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# Four-channel optical demultiplexer based on hexagonal photonic crystal ring resonators

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## Abstract

In this paper, photonic crystal ring resonators with hexagonal lattice structure are used to design a four-channel optical demultiplexer. The structure size, the average transfer coefficient, the quality factor, and the channel spacing are equal to 424.5 µm², 95.8%, 1943, and 2 nm, respectively. The average crosstalk is also computed to be −18.11 dB. In this study, the plane wave expansion (PWE) and finite-difference time-domain (FDTD) methods are used, respectively, to characterize the photonic bandgap and to investigate the optical behavior of the structure. The proposed design can be used in dense wavelength division multiplexing (DWDM) systems.
1 23
Optical Review
ISSN 1340-6000
Volume 24
Number 4
Opt Rev (2017) 24:605-610
DOI 10.1007/s10043-017-0353-8
Four-channel optical demultiplexer
based on hexagonal photonic crystal ring
resonators
Vahid Fallahi, Mahmood Seifouri, Saeed
Olyaee & Hamed Alipour-Banaei
1 23
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REGULAR PAPER
Four-channel optical demultiplexer based on hexagonal photonic
crystal ring resonators
Vahid Fallahi
1
Mahmood Seifouri
1
Saeed Olyaee
2
Hamed Alipour-Banaei
3
Received: 10 March 2017 / Accepted: 29 June 2017 / Published online: 5 July 2017
ÓThe Optical Society of Japan 2017
Abstract In this paper, photonic crystal ring resonators
with hexagonal lattice structure are used to design a four-
channel optical demultiplexer. The structure size, the
average transfer coefﬁcient, the quality factor, and the
channel spacing are equal to 424.5 lm
2
, 95.8%, 1943, and
2 nm, respectively. The average crosstalk is also computed
to be -18.11 dB. In this study, the plane wave expansion
(PWE) and ﬁnite-difference time-domain (FDTD) methods
are used, respectively, to characterize the photonic bandgap
and to investigate the optical behavior of the structure. The
proposed design can be used in dense wavelength division
multiplexing (DWDM) systems.
Keywords Demultiplexer Photonic crystal Bandgap
Ring resonator FDTD
1 Introduction
Wavelength division multiplexing is a technique which
uses optical ﬁber to carry many separate and independent
optical channels. To increase the bandwidth of communi-
cation, wavelength division multiplexing is used. By
reducing the channel spacing, one can increase the
transmission capacity of wavelength division multiplexed
systems [1]. There are several platforms on which WDM
can be designed and fabricated, one of which is the use of
photonic crystals (PhCs) [2].
Photonic crystals can provide an optical medium in
which the refractive index changes periodically [3,4]. The
most important feature that reveals the practical signiﬁ-
cance of photonic crystals is the photonic bandgap (PBG).
The photonic bandgap determines the energy or frequency
range, for which light propagation in photonic crystals is
not allowed, so that by creating some defects, the light
within the structure can be controlled [5]. Moreover, PhCs
can enable compact and efﬁcient photonic devices and also
their large-scale integration. What sets photonic crystals
apart from the conventional integrated optical circuits is
their ability to interact with light on a wavelength scale,
thus allowing the creation of devices, components, and
circuits that are several orders of magnitude smaller than
currently possible [6].
The photonic crystals are applicable with or without
controlled defects in the structure [79]. Among various
defects, ring resonators are more taken into consideration
due to their speciﬁc characteristics including ease of design
and higher sensitivity compared to other known defects
[10]. The above characteristics in ring resonators are the
main basis for designing and manufacturing photonic
crystal-based devices such as optical ﬁlters [1114], optical
switches [15], optical logic gates [16,17], optical sensors
[18], and optical demultiplexers [1922].
So far, numerous papers have been presented on
designing optical demultiplexers based on photonic crystal
using linear defects, which have low transfer coefﬁcients
and high crosstalks [2327], while such problems can
easily be overcome using ring resonators. In recent years,
ring resonators have received considerable attention due to
&Mahmood Seifouri
mahmood.seifouri@srttu.edu
1
Faculty of Electrical Engineering, Shahid Rajaee Teacher
Training University, Tehran, Iran
2
Nano-photonics and Optoelectronics Research Laboratory
(NORLab), Shahid Rajaee Teacher Training University,
Tehran, Iran
3
Department of Electronics, Tabriz Branch, Islamic Azad
University, Tabriz, Iran
123
Opt Rev (2017) 24:605–610
DOI 10.1007/s10043-017-0353-8
Author's personal copy
their high transmission efﬁciency, high quality factor, low
crosstalk, and ﬂexibility in selecting an appropriate wave-
length. So far, various ring resonators have been presented
for designing optical demultiplexers, including square
resonators [20,28,29], quasi-shaped resonators
[19,30,31], X-shaped resonators [32], and octagonal res-
onators [33].
