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Realization of tunable optical channel drop filter based on photonic crystal octagonal shaped structure
Accepted Manuscript Title: Realization of Tunable Optical Channel Drop Filter based on Photonic Crystal Octagonal Shaped Structure Authors: Esmat Rafiee, Farzin Emami PII: DOI: Reference:
S0030-4026(18)30956-2 https://doi.org/10.1016/j.ijleo.2018.06.146 IJLEO 61149
To appear in: Received date: Accepted date:
6-5-2018 28-6-2018
Please cite this article as: Rafiee E, Emami F, Realization of Tunable Optical Channel Drop Filter based on Photonic Crystal Octagonal Shaped Structure, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.06.146 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Realization of Tunable Optical Channel Drop Filter based on Photonic Crystal Octagonal Shaped Structure
IP T
Esmat RafieeA, Farzin EmamiB A PhD Candidate, Modarres st., Shiraz, Iran, Tel.: +989177040496; Fax: +98-713-7353-502, [email protected], B Associate professor, Modarres st., Shiraz, Iran, Tel.: +989173159199; Fax: +98-713-7353502, [email protected] *
Corresponding author : Esmat Rafiee
SC R
Abstract
A
N
U
Photonic crystals (PhCs) are artificial dielectric nanostructure materials. In these structures, a periodic modulation of the material dielectric constant results in a photonic band gap (PBG). By employing defects in the photonic crystals, light can steer in specific direction. Consequently, defects are used in most of the PhC structures. In this work, a novel channel drop filter (CDF) based on two dimensional (2-D) photonic crystal with octagonal shaped structure is designed and numerically analyzed by using the finite difference time domain (FDTD) and plane wave expansion (PWE) techniques. The proposed filter is an octagonal shaped structure of Si rods between two waveguides; consisting of 19*18 silicon rods with the refractive index of 3.5 and rod radius of 0.16a; where a is a lattice constant and equals 0.6μm. By analyzing the structure, wide ranges of TE photonic band gap (PBG) would be achieved. It will be stated that the proposed CDF has appropriate characteristics and could be used in the future wavelength division multiplexing (WDM) communication systems.
ED
M
Key words: Channel drop filter; Octagonal shaped structure; Photonic band gap; Photonic crystal; WDM.
1. Introduction
PT
Photonic crystals (PhCs) are the best platforms for designing all optical devices suitable
CC E
for all optical integrated circuits. PhCs, also known as photonic band gap (PBG) materials, can manage the spontaneous emission and the propagation of electromagnetic (EM) waves [1–6]. By engineering the photonic band gap, the confinement of light in given wavelengths can be
A
tuned. It means that, we can manage the transmittance and reflectance wavelengths intervals by adjusting the band gap of each PhC structure. Actually, PhC structures suggest high spectral selectivity that is necessary for filter designing [7-9]. For Wavelength Division Multiplexing (WDM) systems, optical channel drop filter is one of the important components to select a single or multiple wavelength channels. So far, several topologies have been 1
proposed for channel drop filters, such as using ring shaped, X shaped, hexagonal… structures [10-12]. PhCs have applications in various areas of optical engineering such as optical filters [13-15], beam splitters [16-18], demultiplexers [17, 19] and ring resonators [20, 21]. Researchers had designed a tunable two dimensional (2D) channel drop filter based on photonic crystal ring resonators (PCRR), which indicated improvements in dropping
IP T
efficiency and Q factor [22]. In another work, a new optical channel drop filter using 2D
photonic crystal ring resonators (PCRRs) in triangular lattice photonic crystal silicon rods is
SC R
presented [23]. In [24], a new T-shaped channel drop filter based on photonic crystal ring resonator with transmission efficiency and quality factor of 90% and 387 respectively, is
U
designed. Recently, the crosstalk in the channel-drop filters with a coupled cavity based
N
wavelength selective reflection feedback had been investigated analytically [25]. In another
A
research a novel hexagonal shaped channel drop filter based on two-dimensional photonic
communication systems [26].
