Resonance phenomena in one-dimensional grating-based structures
Enhanced optical transmission through metallic 1-D grating-based structures has been studied using the rigorous coupled wave analysis. The results have shown that optical transmission is determined by the waveguide properties of the grating slit, and there is a minimum width of slit for TE polarizat...
Gespeichert in:
| Veröffentlicht in: | Semiconductor Physics Quantum Electronics & Optoelectronics |
|---|---|
| Datum: | 2017 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214907 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Resonance phenomena in one-dimensional grating-based structures / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 85-90. — Бібліогр.: 22 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860295857127030784 |
|---|---|
| author | Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. |
| author_facet | Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. |
| citation_txt | Resonance phenomena in one-dimensional grating-based structures / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 85-90. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Enhanced optical transmission through metallic 1-D grating-based structures has been studied using the rigorous coupled wave analysis. The results have shown that optical transmission is determined by the waveguide properties of the grating slit, and there is a minimum width of slit for TE polarization, when high transmission occurs due to the waveguide effect. In contrast, this limitation doesn’t exist for TM polarization, and extraordinary transmission is obtained at the sub-wavelength slit. As a result, high transmission is reached due to the resonance of the electromagnetic field inside the grating slit.
|
| first_indexed | 2026-03-21T18:06:19Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
85
PACS 42.25 Bs, 42.25 Hz, 42.79 Ci
Resonance phenomena in one-dimensional grating-based structures
I.Ya. Yaremchuk1, V.M. Fitio1, Ya.V. Bobitski1,2
1Department of Photonics, Lviv Polytechnic National University,
12, Bandera str., 79013 Lviv, Ukraine
Phone: (8-032)-258-25-81, e-mail: iryna.y.yaremchuk@lpnu.ua
2Faculty of Mathematics and Natural Sciences,
University of Rzeszow, Pigonia Str.1, 35959 Rzeszow, Poland
Abstract. Enhanced optical transmission through metallic 1-D grating-based structures
has been studied using the rigorous coupled wave analysis. The results have shown that
optical transmission is determined by waveguide properties of the grating slit, and there
is a minimum width of slit for TE polarization, when high transmission occurs due to
waveguide effect. In contrast, this limitation doesn’t exist for TM polarization, and
extraordinary transmission is obtained at the sub-wavelength slit. As a result, high
transmission is reached due to resonance of electromagnetic field inside the grating slit.
Keywords: enhancement of optical transmission, grating, waveguide and surface
plasmon-polariton resonance.
Manuscript received 15.11.16; revised version received 26.01.17; accepted for
publication 01.03.17; published online 05.04.17.
1. Introduction
Enhanced optical transmission through grating-based
structures has received growing interest among
researchers due to possibility of light manipulation in a
wide wavelength region. The enhancement of optical
transmission through metallic periodic structure has been
studied a lot of years ago [1], and still interest in such
type transmission is stimulated by their applications in
fields of optics and photonics. A phenomenon of
enhanced optical transmission is explained by high
contrast between the dielectric permittivity of metal and
sub-wavelength holes [2, 3]. Moreover, the high
efficiencies of transmission and enhancements of local
field at certain wavelengths can be obtained using
specific geometry of the metal surface [4]. The main
model for studying the physical mechanism of
extraordinary transmission is one-dimensional metal
grating, since there TE and TM polarizations are
separated [5, 6]. There are a few theories to explain
phenomenon of the extraordinary optical transmission
[7-10]. In general, it is agreed that the enhanced optical
transmission occurs as a result of confined surface
plasmon-polariton modes at the interface of
metal/dielectric. In the works [11, 12], it is shown that
surface electromagnetic modes play a key role in
appearance of resonant optical transmission. However,
there are other explanations for the nature of high
enhanced transmission. Presented in the works [5, 13]
are the models, where transmission is modulated not by
coupling to the surface plasmons but by interference of
the diffracted evanescent waves, generated by sub-
wavelength features at the surface. It was indicated [5,
14] that for lamellar transmission metallic gratings, there
are two transmission resonances: one of them is coupled
to the surface plasmon-polariton modes that appear on
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
86
horizontal surfaces of the metallic grating, and the
second one is related to the waveguide modes or cavities
located inside the slits. In the work [15], the influence of
two different mechanisms on the diffraction efficiencies –
waveguide and surface plasmon-polariton resonances
excited in the structure was studied. However, in scientific
publications one can find a lot of researches aimed at TM
polarization waves and corresponding transmission
spectral dependences of the grating. Simultaneously,
researches regarding TE polarization can explain the
anomaly of enhanced transmission in these gratings [16-
18]. Moreover, the elements based on this mechanism can
demonstrate novel optical properties and offer new
functional capabilities. The primary application of these
resonant periodic structures is to design narrow-band
reflection filters. Understanding the coupling of waves in
metallic micro- and nanostructures has fundamental
interest and practical importance in designing the optical
devices that could become important elements for future
micro- and nanooptical systems.