In this paper, four hexagonal photonic crystal ring res-
onators with hexagonal lattice are theoretically used to
design a four-channel optical demultiplexer with average
channel spacing of 2 nm. The channel spacing of the
proposed design is comparatively much narrower than
those of the previously proposed structures. Moreover, the
values for the transfer coefﬁcient, the quality factor, and
the crosstalk of our design are improved with respect to
other structures in the literature and this makes our device
justiﬁable to be used as an efﬁcient demultiplexer in
DWDM systems.
The rest of the paper is organized as follows: In Sect. 2,
the band-gap structure is described. Sect 3focuses on the
demultiplexer design. In Sect. 4, simulation and results
obtained are presented and discussed, and ﬁnally, the
conclusions are presented in Sect. 5.
2 Band-gap structure
First, to design the proposed optical demultiplexer, a 59 9
21(The number of rods in xand zdirections are 59 and 21,
respectively) structure with a hexagonal lattice of dielectric
rods immersed in air is used. To determine the physical
structural parameters of our proposed demultiplexer, one
requires to calculate the gap map diagrams of the design. It
should be mentioned that a bandgap appropriate for optical
telecommunication system is considered in the design.
Hence, for a good design, it is better to use the gap map
diagrams. The photonic bandgap is extracted using PWE
calculations. Subsequently, to obtain the gap map dia-
grams, the band structure is calculated at various values of
the photonic crystal parameters, namely the refractive
index, the rod radius, and the lattice constant [34]. This is
presented in Fig. 1. As can be seen in Fig. 1a, by
increasing the refractive index, the photonic bandgap shifts
towards lower frequencies. Furthermore, as can be seen in
Fig. 1b, by increasing the R/aratio, the photonic bandgap
shifts towards lower frequencies.
For obtaining the best results, the gap map diagrams are
considered. By considering the gap map diagrams, appro-
priate parameters for designing the proposed structure can
be obtained [34]. Thus, for our structure, the refractive
index, the dielectric rod radius, and the lattice constant are
taken to be, n=4.1 [13,32], R=106 nm, and
a=610 nm, respectively. As far as the refractive index of
4.1 of our structure is concerned, there are high-refractive
index composite materials for enabling THz optical com-
ponents [35], and germanium with a refractive index of 4.1
is also a suitable material that is widely used in advanced
semiconductor processes [36]. Based on the above values,
the photonic bandgap is obtained, as shown in Fig. 2.As
can be seen in the ﬁgure, the structure contains two
Fig. 1 Gap map diagrams: variation of PBG versus arefractive index
and bR/aratio
Fig. 2 Band structure of the fundamental structure
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photonic bandgaps in transverse magnetic (TM) modes and
transverse electric (TE) modes, amongst which the pho-
tonic bandgap in the TM mode is suitable. This is because
TM mode includes appropriate telecommunication chan-
nels. The values for the TM mode lie between 0.256 Ba/k
B0.45 which is equivalent to the wavelength range of
1355 nm BkB2382 nm.
3 Demultiplexer design
The proposed four-channel optical demultiplexer is
designed through eliminating some of the dielectric rods
and using 4 hexagonal ring resonators for the purpose of
ﬁltering the proposed wavelengths. The general schematic
of the ring resonators used in the structure is shown in
Fig. 3.
To improve the wavelength selectivity, we have
introduced four scattering rods for each hexagonal ring,
which are highlighted with black color in Fig. 3.We
have called the radius of these scattering rods Rs. The
diffraction losses in the resonators [32]. The four
scattering rods with the radius of R
s
=115 nm are used
in each resonator. The structure has one input port and
four output ports for obtaining the wavelength of the
corresponding telecommunication channels. Moreover,
to have a better control over the wavelength selectivity
of the rings, we have introduced other defects in the
hexagonal rings, having rods with diameter larger than
that of the outer rods. The proposed four-channel
demultiplexer is shown in Fig. 4. The radii of the inner
rods equal to R
1
=180 nm, R
2
=182 nm,
R
3
=184 nm, and R
4
=186 nm, for the ﬁrst, second,
third, and fourth channels, respectively.
4 Simulation and results
For accurate modeling of the demultiplexer, we need 3D
simulation, but this requires a great amount of computa-
tional time. Subsequently, we have used the effective
index approximation method of PhCs, and with this
approximation, we have used 2D rather that 3D simula-
tions [32].
The 2D-FDTD method is used to simulate the proposed
structure. To use this method, the structure should be
meshed precisely. Thus, the meshing size of the structure is
Dx=Dz=a/16, which equals Dx=Dz=38.1 nm,
based on the lattice constant a=610 nm. Due to the time
step formula Dt1=cﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1
Dx

2þ1
Dz

2
r, the time step for
calculation equals DtB0.0244.
