Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires
We consider the two-dimensional scattering of the H-polarized electromagnetic plane waves of the visible range by three types of gratings made of periodically arranged circular cylindrical sub-wavelength wires. Using the field expansions in local coordinates and addition theorems for cylindrical...
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| Date: | 2012 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
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| Cite this: | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires / D.M. Natarov, R. Sauleau, A.I. Nosich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 204-208. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859471197867081728 |
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| author | Natarov, D.M. Sauleau, R. Nosich, A.I. |
| author_facet | Natarov, D.M. Sauleau, R. Nosich, A.I. |
| citation_txt | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires / D.M. Natarov, R. Sauleau, A.I. Nosich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 204-208. — Бібліогр.: 8 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | We consider the two-dimensional scattering of the H-polarized
electromagnetic plane waves of the visible range by three types of gratings made of
periodically arranged circular cylindrical sub-wavelength wires. Using the field
expansions in local coordinates and addition theorems for cylindrical functions, we
obtain a block-type matrix equation for the field expansion coefficients. This equation is
of the Fredholm second-kind form that guarantees convergence of numerical solution.
The scattering and absorption cross-sections and the near-field patterns are computed.
The interplay of plasmon and grating-type resonances is studied for two and three-layer
gratings of identical periods, stacked two-period gratings, and in-line two-period gratings
made of nano-diameter silver wires.
|
| first_indexed | 2025-11-24T09:08:34Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 204-208.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
204
PACS 42.79.Dj, 78.35.+c
Resonance scattering and absorption of light
by finite two-period gratings of circular silver nanowires
D.M. Natarov1, R. Sauleau2, A.I. Nosich1
1Institute of Radio-Physics and Electronics, NAS of Ukraine,
12, Proskury str. 61085 Kharkiv, Ukraine
E-mail: den.natarov@gmail.com
2IETR, University of Rennes 1, Campus Beaulieu, bat 11-D, 35042 Rennes Cedex, France
E-mail: ronan.sauleau@univ-rennes1.fr
Abstract. We consider the two-dimensional scattering of the H-polarized
electromagnetic plane waves of the visible range by three types of gratings made of
periodically arranged circular cylindrical sub-wavelength wires. Using the field
expansions in local coordinates and addition theorems for cylindrical functions, we
obtain a block-type matrix equation for the field expansion coefficients. This equation is
of the Fredholm second-kind form that guarantees convergence of numerical solution.
The scattering and absorption cross-sections and the near-field patterns are computed.
The interplay of plasmon and grating-type resonances is studied for two and three-layer
gratings of identical periods, stacked two-period gratings, and in-line two-period gratings
made of nano-diameter silver wires.
Keywords: plasmon resonance, grating resonance, finite grating, nanowire, scattering,
absorption, cross-section.
Manuscript received 08.05.12; revised version received 08.06.12; accepted for
publication 14.06.12; published online 25.09.12.
1. Introduction
Two fundamental effects are known to influence the
scattering of light by periodically structured metal
scatterers. On the one hand, surface-plasmon resonances
are observed for sub-wavelength noble-metal particles
and wires in the mid-infrared and optical bands [1, 2].
Nanosize objects can exhibit resonance behavior at
certain frequencies for which the object permittivity is
negative. This results in powerful enhancement of
scattered and absorbed light that is used in the design of
optical antennas and biochemical sensors for advanced
applications. In the leading terms, the plasmon
resonance wavelength depends on the object shape but
not on its dimensions.
On the other hand, periodically structured
scatterers, or finite and infinite gratings, arrays or chains
of particles and holes in metallic screens (in D-3 ) or
wires and slots (in D-2 ), are attracting large attention
of researchers in today nano-optics [ 6-3 ]. This is
caused by the effects of extraordinarily large reflection,
transmission, emission, and near-field enhancement that
have been found in the scattering of light by periodic
scatterers. Recently, it has been discovered that these
phenomena are explained by the existence of the so-
called grating resonances or poles of the field function
[ 6-4 ] (a.k.a. geometrical, lattice and Bragg
resonances). Their wavelengths lay near the Rayleigh
wavelengths [7], i.e. near to period being a multiple of
the wavelength, if all elementary scatterers of a grating
are excited in the same phase, and their size is a fraction
of the period. In the wave scattering by infinite gratings,
they lead to almost total reflection of the incident field
by a sparse thin-dielectric-wire grating in narrow
wavelength bands [3, 5].
The goal of our paper is extension of this study to
more complicated periodically structured silver-wire
configurations where both plasmon and grating
resonances are present.
