Enhanced optical transmission of the triple-layer resonant waveguide structure
In this paper, we propose and demonstrate a novel guided-mode resonant filter based on a metallic grating sandwiched between two dielectric layers for TE polarization. A theoretical model based on rigorous coupled wave analysis has been developed. The transmission spectra of the grating-based struct...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2016
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| Цитувати: | Enhanced optical transmission of the triple-layer resonant waveguide structure / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 156-161. — Бібліогр.: 34 назв. — англ. |
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irk-123456789-1215542017-06-15T03:05:08Z Enhanced optical transmission of the triple-layer resonant waveguide structure Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. In this paper, we propose and demonstrate a novel guided-mode resonant filter based on a metallic grating sandwiched between two dielectric layers for TE polarization. A theoretical model based on rigorous coupled wave analysis has been developed. The transmission spectra of the grating-based structure show a high transmission band with the corresponding amplitude up to 70% inside the infra-red region. Moreover, the observed optical properties can be exactly tuned by the structural parameters. These properties allow using such structures as compact optical filters, and their spectral characteristics can be easily tuned and scaled. 2016 Article Enhanced optical transmission of the triple-layer resonant waveguide structure / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 156-161. — Бібліогр.: 34 назв. — англ. 1560-8034 DOI: 10.15407/spqeo19.02.156 PACS 42.25 Bs, 42.25 Hz, 42.79 Ci http://dspace.nbuv.gov.ua/handle/123456789/121554 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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In this paper, we propose and demonstrate a novel guided-mode resonant filter based on a metallic grating sandwiched between two dielectric layers for TE polarization. A theoretical model based on rigorous coupled wave analysis has been developed. The transmission spectra of the grating-based structure show a high transmission band with the corresponding amplitude up to 70% inside the infra-red region. Moreover, the observed optical properties can be exactly tuned by the structural parameters. These properties allow using such structures as compact optical filters, and their spectral characteristics can be easily tuned and scaled. |
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Article |
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Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. |
| spellingShingle |
Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. Enhanced optical transmission of the triple-layer resonant waveguide structure Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Yaremchuk, I.Ya. Fitio, V.M. Bobitski, Ya.V. |
| author_sort |
Yaremchuk, I.Ya. |
| title |
Enhanced optical transmission of the triple-layer resonant waveguide structure |
| title_short |
Enhanced optical transmission of the triple-layer resonant waveguide structure |
| title_full |
Enhanced optical transmission of the triple-layer resonant waveguide structure |
| title_fullStr |
Enhanced optical transmission of the triple-layer resonant waveguide structure |
| title_full_unstemmed |
Enhanced optical transmission of the triple-layer resonant waveguide structure |
| title_sort |
enhanced optical transmission of the triple-layer resonant waveguide structure |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2016 |
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http://dspace.nbuv.gov.ua/handle/123456789/121554 |
| citation_txt |
Enhanced optical transmission of the triple-layer resonant waveguide structure / I.Ya. Yaremchuk, V.M. Fitio, Ya.V. Bobitski // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 156-161. — Бібліогр.: 34 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT yaremchukiya enhancedopticaltransmissionofthetriplelayerresonantwaveguidestructure AT fitiovm enhancedopticaltransmissionofthetriplelayerresonantwaveguidestructure AT bobitskiyav enhancedopticaltransmissionofthetriplelayerresonantwaveguidestructure |
| first_indexed |
2025-07-08T20:06:39Z |
| last_indexed |
2025-07-08T20:06:39Z |
| _version_ |
1837110610824790016 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 156-161.
doi: 10.15407/spqeo19.02.156
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
156
PACS 42.25 Bs, 42.25 Hz, 42.79 Ci
Enhanced optical transmission of the triple-layer resonant
waveguide structure
I.Ya. Yaremchuk1, V.M. Fitio1, Ya.V. Bobitski1,2
1Lviv Polytechnic National University, Department of Photonics,
12, Bandera str., 79013 Lviv, Ukraine
Phone: 8-032-2582581, e-mail: iryna.y.yaremchuk@lpnu.ua
2Faculty of Mathematics and Natural Sciences,
University of Rzeszow, Pigonia Str. 1, 35959 Rzeszow, Poland
Abstract. In this paper, we propose and demonstrate a novel guided-mode resonant filter
based on a metallic grating sandwiched between two dielectric layers for TE polarization.