M
crystals was proposed and designed which indicated appropriate characteristics for WDM
ED
In this paper, an optical channel filter has been designed by using octagonal shaped photoic crystal structure. The distinctive feature of this structure is that the resonant
PT
wavelengths of the structure are tunable. The structure is appropriate for WDM applications
CC E
due to its BPG region. The simulations are done with PWE and FDTD methods.
2. Design of the Novel Photonic Crystal Channel Drop Filter
A typical octagonal shaped channel drop filter is obtained by removing an octagonal
A
shape of columns from a square lattice of dielectric rods in air background as displayed in Fig. 1.
2
IP T SC R
Fig. 1. The proposed channel drop filter.
U
The dielectric rods (Si) have a refractive index (n) of 3.5, radius r = 0.16a, where a is a
N
lattice constant and equals 0.6μm. To diminish the effect of counter propagating mode
A
resulting from back reflections at the sharp corners of the octagon, we add one scatterer rod at
M
each corner at half lattice constant as shown in Fig. 1. This additional rod at each corner acts as a right angled reflector reducing the back reflection at the corresponding corner [27-29].
ED
By putting a waveguide beside the octagon, the waveguide at its resonant wavelength can be coupled to the octagon. It traps the electromagnetic energy propagating in the waveguide and
PT
localizes it in the ring resonator. In other words, the octagon drops light from the left
CC E
waveguide and sends it to the right waveguide. This structure consists of an input port labels A and two output ports as B and C. In the normal case when the octagon does not resonate, the input power remains in the horizontal bus waveguide and moves toward port B. At
A
resonance cases, some of the power transfers to the bottom waveguide and moves toward port C.
3. Simulations and Results For this structure, the PBG regions for TE/TM modes are depicted in Fig. 2. 3
IP T SC R
Fig. 2. Diagram of PBG regions.
Fig. 2, shows that there are two PBG regions for TE mode while there is none for TM
U
mode. TE PBGs are 1.26μm < λ < 1.82μm and 1.84μm < λ < 1.93μm. As can be seen TE
N
mode is suitable for WDM applications, so all the simulations will be done in TE mode.
Table 1: TE bandgaps
M Bandgap (µm) (1.26 – 1.82) , (1.84 – 1.93)
[30]
(1.22 – 1.65) , (0.64 – 0.66)
[31]
(1.15 – 1.6) , (0.7 – 0.72)
[32]
(1.28 – 1.75) , (0.65-0.67)
[33]
(1.29 – 1.75) , (0.71 – 0.725)
CC E
Present work
PT
Ref
ED
results of this works is presented.
A
In the following, a table comparing the bandgap regions of the previous works with the
A
After calculating the PBG regions, electric field distributions in the structure for different
wavelengths are discussed. The simulations are conducted with FDTD method.
4
3.1 λ=1.5μm Firstly the electric field is applied at λ=1.5μm, which is in the middle of TE PBG region. After applying the input Gaussian field to port A, pulse would propagate in the structure as
U
SC R
IP T
shown in Fig. 3.a.
(b)
PT
ED
M
A
N
(a)
CC E
Fig. 3. a) schematic of pulse propagation in CD filter in λ=1.5μm, b) schematic of transmitted powers in different ports.
It can be seen from Fig. 3. b, that in this wavelength, the structure shows a satisfying CD
A
filter behavior.
3.2 λ=1.7μm Fig. 4, shows the propagation of the electric field near the boundary of the TE PBG
region.
5
IP T M
A
N
U
SC R
(a)
(b)
ED
Fig. 4. a) schematic of pulse propagation in CD filter in λ=1.7μm, b) schematic of transmitted powers in different ports.
In this wavelength, a little part of input power is transmitted to port C, while most of it is
PT
transferred to port B.
