practical purposes, especially in biophysics
and sensorics, it is necessary to take into account the
influence of surrounding medium on optical properties
of nanoparticles. Fig. 1 depicts spectral dependences of
the optical radiation efficiency ηopt for spherical gold and
silver nanoparticles of various diameters immersed into
different surrounding media, namely: air, water, and
fused silica. Note that optical efficiency of Au
nanoparticles spreads over substantially narrower
spectral range due to the strong interband transition at
~2.4 eV (515 nm).
It is seen from Fig. 1 that the optical efficiency of Au
and Ag nanoparticles has a trend to increase with
increasing the particles’ diameter. It occurred firstly due
to increasing of the polarizability of larger particles,
secondly as a consequence of fast scaling of the
scattering cross-section (~R6) as compared to R3 scaling
of the absorption cross-section [12]. Calculations of the
electric field distribution around the particle also
confirm the size influence on the optical efficiency. In
Fig. 2, the electric field distribution around Ag
nanoparticles with the diameters 60 and 100 nm is
shown. The curves correspond to the electric field
distribution along Oy direction, while incident beam
propagates along z direction with polarization plane xz.
One can see that for larger particles the electric field
close to the particle’s surface is more strong leading to
the enhancement of the light-nanoparticle interaction.
Thus, 100-nm silver nanoparticles act as more efficient
scatterers. The calculations were performed employing
field simulator freely available online [13].
Apparently, the size of the particles cannot be increased
indefinitely where geometrical optics laws take place,
while in Mie theory formalism the particles must be
smaller than the optical wavelength. Quasi-static
approximation also yields only rough values of the
optical efficiency. From the calculations performed by
Tanabe [9], it follows that the optical efficiency of silver
nanoparticles in the visible spectral range exceeds 90%,
370
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 369-373.
Fig. 1. Optical radiation efficiency of Ag (left-hand panel) and Au (right-hand panel) nanoparticles in air (nm = 1), water
(nm = 1.33) and fused silica (nm = 1.46). The lowest curves in all the plots correspond to the particles diameter of 20 nm, while
the highest ones to the diameter of 200 nm with the 10-nm step.
when the particles’ diameter reaches 150 nm. This value
is rather underestimated, since the corresponding
diameter obtained from the Mie theory amounts 90 nm.
Fig. 3 depicts the diagram particle diameter – spectral
range that represents the lines of the same optical
efficiency of Ag and Au nanoparticles in air at 90 and
95%.
Surrounding medium constitutes another important
issue, which determines optical properties of the
nanoparticles. Its influence was thoroughly studied in
[1, 13]. In particular, it has been shown that the
extinction maxima in the wavelength scale red-shift
linearly with increasing the refractive index of the
medium [13]. In the cited papers, only spectral position
of the extinction maxima with nm is discussed, while the
absolute values of the maxima are not considered. It is
established that extinction (scattering) cross-sections
increase with increasing nm.
Fig. 1 demonstrates that optical efficiency curves
do not exhibit notable spectral changes in different
surrounding media. Besides, the values of ηopt increase
with increasing the refractive index of surroundings. It
can be explained from the fact that metals possess the
negative permittivity. In that case, the optical contrast
increases with increasing nm following by domination of
scattering over the absorption. In a sense, surrounding
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
371
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 369-373.
medium amplifies the effect from metal nanoparticles.
Augmentation of the optical efficiency due to increasing
of nm is more notable for the particles with a diameter of
20-70 nm. For larger particles, the increase of the optical
efficiency with the refractive index of surrounding
medium is less pronounced.
Fig. 2. Electric field distribution around 60-nm ( ) and 100-
nm ( ) diameter silver nanoparticles embedded in air (nm = 1).
R and R0 denote a distance from the surface of the particle and
radius of the particle, respectively.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 3. The diagram diameter – spectral range representing the
optical efficiency of 90-nm Ag and Au nanoparticles in air.
The same intensity lines of the optical efficiency at the values
of 0.9 and 0.95 are shown.
4. Conclusions
The optical radiation efficiency of metal nanoparticles or
energy fraction of the incident light reradiated from the
particle, but not wasted as heat due to absorption is one
of the important characteristic of the nanoparticles.
Using the Mie theory, we calculated the extinction and
scattering cross-sections of gold and silver spherical
nanoparticles of various diameters and obtained optical
efficiencies defined by the ratio of the scattering cross-
section to the extinction cross-section. The calculations
were performed for different surrounding media,
namely: air, water, and fused silica. Silver nanoparticles
exhibit a larger optical efficiency in a broad spectral
range than the gold ones of the same diameter. The
optical efficiency for both metals has a trend to increase
with growing the particles’ size. For 90-nm silver
nanoparticles, the optical efficiency exceeds 90% over
the whole visible range. The optical efficiency of Au and
Ag nanoparticles increases, when nanoparticles are
embedded into the medium with higher refractive index.
The obtained data might be useful for the selection of
materials and sizes of nanoparticles for various
photonics devices.
Acknowledgments
We thank Prof. G. Chumanov (Clemson University,
USA) for collaboration and fruitful discussions.
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© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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