In this work, the grating-based structures
transmitting TM and TE polarized light have been
investigated. Comparison between transmissions of the
TE and TM polarizations contributes to understanding
the origin of enhanced optical transmission in submicron
structures. Particularly, we have researched the intensity
of the fields distributed inside the slit and on the surfaces
of the metallic 1-D grating. This allowed us to explain
nature of the resonances and to determine conditions for
high transmission.
2. Results and discussions
The mechanism of extraordinary optical transmission
through grating-based structures was studied using the
rigorous coupled-wave analysis (RCWA) [19, 20].
Specifically, the RCWA and analytical transmission
functions based on the same principles [5, 14, 21] are in
very good agreement with different experimental results
in various geometries. The dielectric function of
materials and electromagnetic fields were expanded in a
Fourier series when applying the RCWA method to one-
dimensional grating-based structures. Infinite series of
coupled equations was formed when substituting both
Fourier series into Maxwell’s equations. RCWA reduces
the electromagnetic field calculation to an algebraic
eigenvalue problem. The problem is described by the
system of linear differential equations for TE and TM
polarizations, respectively [22].
At the first stage of our researches, we have
performed numerical calculations of transmission (T) as
well as sum of transmission and reflection (T+R) versus
the thickness of one-dimension metallic grating for the
wavelength 1.5 μm with the following parameters: the
grating period (Λ), width (a) and height (dm) of the slit.
The layers bounding the structure are characterized by
dielectric constants ε1, ε3, groove and ridge – by ε21, ε22,
correspondingly (see Fig. 1).
Fig. 1. Schematic structure of the grating.
The parameters of the grating for TE and TM
polarization are as follows: Λ = 1.3 μm, ε21 = 9.0, a =
0.26 μm; Λ = 1.46 μm, ε21 = 1.0, a = 0.143 μm [7].
Silver (Ag) was chosen as grating material due to typical
noble metal properties. The dielectric constant of silver
was extrapolated using the equation
( )22
22 71.038.0544 λ+λ+λ−=ε i for the wavelengths
1 μm ≤ λ ≤ 2 μm. The results of calculations are
presented in Fig. 2a (for TE) and in Fig. 2b (for TM). It
is easy to see that high optical transmission can be
obtained for both TE and TM polarizations. Fig. 2
indicates that in local maxima of transmission the
reflection is low and, when the grating depth increases,
then absorption increases in the grating.
At first, let us consider the case of TE polarization
in detail. Fig. 3 shows the calculated transmission and
sum of transmission and reflection spectra for the silver
grating. The parameters used in these calculations are as
follows: ε21 = 9.0, a = 0.26 μm and Λ = 1.0 μm.