CC E
3.3 λ=1.8 μm
For the last simulation, the behavior of the structure at 1.8μm which is exactly at the
A
boundary of the TE PBG region is being investigated.
6
IP T M
A
N
U
SC R
(a)
(b)
ED
Fig. 5. a) schematic of pulse propagation in CD filter in λ=1.8μm, b) schematic of transmitted powers in different ports.
In this section, all the input power would be transferred to port B, showing the
PT
wavelength is out of the TE PBG region. Therefore, it is occluded from Fig. 5, that CD filter
CC E
would act as a straight waveguide in λ=1.8μm.
4. Conclusion
A
In this paper, a novel channel drop filter based on 2D photonic crystal with octagonal
shaped structure has been proposed. The proposed structure consists of 19*18 silicon rods in the air background with the refractive index of 3.5 and rod radius of 0.16a; where a is a lattice constant and equals 0.6μm. The simulations has been conducted with PWE and FDTD methods. The structure indicated wide TE PBG regions in 1.27μm < λ < 1.8μm and 1.84μm < 7
λ < 1.93μm. As a result, the proposed CDF has appropriate characteristics and could be used
A
CC E
PT
ED
M
A
N
U
SC R
IP T
in future wavelength division multiplexing (WDM) communication systems.
8
REFERENCES
[1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton : NJ, USA, 1995. [2] H.Z. Wang, W.M. Zhou, J.P. Zheng, "A 2D rods-in-air square-lattice photonic crystal optical
IP T
switch", Optik, (2010), Vol. 121, pp. 1988–1993. [3] M. Mehrabi, J. Barvestani, "Localized photonic modes in photonic crystal heterostructures", Opt. Commu., (2011), Vol. 284, pp. 5444-5447.
SC R
[4] A. Rostami, H. Alipour Banaei, F. Nazari, A. Bahrami, "An ultra compact photonic crystal
wavelength division demultiplexer using resonance cavities in a modified Y-branch structure", Optik, (2011), Vol. 122, pp. 1481–1485.
[5] A. Taher Rahmati, N. Granpayeh, "Kerr nonlinear switch based on ultra-compact photonic crystal
U
directional coupler", Optik, (2011), Vol. 122, pp. 502–505.
[6] Y. Wan, M. Yun, L. Xia, X. Zhao, "1 × 3 Beam splitter based on self-collimation effect in two-
N
dimensional photonic crystals", Optik, (2011), Vol. 122, pp. 337–339.
A
[7] M.R. Rakhshani, M.A. Mansouri-Birjandi, "Heterostructure four channel wave-length demultiplexer using square photonic crystals ring resonators", J. Electromagn. Waves Appl., (2012),
M
Vol. 26, pp. 1700–1707.
[8] M. Djavid, M.S. Abrishamian, "Multi-channel drop filters using photonic crystal ring resonators",
ED
Optik, (2010), Vol. 123, pp. 167–170.
[9] H. Guan, P. Han, Y. Li, X. Zhang, W. Zhang, "Analysis and optimization of a new photonic crystal filters in near ultraviolet band", Optik, (2012), Vol. 123, pp. 1874–1878.
PT
[10] M. A. Mansouri-Birjandi, M. Ghadrdan, "All-optical ultra compact photonic crystal switch based on nonlinear micro ring resonators", Int. Res. J. Appl. Basic Sci., (2013), Vol. 4, pp. 972–975.
CC E
[11] N. Zhu, L. Xu, "Research on slow light for slotted photonic crystal waveguide with mixed dielectric constant", Optik, (2013), Vol. 124, pp. 2817-2820. [12] T. Uthayakumar, R. Vasantha Jayakantha Raja, "Designing a class of asymmetric twin core photonic crystal fibers for switching and multi-frequency generation", Opt. Fiber Tech., (2013), Vol.
A
19, pp. 556-564.