A theoretical model based on rigorous coupled wave analysis has been developed. The
transmission spectra of the grating-based structure show a high transmission band with
the corresponding amplitude up to 70% inside the infra-red region. Moreover, the
observed optical properties can be exactly tuned by the structural parameters. These
properties allow using such structures as compact optical filters, and their spectral
characteristics can be easily tuned and scaled.
Keywords: filter, transmission, wave-guide resonance.
Manuscript received 19.01.16; revised version received 27.04.16; accepted for
publication 08.06.16; published online 06.07.16.
1. Introduction
Extraordinary transmission and directional beaming of
light through grating structures have attracted much
attention due to their fundamental importance for
manipulating light at a subwavelength scale [1] and
potential applications in optics and photonics [2–4].
Interest in the extraordinary optical transmission process
arises due to high available contrast between the metal
and the subwavelength apertures. Moreover, the
extraordinary optical transmission offers the prospect of
a multitude of applications, since remarkably high
transmission efficiencies and, concomitantly, high local
field enhancements at certain wavelengths can be
achieved through the geometry of metal surface [5]. The
explanation of the extraordinary optical transmission is
still under debate [6–9], although many different theories
have been reported to explain this phenomenon [10–13].
It is shown [14, 15] that surface electromagnetic modes
play a key role in the emergence of the resonant
transmission. However, in works [16–18] it was reported
that there are two transmission resonances for lamellar
transmission metallic gratings: one of them is coupled to
the surface plasmon polaritons modes on both the
horizontal surfaces of the metallic grating, and the
second one is related to the cavity or waveguide modes
located inside the slits. However, in scientific literature
one can find a lot of researches aimed at using only TM
polarization waves and corresponding spectral
dependences of the grating transmission. At the same
time, the transmission dependence for TE polarization
on the thickness and characteristics of the structures can
give useful information to explain the anomaly high
transmission of such gratings [19–22]. On the other
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 156-161.
doi: 10.15407/spqeo19.02.156
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
157
hand, the elements exploiting this mechanism can
demonstrate novel optical properties and offer new
possibilities. Understanding the coupling of waves by
metallic nanostructures has fundamental interest and
practical importance in designing optical devices that
could become important elements for future nano-optical
systems. The primary application of such resonant
periodic structures are: filters based on a dielectric layer
sandwiched between two metal–dielectric gratings [23];
resonant waveguide-metallic subwavelength grating
[24]; subwavelength compound metallic grating
deposited on the waveguide structure [25]; nano-deep
corrugated long-period waveguide gratings [26] etc.
In this work, the intensity of distribution fields
inside the slit and on the surfaces of the metal grating
sandwiched between two dielectric layers have been
researched. This allowed us to explain nature of the
resonances and to determine conditions for the high
transmission. It has been demonstrated that metallic
grating sandwiched between two dielectric layers can
give rise to the enhanced transmission phenomena in the
infrared region without the surface plasmon-polariton
modes. The proposed structure allows enhanced
transmission for the TE polarized field in a narrow band
of wavelengths. The value and position of the
transmission peak strongly depend on the structure
geometric parameters.
2. Theoretical background
The mechanism of extraordinary optical transmission
through grating-based structures is studied by rigorous
coupled-wave analysis (RCWA) [27–29]. Specifically,
the RCWA and analytical transmission functions based
on the same principles [7, 17, 30, 31] are in very good
agreement with various experimental results in different
configurations. Using the RCWA method to the periodic
structure shown in Fig. 1, the dielectric function of
materials and electromagnetic fields are expanded in a
Fourier series. An infinite series of coupled equations is
created 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 [32]:
on,polarizatiTMfor
on,polarizatiTEfor
122
2
212
2
FBFBBF
GBGBBG
m
e
dz
d
dz
d
==
==
(1)
where G and F are the vectors containing the
expansion coefficients of the electric and magnetic
fields, respectively; ,I 11
001 jjpj kkikik −− ε+−=B
1
02
1 −
ε
−=
jp
ikB , jpε is the Toeplitz matrix composed
of the coefficients of expansion of the grating material
dielectric constant in the Fourier complex series, I – unit
matrix, 2
jk – diagonal matrix, elements of which equal
to 2
jxk ,
Λ
π
−=
2
,0, jkk xxj , 0,11,0 sin2
θε
λ
π
=xk , 0,1θ –
angle of incidence of the plane wave in surrounding
medium.