Numbers near the curves indicate the grating depth
expressed in micrometers. Fig. 3 indicates that
transmission in local points decreases when the
wavelength increases, and it is close to zero for the
wavelengths longer than 1.8 μm. These facts can be
explained by absence of the waveguide effect inside the
slit for the wavelengths longer than 1.8 μm (for TE
polarization). Therefore, the slit represents a
microresonator for a certain wavelength, which forms
standing and travelling waves. This conclusion is
confirmed by Fig. 3, which represents distribution of the
tangential component of the modulus of electric field
intensity along the coordinate x, i.e. along the period of
grating for the grating depth dm = 0.05 μm (Fig. 4a) and
for dm = 0.2807 μm (Fig. 4b) and wavelength 1.1 μm.
In Fig. 4, the curve 1 corresponds to the field
distribution calculated at z = 0, the curve 2 is calculated
at 4mdz = , curve 3 is calculated at 2dz = , curve 4 is
calculated at 43dz = , and curve 5 is calculated at
z = d, where d is the slit depth. The curve 3 (Fig. 4a)
describes the field distribution in the antinodes of the
standing wave. The curves 2 and 4 (see Fig. 4b)
correspond to the antinodes of standing wave, and the
curve 3 corresponds to the node of the standing wave.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
87
Fig. 2. Transmission and the sum of transmission and reflection spectra on the grating depth.
Fig. 3. Transmission, sum of transmission and reflection spectra vs. the wavelength for different grating depths at TE polarization.
Fig. 4. Distributions of the tangential component for the modulus of electric field intensity along of the gratings period at the
wavelength 1.1 μm for different grating thicknesses: 0.05 μm (a) and 0.2807 μm (b), respectively.
The field intensity exceeds the unitary amplitude of
the incident wave by several times within the grating slit,
and it is less than unity outside the slits. Electromagnetic
field is concentrated above the slit at certain grating
parameters, when the resonance of field appears inside
the slit. As a result, we have obtained extraordinary
transmission with the simultaneous enhancement of
absorption. It should be noted that modules of the field
intensities are practically equal at the points that are
symmetric relatively to the plane 2dz = .
More detailed analysis shows that the following
expression is correct:
( ) ( ) ( )zdxEzxE x
m
x −−≈ + ,1, 1 , (1)
where m = 1, 2, 3, …. As it follows from (1), for even
numbers m at 2dz = , node of the standing wave is
located inside the slit, and for odd m there is an antinode
of the standing wave.
In the case of TM polarization, spectral curves
(Fig. 5) have been calculated at ε21 = 1.0, a = 0.143 μm
and Λ = 1.0 μm. The numbers near the curves indicate
the grating depth in micrometers. The curve with the
number 0.01 represents transmission of the metallic thin
film placed in medium with the refractive index 1.0.
There is only one propagation mode inside the slit
unfilled with dielectric.
One can see that the transmission for the wavelength
in the range of 1 μm is significantly less than that for the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
88
Fig. 5. Transmission, sum of transmission and reflection spectra of the silver grating with different grating depths at TM
polarization.
Fig. 6. Distributions of the tangential component for the electric field intensity moduli along the grating period for the grating
depth 1.0 μm at different wavelengths: 1.02355 μm (a) and 1.349 μm (b); for the grating depth 0.05 μm at the wavelength
1.00816 μm: (c) the imaginary part of the metal dielectric constant was taken into account in calculations; (d) imaginary part of the
metal dielectric constant was neglected.
longer wavelengths (e.g., at the wavelength 1.01 μm for
the thickness 0.05 μm (see the insert in Fig. 5a). In these
cases, absorption increases in the grating, and respective
peaks are narrower than others. Closeness of values for
these wavelengths to the grating period indicates that this
effect can be caused by surface plasmon-polariton
resonance on the grating surface. This fact is confirmed by
the dependences of distribution inherent to the tangential
component of the intensity modulus for the electric field
along the coordinate x for the grating with the depth
1.0 μm (Fig. 6). Fig. 6a corresponds to the wavelength
1.02355 μm, and Fig. 6b corresponds to 1.349 μm. The
field intensity on the surface of metallic grating reaches 2
unities for the wavelength 1.02355 μm causing significant
surface currents and thus leading to Joule’s losses. As a
result, absorption in a narrow spectral range and relatively
low transmission are observed. The curve 3 corresponds
to the node of the standing wave, curves 2 and 4
correspond to antinodes of the standing wave for the
wavelength 1.02355 μm, d0 = 0.1108 μm, Δd =
0.4446 μm, and m = 2. Therefore, two antinodes and three
nodes of standing wave fit into the slit of the grating with
the depth 1.0 μm.