[13] Z. Hu, H. Wu, "Temporal response and reflective behaviors in all-optical switch based on InAs/GaAs one-dimensional quantum-dot resonant photonic crystal", Opt. Commun., (2013), Vol. 288, pp. 76-81. [14] L. Li, G.Q. Liu, "Photonic crystal ring resonator channel drop filter", Optik, (2013), Vol. 124, pp. 2966-2968.
9
[15] S. Feng, Y. Weng, "Unidirectional wavelength filtering characteristics of the two-dimensional triangular-lattice photonic crystal structures with elliptical defects", Opt. Mate., (2013), Vol. 35, pp. 2166-2170. [16] A. Mehr, F. Emami, "Tunable photonic crystal filter with dispersive and non-dispersive chiral rods", Opt. Commun., (2013), Vol. 301–302, pp. 88-95. [17] M. Ym Mahmoud, "A new optical add–drop filter based on two-dimensional photonic crystal ring Resonator", Optik, (2013), Vol. 124, pp. 2864– 2867.
IP T
[18] Z. Hu, H. Wu, "Temporal response and reflective behaviors in all-optical switch based on In As/GaAs one-dimensional quantum-dot resonant photonic crystal", Opt. Commun., (2013), Vol. 288, pp. 76-81.
SC R
[19] L. Li, G.Q. Liu, "Photonic crystal ring resonator channel drop filter", Optik, (2013), Vol. 124, pp. 2966-2968.
[20] E. Rafiee, F. Emami, N. Nozhat, "Coupling coefficient increment and free spectral range decrement by proper design of microring resonator parameters", Opt. Eng., (2014), Vol. 53, 123108.
U
[21] E. Rafiee, F. Emami, "Investigating the effects of structural parameters on the optical
N
characteristics of add-drop filters", Optik, (2016), Vol. 127, pp. 1690-1694. [22] M. R. Rakhshani, M. A, Mansouri-Birjandi, "Realization of tunable optical filter by photonic
A
crystal ring resonators", Optik, (2013), Vol. 124, pp. 5377– 5380.
M
[23] M. Y. Mahmoud, "Channel drop filter using photonic crystal ring resonators for CWDM communication systems", Optik, (2014), Vol. 125, pp. 4718–4721. [24] M. Jahanara, "T-shaped channel drop filter based on photonic crystal ring resonator", Optik,
ED
(2014).
[25] K. Fasihi, "Crosstalk investigation in channel-drop filters with coupled-cavity based wavelength-
PT
selective reflection feedbacks", Optik, (2016), Vol. 127, pp. 2294–2297. [26] E. Rafiee, F. Emami, "Design and Analysis of a Novel Hexagonal Shaped Channel Drop Filter Based on Two Dimensional Photonic Crystals", J. of Optoelec. Nanostruc., (2016), Vol. 1.
CC E
[27] B. Saghirzadeh Darki, N. Granpayeh, "Improving the performance of a pho-tonic crystal ringresonator- based channel drop filter using particle swarm optimization method", Opt. Commun., (2010), Vol. 283, pp. 4099–4103. [28] V. Dinesh Kumar, T. Srinivas, A. Selvarajan, "Investigation of ring resonators in photonic crystal
A
circuits", Photon. Nanostruct., (2004), Vol. 2, pp. 199–206. [29] E. Rafiee, F. Emami, "Design of a Novel All-Optical Ring Shaped Demultiplexer based on TwoDimensional Photonic Crystals", Optik, (2017), vol. 140, pp. 873-877. [30] L. Li, G.Q. Liu, Y.H. Chen, F.L. Tang, K. Huang, L.X. Gong, "Photonic crystal multi-channel drop filters with Fabry–Pérot microcavity reflection feedback", Optik, (2013), Vol. 124, pp. 2608– 2611.