The reader may refer to several papers [27, 28, 32]
describing in detail the mathematical procedure used in
this simplified model.
The enhanced transmission can be obtained for the
grating with the thickness defined by the expression
[19]:
( ) ( ) dmddmddd Δ−+=Δ−++= 11 01311max , (2)
where 11d , 13d are parts of grating thickness that are
adjoining to 1 and 3 homogeneous media and are
defined by the grating parameters, the wavelength and
dielectric constants of the corresponding medium;
,...3,2,1=m ; dΔ is determined by the propagation
constant β inside the slit, according to the expression
( )βπ=Δ Red [33]. The propagation constant β can be
expressed according to TE and TM waves as follows:
( ) ( ) ))cos()sin(()sin()cos( uvuuuuvuuwD −−+=β , (3)
,)cos()sin(
)sin()cos()(
222222
222221
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ε
−
εε
−
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ε
+
εε
=β
uvuuu
uvuuwD
(4)
where a is the attenuation constant, 22
21 β−ε= kau ,
22
22 β−ε== kiavw , λπ= 2k . The waveguide
modes with β constant, for which 0)( =βD , can be
only propagating.
Fig. 1. Geometry of the metallic grating sandwiched between
two dielectric layers.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 156-161.
doi: 10.15407/spqeo19.02.156
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
158
It should be noted that β constant, which has been
determined on the base of the equations (3) and (4), is
satisfied by the expression:
β≈μ− i , (5)
where μ is the eigenvalue of eB or mB matrix of the
system equation (1). The number of accounted
diffraction orders for the diffraction analyses (dimension
of matrix eB or mB ) determines accuracy of
determining the propagation constant.
3. Results and discussions
It is known that subwavelength metallic grating covered
with a thin dielectric layer shows extraordinary optical
transmission under TE polarization. Since, excitation of
TE-polarized dielectric waveguide modes inside the
dielectric film strongly increases the TE-polarized
transmission [34]. We present series of calculations for
TE-polarized light being normally incident on the
structure with the following grating parameters:
0.922 =ε , mε=ε21 , μm3.1=Λ , and μm143.0=a to
research the mechanism of the enhanced transmission by
the metallic grating sandwiched between two dielectric
layers (see Fig. 1). The dielectric constant of dielectric
layers is 0.9=εd .
The waveguide effect with low attenuation inside the
slit is impossible for such grating parameters. The
propagation constant is ( ) 1μm23.110715.0 −−=β i for
this slit. Therefore, binary metallic grating with the depth
1.0 μm and without dielectrics layers has transmission less
than 0.0001 [19]. If the grating is confined by the
dielectric layers realizing the waveguide effect, then one
can achieve the enhanced transmission (Fig. 2).
Fig. 2a shows dependences of the transmission and
reflection for the lowest resonance thickness of the
dielectric layers dd at the grating depth 0.2 μm, the
operating wavelength is 1.5 μm. One can see that
significant transmission at a fixed thickness of the
dielectric layers is possible. One can also suppose that
such high transmission is a result of the waveguide effect
in the dielectric layers. The lowest resonance thickness of
the dielectric layer depends on the grating depth. Grating
depth dm = 0.1 μm corresponds to the thickness of
dielectric layers dd = 0.1146 μm, dm = 0.2 μm,
respectively, to dd = 0.1204 μm, and dm = 0.3 μm to dd =
0.1212 μm. It must be noted that thicknesses of dielectric
layers are equal and designated as dd. Thus, the grating
depth has only insignificant effect on the resonant
thickness of the dielectric layers. This result agrees with
the waveguide theory, so far as the phase of the reflected
wave at the boundary between dielectric and metal
changes a bit with changing the thickness of metallic film
within the range 0.1…0.3 μm. The waveguide modes,
which are distributed inside the adjacent slits, together do
not interact due to the fact that the electromagnetic field
penetrates into the metal to a depth of the skin layer.