The field intensity on the surface of metallic
grating is significantly less than one unity for the
wavelength 1.349 μm, and Joule’s losses are negligible.
Thus, surface plasmon resonance is missed, and, as a
result, high transmission is observed. The curve 3
corresponds to the antinode of the standing wave, curves
2 and 4 correspond to nodes of the standing wave for
this wavelength, d0 = 0.41185 μm, Δd = 0.58815 μm,
and m = 1. These two nodes and one node of standing
wave fit into the slit of the grating with the depth
1.0 μm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
89
The modules of the field intensities at the points
symmetric relatively to the plane 2dz = are equal (like
to the case of TE polarization). More detailed analysis
shows that for diffraction wave of TM polarization by
the binary metallic grating the following expression can
be applied:
( ) ( ) ( )zdxEzxE x
m
x −−≈ ,1, , (2)
where m = 1, 2, 3, …. As it follows from (2), for odd
numbers m at 2dz = , the node of the standing wave
lies inside the slit, and for even m there is an antinode of
the standing wave, i.e. the situation is opposite to the
case of TE polarization. Eqs. (1) and (2) indicate that for
even m the field distribution by grating at TE
polarization describes the sum of both the symmetric and
asymmetric functions relatively to the axis z. It should be
noted that the value of symmetric function is much less
than that of the asymmetric one at TE polarization, and
vice versa for TM one. The situation is opposite for odd
m. This conclusion was made on the base of numerical
calculations of the field distribution inside the slit and on
the grating surface. According to these calculations, if
we move inside the slit from z = 0 (if slit is long
enough), the first will be the antinode of standing wave,
then the second node of standing wave, then again
antinode etc. for TE polarization. The situation is
opposite for TM polarization.
One can conclude that the plasmon resonance on
grating surface results in Joule’s losses and low
transmission. This conclusion is confirmed by Figs. 6c
and 6d, which shows distribution of the intensity
modulus for electric field along the grating period for the
following parameters: wavelength 1.00816 μm, grating
depth 0.05 μm. Fig. 6c shows the results when the
imaginary part of the dielectric function for silver was
taken into account. The calculation results, in case when
imaginary part of the metal dielectric constant is
negligible, are presented in Fig. 6d. Transmission of this
grating for actual metal is 0.04 for the wavelength
1.00816 μm (see Fig. 5a). Significant field intensities
(3 a.u.) are on the grating surfaces, thus there the
plasmon resonance takes place (Fig. 6c).
One can expect significant Joule’s losses in the case
when imaginary part of the metal dielectric constant is
taken into account. In case of neglected imaginary part of
dielectric constant of metal, fields are increased on grating
boundaries with homogeneous media to 20 a.u. and inside
the slit to 50 a.u. Thus, the plasmon resonance takes place
both at the grating surface and in the slit. Transmission of
this grating equals to unity for the wavelength
1.00816 μm. Both gratings have different characteristics
at the wavelength 1.00816 μm with increasing the depth.
Transmission of the grating with losses is less than 0.04;
transmission of the grating without losses is equal to unity
at the resonance depths d0 = 0.05 μm, d1 = 0.473 μm, and
d2 = 0.911 μm. In fact, our numerical calculations show
that transmission is higher than 0.997 for all the analyzed
depths. The grating without losses has the propagation
constant 1μm1755.7 −=β and, correspondingly,
μm438.0=βπ=Δd .
4. Conclusions
The transmission and reflection of the periodic structures
based on the metallic grating have been investigated.