10
[31] L. Li, G.Q. Liu, "Photonic crystal ring resonator channel drop filter", Optik, (2013), Vol. 124, pp. 2966– 2968. [32] S. Robinson, R. Nakkeeran, "Two dimensional Photonic Crystal Ring Resonator based Add Drop Filter for CWDM systems", Optik, (2013), Vol. 124, pp. 3430– 3435. [33] Zohreh Rashki, Seyyed Javad Seyyed Mahdavi Chabok, "Novel design of optical channel drop
A
CC E
PT
ED
M
A
N
U
SC R
IP T
filters based on two-dimensional photonic crystal ring resonators", Opt. Commun. (2016).
11
S0030-4026(18)30956-2 https://doi.org/10.1016/j.ijleo.2018.06.146 IJLEO 61149
To appear in: Received date: Accepted date:
6-5-2018 28-6-2018
Please cite this article as: Rafiee E, Emami F, Realization of Tunable Optical Channel Drop Filter based on Photonic Crystal Octagonal Shaped Structure, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.06.146 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Realization of Tunable Optical Channel Drop Filter based on Photonic Crystal Octagonal Shaped Structure
IP T
Esmat RafieeA, Farzin EmamiB A PhD Candidate, Modarres st., Shiraz, Iran, Tel.: +989177040496; Fax: +98-713-7353-502, [email protected], B Associate professor, Modarres st., Shiraz, Iran, Tel.: +989173159199; Fax: +98-713-7353502, [email protected] *
Corresponding author : Esmat Rafiee
SC R
Abstract
A
N
U
Photonic crystals (PhCs) are artificial dielectric nanostructure materials. In these structures, a periodic modulation of the material dielectric constant results in a photonic band gap (PBG). By employing defects in the photonic crystals, light can steer in specific direction. Consequently, defects are used in most of the PhC structures. In this work, a novel channel drop filter (CDF) based on two dimensional (2-D) photonic crystal with octagonal shaped structure is designed and numerically analyzed by using the finite difference time domain (FDTD) and plane wave expansion (PWE) techniques. The proposed filter is an octagonal shaped structure of Si rods between two waveguides; consisting of 19*18 silicon rods with the refractive index of 3.5 and rod radius of 0.16a; where a is a lattice constant and equals 0.6μm. By analyzing the structure, wide ranges of TE photonic band gap (PBG) would be achieved. It will be stated that the proposed CDF has appropriate characteristics and could be used in the future wavelength division multiplexing (WDM) communication systems.
ED
M
Key words: Channel drop filter; Octagonal shaped structure; Photonic band gap; Photonic crystal; WDM.
1. Introduction
PT
Photonic crystals (PhCs) are the best platforms for designing all optical devices suitable
CC E
for all optical integrated circuits. PhCs, also known as photonic band gap (PBG) materials, can manage the spontaneous emission and the propagation of electromagnetic (EM) waves [1–6]. By engineering the photonic band gap, the confinement of light in given wavelengths can be
A
tuned. It means that, we can manage the transmittance and reflectance wavelengths intervals by adjusting the band gap of each PhC structure. Actually, PhC structures suggest high spectral selectivity that is necessary for filter designing [7-9]. For Wavelength Division Multiplexing (WDM) systems, optical channel drop filter is one of the important components to select a single or multiple wavelength channels. So far, several topologies have been 1
proposed for channel drop filters, such as using ring shaped, X shaped, hexagonal… structures [10-12]. PhCs have applications in various areas of optical engineering such as optical filters [13-15], beam splitters [16-18], demultiplexers [17, 19] and ring resonators [20, 21]. Researchers had designed a tunable two dimensional (2D) channel drop filter based on photonic crystal ring resonators (PCRR), which indicated improvements in dropping
IP T
efficiency and Q factor [22]. In another work, a new optical channel drop filter using 2D
photonic crystal ring resonators (PCRRs) in triangular lattice photonic crystal silicon rods is
SC R
presented [23]. In [24], a new T-shaped channel drop filter based on photonic crystal ring resonator with transmission efficiency and quality factor of 90% and 387 respectively, is
U
designed. Recently, the crosstalk in the channel-drop filters with a coupled cavity based
N
wavelength selective reflection feedback had been investigated analytically [25]. In another
A
research a novel hexagonal shaped channel drop filter based on two-dimensional photonic
communication systems [26].