Fig. 2b shows the dependences of transmission and
reflection on the grating depth for the thickness of
dielectrics layers 0.1204 μm. The transmission approaches
to zero, when the grating depth increases up to 0.6 μm. On
the other hand, reflection doesn’t reach unity. The
transmission is higher than 0.69 at the grating depth
0.2 μm.
Fig. 3 shows the dependence of transmission on the
wavelength. The transmission has singularity within a
narrow spectral band, which can be explained by a
resonance.
Fig. 2. The calculated dependence of transmission and
reflection spectra of the metallic grating.
Fig. 3. The calculated transmission spectrum of the metallic
grating placed between two dielectric layers with the thickness
of dielectric layers 0.1204 μm and that of the grating depth
0.2 μm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 156-161.
doi: 10.15407/spqeo19.02.156
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
159
Distribution of the modulus electric field intensity
along the coordinate x , i.e., along the grating period, is
presented in Fig. 4. The curves 1 and 5 correspond to the
field distribution at the boundary of the dielectric layers
and the homogeneous media with the dielectric constant
0.1=ε ( 31 ε=ε=ε ); curves 2 and 4 correspond to the
field distribution near the boundary between grating and
dielectrics layers; curve 3 corresponds to the field
distribution in the middle of the grating placed between
two dielectric layers on the thickness of dielectric layers
at the constant grating depth 0.2 μm (a) and on grating
depth at the constant thickness of the dielectric layers
0.1204 μm (b).
Fig. 4a presents the calculation results when the
imaginary part of dielectric constant of metal was taken
into account. The results presented in Fig. 4b correspond
to the case when imaginary part of the dielectric constant
of metal is negligible. One can see that, in the case of
neglected imaginary part of dielectric constant of metal,
the transmission is equal to unity and the reflection is
equal to 0. There is excellent coincidence of curves 1, 5
and 2, 4 for this case.
Fig. 4. The distributions of tangential component of the
modulus of electric field intensity along the grating period for
the thickness of dielectric layers 0.1204 μm and that of the
grating depth 0.2 μm: (a) the imaginary part of the dielectric
constant for metal was taken into account in calculations, (b)
imaginary part of the dielectric constant for metal is negligible.
The points represent curve 4 and 5 in (b).
The amplitudes of the field in arbitrary units are
significantly higher than the unity amplitude of the
incident wave. Thus, resonance of field occurs in the
dielectric layers. On the other hand, the intensity of this
resonance is determined by the grating depth. Curves 1,
5 and 2, 4 are separated with the increase of the grating
depth. In this case, the field decreases inside the slit, if
the imaginary part of the dielectric constant of metal is
taken into account. The resonance is missed inside the
slit, since the propagation constant has large imaginary
component in the slit.
One can consider that two waveguides (resonators)
are interconnected by the slit and the coupling
coefficient is determined by the length of slit (grating
depth). High transmission is achieved as a result of
intense field that is formed by the grating in the
dielectric layer over the slit. This mechanism of the
enhanced transmission is impossible for TM
polarization, since the propagation constant has a
insignificant imaginary part even for the slit width much
less than the wavelength. Therefore, presence of the
dielectric layers only decreases transmission as a result
of propagation of the wave under participation of the
dielectric layers like that in a waveguide. This gives
additional losses of electromagnetic energy caused by
the interaction field with the metallic surface.
4. Conclusions
The resonant transmission for TE polarization occurs
due to the waveguide effect, and there is a minimum
width of slit, where the waveguide effect and,
consequently, high transmission are possible. Optical
transmission of the metallic grating sandwiched between
two dielectric layers is found to be surprisingly large at
particular wavelengths for TE polarization. Resonant
transmission is achieved as a result of the intense field
formed by the grating inside the dielectric layer over the
slit. The transmission profile can be adapted by adjusting
four major parameters: the metallic grating period and
thickness, thickness of dielectric layers and refractive
indices of grating and dielectric layers. The high
transmission of the metallic grating confined between
dielectric layers opens up a new dimension in the design
and operation of selective narrow-band filters.
Acknowledgments
The work was supported by Ministry of Education and
Science of Ukraine (grant DB\Tekton no 0115U000427).
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