The resonant transmission for TM polarization is
achieved due to the waveguide effect and excitation of
plasmon-polaritons on metallic surfaces due to metallic
grating that makes a slight perturbation in the plane of
the metal. The absorption increases in the grating as a
result of the plasmon resonance, and thus the
transmittance is reduced. The waveguide effect inside
the slit is possible for any width of slit, and thus it can
provide abnormally high transmittance. The resonant
transmission for TE polarization only occurs due to the
waveguide effect, and there is a minimum width of slit,
when the waveguide effect and, consequently, high
transmission are possible. The metallic grating period
and thickness, refractive indices of grating and grating
slit are the main parameters that control the peak
positions and transmission amplitudes. This structure
can be used in the design of selective transmission
narrow-band filter for an infrared region.
Acknowledgments
The work was supported by Ministry of Education and
Science of Ukraine (grant DB\Tekton No.
0115U000427).
References
1. Ebbesen T.W., Lezec H.J., Ghaemi H.F., Thio T.,
Wolff P.A. Extraordinary optical transmission
through sub-wavelength hole arrays. Nature. 1998.
391(6668). P. 667–669.
2. Karabchevsky A., Krasnykov O., Abdulhalim I.,
Hadad B., Goldner A., Auslender M., Hava S.
Metal grating on a substrate nanostructure for
sensor applications. Photonics and Nanostructures
– Fundamentals and Applications. 2009. 7, No. 4.
P. 170–175.
3. Lindquist N.C., Nagpal P., McPeak K.M., Norris
D.J., Oh S.H. Engineering metallic nanostructures
for plasmonics and nanophotonics. Repts. Progr.
Phys. 2012. 75, No. 3. P. 036501.
4. De Ceglia D., Vincenti M.A., Scalora M., Akozbek
N., Bloemer M. Plasmonic band edge effects on the
transmission properties of metal grating. AIP Adv.
2011. 1. P. 032151-1–032151-15.
5. Cao Q., Lalanne P. Negative role of surface
plasmons in the transmission of metallic gratings
with very narrow slits. Phys. Rev. Lett. 2002. 88,
No. 5. P. 057403.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 85-90.
doi: https://doi.org/10.15407/spqeo20.01.085
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
90
6. Porto J.A., Garcia-Vidal F.J., Pendry J.B.
Transmission resonances on metallic gratings with
very narrow slits. Phys. Rev. Lett. 1999. 83, No. 14.
P. 2845.
7. Treacy M.M.J. Dynamical diffraction explanation
of the anomalous transmission of light through
metallic gratings. Phys. Rev. B. 2002. 66, No. 19. P.
195105.
8. Barbara A., Quémerais P., Bustarret E., Lopez-Rios
T. Optical transmission through subwavelength
metallic gratings. Phys. Rev. B. 2002. 66, No. 16. P.
161403.
9. Martin-Moreno L., Garcia-Vidal F.J., Lezec H.J.,
Pellerin K.M., Thio T., Pendry J.B., Ebbesen T.W.
Theory of extraordinary optical transmission
through subwavelength hole arrays. Phys. Rev. Lett.
2001. 86, No. 6. P.1114.
10. Yao N., Pu M., Hu C., Lai Z.A., Zhao Z., Luo X.
Dynamical modulating the directional excitation of
surface plasmons sources. Optik – Intern. Journal
for Light and Electron Optics. 2012. 123, No. 16.
P. 1465–1468.
11. Liu H., Lalanne P. Microscopic theory of the
extraordinary optical transmission. Nature. 2008.
452(7188). P. 728–731.
12. Garcia-Vidal F.J., Martin-Moreno L., Ebbesen T.W.,
Kuipers L. Light passing through subwavelength
apertures. Rev. Mod. Phys. 2010. 82, No. 1. P. 729.
13. Lezec H., Thio T. Diffracted evanescent wave
model for enhanced and suppressed optical
transmission through subwavelength hole arrays.