The output spectra of the demultiplexer are presented
in Fig. 5. As can be observed from the ﬁgure, this
demultiplexer can separate four channels with central
wavelengths equal to k=1583 nm, k=1585.5 nm,
k=1587.2 nm, and k=1589 nm. Furthermore, the
transfer coefﬁcient, the quality factor, and the spectral
width of each channel is presented in Table 1. For better
understanding of WDM, Fig. 6is presented and according
Fig. 3 Schematic of hexagonal ring resonator
Fig. 4 Sketch of the proposed demultiplexer
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to which, the light propagates through channels 1 and 3 at
the wavelengths of k=1583 nm and k=1587.2 nm,
respectively. In addition, the crosstalk of each channel is
presented in Table 2.
In our structure, the average channel spacing, quality
factor, and structure transfer coefﬁcient equal to 2 nm,
1943, and 95.8%, respectively. Besides, the minimum and
maximum crosstalks are -14 and -27 dB, respectively.
Fig. 5 Output spectra of the
demultiplexer. aLinear and
bdB scale
Table 1 Simulation results of the proposed demultiplexer
Channel Central wavelength (nm) Resonant rod (nm) Spectral width (nm) Quality factor Transmission (%)
Channel 1 1583 180 0.7 2261.5 100
Channel 2 1585.2 182 0.8 1981.5 96.5
Channel 3 1587.2 184 0.9 1763.5 94
Channel 4 1589 186 0.9 1765.5 93
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Compared to other defects including point-defect or
line-defect PC cavities, ring resonators offer scalability
in size, ﬂexibility in mode design due to their multi-
mode nature, and adaptability in structure design
because of numerous design parameters. The design
parameters can be the radius of the scatters, coupling
rods, and the dielectric constant of the structure. In
their ﬂexible design of backward and forward dropping.
Owing to the above-mentioned reasons, here, we have
considered ring resonator-based demultiplexers [37].
Table 3compares the results of our demultiplexer with
other reported ones.
According to the above table, our four-channel demul-
tiplexer has a narrower channel spacing when compared to
the reported structures [19,20,2833], so it is very suit-
able for DWDM systems. Our structure has also an
appropriate transfer coefﬁcient, quality factor, and cross-
talk, while previously reported demultiplexers have some
restrictions to all or some of the above-mentioned
parameters.
5 Conclusion
In this paper, a four-channel optical demultiplexer is
proposed based on photonic crystal hexagonal ring res-
onator. The proposed structure has an average transfer
coefﬁcient and quality factor above 95.8% and 1943,
respectively. Besides, its minimum and maximum
crosstalks are -14 and -27 dB, respectively. Moreover,
the structure size is about 424.5 lm
2
having suitable transfer coefﬁcient and quality factor,
this structure has a channel spacing of 2 nm, which is
much narrower than those of the previously reported
structures. Hence, it is highly suitable to be used in
DWDM systems. The proposed structure has also a
simple design.
Fig. 6 Electric ﬁeld distribution of proposed demultiplexer.
ak1=1583 nm and bk3=1587.2 nm
Table 2 Crosstalk values of the proposed demultiplexer (dB)
Channel 1 Channel 2 Channel 3 Channel 4
Channel 1 -14.2 -15 -15
Channel 2 -21.2 – -16 -16.5
Channel 3 -25.5 -17 – -15
Channel 4 -27 -22 -14 –
Table 3 Comparison of the proposed demultiplexer with reported one
Reference Ring resonator
type
Spectral
width (nm)
Channel
spacing (nm)
Quality
factor
Transmission
(%)
Crosstalk
(dB)
Number of
channels
Dimension
(lm
2
)
Proposed DMUX Hexagonal 0.82 2 1943 95.8 -18.1 4 424.5
[20] Square 1.8 4.2 825 81 8 490.68
[19] Quasi-shaped 1.35 3.13 1224 96.2 -24.5 4
[29] Square 0.3 3 5969 90 -16.5 2 681.36
[33] Octagon-shaped 0.47 2.66 3409 98 -26.1 4
[32] X-shaped 1.7 3 1234 53 -15.4 4 422.4
[30] Quasi-shaped 2.8 8 608.3 90 -29 3 317
[28] Square 30 28 — 85 4
[31] Quasi-shaped 2.75 6.1 567 95 3 294.25
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Compliance with ethical standards
Conﬂict of interest On behalf of all authors, the corresponding
author states that there is no conﬂict of interest.
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... They separate the multiplexed channels in accordance with their central wavelengths. Channel drop/add filters are very crucial elements that can be employed as multichannel demultiplexers/multiplexers (Alipour-Banaei et al. 2015;Fallahi et al. 2017Fallahi et al. , 2019 and optical drop/add units (Qiang et al. 2007;Vegas Olmos et al. 2010) for wavelength division multiplexing systems. They can be also used as optical sensors. ...
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