2. Scattering problem and its numerical solution
Consider finite collections of M parallel wires
illuminated by an H-polarized plane wave shown in
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 204-208.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
206
300 350 400 450 500
0
200
400
600
800
M=100, a=70, p=360, 1 layer
M
layer
=100, a=70, p
x
=360, p
y
=5a, 2 layers
M
layer
=100, a=70, p
x
=360, p
y
=5a, 3 layers
T
SC
S
/M
, [
nm
]
Wavelength, [nm] a
300 350 400 450 500
0
50
100
150
A
C
S
/M
, [
nm
]
Wavelength, [nm]
M=100, a=70, p=360, 1 layer
M
layer
=100, a=70, p
x
=360, p
y
=5a, 2 layers
M
layer
=100, a=70, p
x
=360, p
y
=5a, 3 layers
b
Fig. 2. Normalized per number of wires TSCS (a) and ACS (b)
as functions of the wavelength for the H-wave normal
incidence on the 1-, 2- and 3-layer gratings of identical silver
wires.
a
b
Fig. 3. Near-field amplitude patterns of the central parts of the
two- and three-layer gratings from Fig. 2 in the TSCS maxima
at the wavelengths 383 (a) and 394 nm (b). The incident plane
wave comes from the upper half-space normally to the grating.
4. Optical response of two-period stacked
and in-line gratings
Two-period linear gratings that consist of two chains or
arms with different periods are interesting for applications
because of existence of two different grating resonances,
in addition to the plasmon resonance of each individual
wire. This feature can be useful for electromagnetic
engineering of the novel wideband absorbers for solar
cells. Our analysis of such gratings have shown that it is
indeed possible to combine the resonances and enhance
the per-wire TSCS and ACS, if the wire radius is 50 nm or
larger and their number is at least 100.
Presented in Fig. 4 are per-wire TSCS and ACS as
functions of wavelength for the normal incidence of the
H-wave on the stacked and in-line double-periodic
gratings of silver nanowires with radii a = 70 nm and
periods p1 = 360 nm (180 or 179 wires) and p2 = 450 nm
(100 wires); the distance between the layers in the
stacked grating is 210 nm. One can see that the cross-
sections for the in-line configuration have more
intensive and sharper resonances of both types,
apparently because such a configuration has no part
shaded by other wires. The TSCS reaches its maximum
value at 374 and 372 nm for the stacked and in-line two-
period gratings, respectively. This resonance is
associated with the smaller period and, in part, with the
plasmon resonance of each wire. The other grating
resonance in the vicinity of the 450 nm wavelength (the
larger period value) has low intensity, especially for
ACS because the bulk losses in silver are smaller there.
300 350 400 450 500
0
100
200
300
400
500
600
700
T
S
C
S/
M
, [
nm
]
Wavelength, [nm]
M
1
=100, M=180, a=70, p
x1
=360, p
x2
=450, p
y
=5a, stacked 2-period gr.
M
1
=100, M=179, a=70, p
x1
=360, p
x2
=450, in-line 2-period gr.
a
300 350 400 450 500
0
50
100
150
200
M
1
=100, M=180, a=70, p
x1
=360, p
x2
=450, p
y
=5a, stacked 2-period gr.
M
1
=100, M=179, a=70, p
x1
=360, p
x2
=450, in-line 2-period gr.
A
C
S/
M
, [
nm
]
Wavelength, [nm] b
Fig. 4. Normalized TSCS (a) and ACS (b) as functions of the
wavelength for the H-wave normally incident on the stacked
and in-line two-period gratings of identical silver nanowires.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 204-208.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
207
a
b
Fig. 5. Near-field amplitude patterns of the central parts of the
stacked two-period grating from Fig. 4 in the grating
resonances at the wavelengths 374 (a) and 449 nm (b). The
incident plane wave comes from the upper half-space normally
to the grating.
a
b
Fig. 6. Near-field amplitude patterns of the central parts of the
in-line two-period grating from Fig. 4 in the grating resonances
at the wavelengths 372 (a) and 449 nm (b). The incident plane
wave comes from the upper half-space normally to the grating.