Opt. Exp. 2004. 12, No. 16. P. 3629–3651.
14. Xie S., Li H., Fu S., Xu H., Zhou X., Liu Z. The
extraordinary optical transmission through double-
layer gold slit arrays. Opt. Communs. 2010. 283.
P. 4017–4024.
15. Yaremchuk I.Y., Fitio V.M., and Bobitski Y.V.
High transmission of light through metallic grating
limited by dielectric layers. LFNM’2013. 2013. P.
74.
16. Skigin D.C., Depine R.A., Resonances on metallic
compound transmission gratings with
subwavelength wires and slits. Opt. Communs.
2006. 262. P. 270–275.
17. Fitio V.M. Transmissions of Metallic Gratings with
Narrow Slots. 2006 International Workshop on
Laser and Fiber-Optical Networks Modeling, June
29 – July 1, 2006. P. 113–116.
18. Moreno E., Martín-Moreno L., García-Vidal F.J.
Extraordinary optical transmission without
plasmons: the s-polarization case. J. Opt. A: Pure
and Appl. Opt. 2006. 8, No. 4. P. S94.
19. Moharam M.G., Gaylord T.K. Rigorous coupled-
wave analysis of planar-grating diffraction. JOSA,
1981. 71, No. 7. P. 811–818.
20. Moharam M.G., Gaylord T.K., Grann E.B.,
Pommet D.A. Formulation for stable and efficient
implementation of the rigorous coupled-wave
analysis of binary gratings. JOSA A. 1995. 12, No.
5. P. 1068–1076.
21. Benabbas A., Halte V., Bigot J. Analytical model
of the optical response of periodically structured
metallic films. Opt. Exp. 2005. 13. P. 8730–8745.
22. Yaremchuk I., Tamulevičius T., Fitio V.,
Gražulevičiūte I., Bobitski Ya., Tamulevičius S.
Numerical implementation of the S-matrix
algorithm for modeling of relief diffraction
gratings. J. Mod. Opt. 2013. 60. P. 1781–1788.
|
| id | nasplib_isofts_kiev_ua-123456789-214907 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T18:06:19Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. 2026-03-03T11:05:12Z 2017 Resonance phenomena in one-dimensional grating-based structures / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 85-90. — Бібліогр.: 22 назв. — англ. 1560-8034 PACS: 42.25 Bs, 42.25 Hz, 42.79 Ci https://nasplib.isofts.kiev.ua/handle/123456789/214907 https://doi.org/10.15407/spqeo20.01.085 Enhanced optical transmission through metallic 1-D grating-based structures has been studied using the rigorous coupled wave analysis. The results have shown that optical transmission is determined by the waveguide properties of the grating slit, and there is a minimum width of slit for TE polarization, when high transmission occurs due to the waveguide effect. In contrast, this limitation doesn’t exist for TM polarization, and extraordinary transmission is obtained at the sub-wavelength slit. As a result, high transmission is reached due to the resonance of the electromagnetic field inside the grating slit. The work was supported by the Ministry of Education and Science of Ukraine (grant DB\Tekton No. 0115U000427). en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Resonance phenomena in one-dimensional grating-based structures Article published earlier |
| spellingShingle | Resonance phenomena in one-dimensional grating-based structures Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. |
| title | Resonance phenomena in one-dimensional grating-based structures |
| title_full | Resonance phenomena in one-dimensional grating-based structures |
| title_fullStr | Resonance phenomena in one-dimensional grating-based structures |
| title_full_unstemmed | Resonance phenomena in one-dimensional grating-based structures |
| title_short | Resonance phenomena in one-dimensional grating-based structures |
| title_sort | resonance phenomena in one-dimensional grating-based structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214907 |
| work_keys_str_mv | AT yaremchukiya resonancephenomenainonedimensionalgratingbasedstructures AT fitiovm resonancephenomenainonedimensionalgratingbasedstructures AT bobitskiyav resonancephenomenainonedimensionalgratingbasedstructures |