Presented in Figs. 5 and 6 are the near-field
amplitude patterns for the central parts of the stacked
and in-line two-period gratings, respectively, in the
grating resonances. In Fig. 5, we show the near-field
patterns at 374 and 449 nm in the grating resonances
associated with the smaller and larger periods,
respectively. Note that in the second case the field
pattern demonstrates that the top grating (tuned into
resonance) efficiently screens the bottom grating, which
remains in the deep shadow. In Fig. 6, we show near-
field patterns at 372 and 449 nm in the grating
resonances for the smaller and larger periods of the in-
line grating. In each case, the standing waves are formed
along the x and y axes, however only near the arm of the
grating that is tuned to the resonance.
5. Conclusions
We have presented results of accurate calculations of the
scattering and absorption spectra for several periodically
structured configurations made of silver nanowires, in
the visible range. They demonstrate co-existence of
plasmon resonances related to each silver wire and
several grating-type resonances in structures with more
than one period. At the wavelength of each grating
resonance, the scattering and absorption demonstrate
maxima. Visualization of in-resonance near fields shows
that the contribution to these maxima comes from the
corresponding sub-gratings whose period is tuned to the
incoming wavelength. Presented results can be useful for
the modelling of optical response of “photonic-
plasmonic molecules” and for engineering the novel
wideband absorbers for solar cells.
Acknowledgments
This work has been partially supported by the National
Academy of Sciences of Ukraine via the State Target
Program “Nanotechnologies and Nanomaterials” and the
European Science Foundation via the Research
Networking Programme “Newfocus”.
References
1. V. Giannini and J.A. Sànchez-Gil, Calculations of
light scattering from isolated and interacting
metallic nanowires of arbitrary cross-section by
means of Green’s theorem surface integral
equations in parametric form // J. Opt. Soc. Am. A,
24(9), p. 241-248 (2007).
2. D.R. Fredkin, I. Mayergoyz, Resonant behavior of
dielectric objects (electrostatic resonances) // Phys.
Rev. Lett. 91, p. 3902-3905 (2003).
3. M. Laroche, S. Albaladejo, R. Gomez-Medina, and
J.J. Saenz, Tuning the optical response of
nanocylinder arrays: an analytical study // Phys.
Rev. B, 74(9), p. 245422-10 (2006).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 204-208.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
208
4. F.J.G. Garcia de Abajo, Colloquium: Light
scattering by particle and hole arrays // Rev. Mod.
Phys. 79(4), p. 1267-1289 (2007).
5. V.O. Byelobrov, J. Ctyroky, T.M. Benson, et al.,
Low-threshold lasing eigenmodes of an infinite
periodic chain of quantum wires // Opt. Lett.
35(21), p. 3634-3636 (2010).
6. D.M. Natarov, V.O. Byelobrov, R. Sauleau,
T.M. Benson, and A.I. Nosich, Periodicity-induced
effects in the scattering and absorption of light by
infinite and finite gratings of circular silver
nanowires // Opt. Express, 19(22), p. 22176-22190
(2011).
7. H.A. Ragheb, M. Hamid, Scattering by N parallel
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8. D. Felbacq, G. Tayeb, and D. Maystre, Scattering
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|
| id | nasplib_isofts_kiev_ua-123456789-118308 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-11-24T09:08:34Z |
| publishDate | 2012 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Natarov, D.M. Sauleau, R. Nosich, A.I. 2017-05-29T16:44:41Z 2017-05-29T16:44:41Z 2012 Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires / D.M. Natarov, R. Sauleau, A.I. Nosich // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 204-208. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 42.79.Dj, 78.35.+c https://nasplib.isofts.kiev.ua/handle/123456789/118308 We consider the two-dimensional scattering of the H-polarized electromagnetic plane waves of the visible range by three types of gratings made of periodically arranged circular cylindrical sub-wavelength wires. Using the field expansions in local coordinates and addition theorems for cylindrical functions, we obtain a block-type matrix equation for the field expansion coefficients. This equation is of the Fredholm second-kind form that guarantees convergence of numerical solution. The scattering and absorption cross-sections and the near-field patterns are computed. The interplay of plasmon and grating-type resonances is studied for two and three-layer gratings of identical periods, stacked two-period gratings, and in-line two-period gratings made of nano-diameter silver wires. This work has been partially supported by the National Academy of Sciences of Ukraine via the State Target Program “Nanotechnologies and Nanomaterials” and the European Science Foundation via the Research Networking Programme “Newfocus”. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires Article published earlier |
| spellingShingle | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires Natarov, D.M. Sauleau, R. Nosich, A.I. |
| title | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| title_full | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| title_fullStr | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| title_full_unstemmed | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| title_short | Resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| title_sort | resonance scattering and absorption of light by finite two-period gratings of circular silver nanowires |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118308 |
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