M
crystals was proposed and designed which indicated appropriate characteristics for WDM
ED
In this paper, an optical channel filter has been designed by using octagonal shaped photoic crystal structure. The distinctive feature of this structure is that the resonant
PT
wavelengths of the structure are tunable. The structure is appropriate for WDM applications
CC E
due to its BPG region. The simulations are done with PWE and FDTD methods.
2. Design of the Novel Photonic Crystal Channel Drop Filter
A typical octagonal shaped channel drop filter is obtained by removing an octagonal
A
shape of columns from a square lattice of dielectric rods in air background as displayed in Fig. 1.
2
IP T SC R
Fig. 1. The proposed channel drop filter.
U
The dielectric rods (Si) have a refractive index (n) of 3.5, radius r = 0.16a, where a is a
N
lattice constant and equals 0.6μm. To diminish the effect of counter propagating mode
A
resulting from back reflections at the sharp corners of the octagon, we add one scatterer rod at
M
each corner at half lattice constant as shown in Fig. 1. This additional rod at each corner acts as a right angled reflector reducing the back reflection at the corresponding corner [27-29].
ED
By putting a waveguide beside the octagon, the waveguide at its resonant wavelength can be coupled to the octagon. It traps the electromagnetic energy propagating in the waveguide and
PT
localizes it in the ring resonator. In other words, the octagon drops light from the left
CC E
waveguide and sends it to the right waveguide. This structure consists of an input port labels A and two output ports as B and C. In the normal case when the octagon does not resonate, the input power remains in the horizontal bus waveguide and moves toward port B. At
A
resonance cases, some of the power transfers to the bottom waveguide and moves toward port C.
3. Simulations and Results For this structure, the PBG regions for TE/TM modes are depicted in Fig. 2. 3
IP T SC R
Fig. 2. Diagram of PBG regions.
Fig. 2, shows that there are two PBG regions for TE mode while there is none for TM
U
mode. TE PBGs are 1.26μm < λ < 1.82μm and 1.84μm < λ < 1.93μm. As can be seen TE
N
mode is suitable for WDM applications, so all the simulations will be done in TE mode.
Table 1: TE bandgaps
M Bandgap (µm) (1.26 – 1.82) , (1.84 – 1.93)
[30]
(1.22 – 1.65) , (0.64 – 0.66)
[31]
(1.15 – 1.6) , (0.7 – 0.72)
[32]
(1.28 – 1.75) , (0.65-0.67)
[33]
(1.29 – 1.75) , (0.71 – 0.725)
CC E
Present work
PT
Ref
ED
results of this works is presented.
A
In the following, a table comparing the bandgap regions of the previous works with the
A
After calculating the PBG regions, electric field distributions in the structure for different
wavelengths are discussed. The simulations are conducted with FDTD method.
4
3.1 λ=1.5μm Firstly the electric field is applied at λ=1.5μm, which is in the middle of TE PBG region. After applying the input Gaussian field to port A, pulse would propagate in the structure as
U
SC R
IP T
shown in Fig. 3.a.
(b)
PT
ED
M
A
N
(a)
CC E
Fig. 3. a) schematic of pulse propagation in CD filter in λ=1.5μm, b) schematic of transmitted powers in different ports.
It can be seen from Fig. 3. b, that in this wavelength, the structure shows a satisfying CD
A
filter behavior.
3.2 λ=1.7μm Fig. 4, shows the propagation of the electric field near the boundary of the TE PBG
region.
5
IP T M
A
N
U
SC R
(a)
(b)
ED
Fig. 4. a) schematic of pulse propagation in CD filter in λ=1.7μm, b) schematic of transmitted powers in different ports.
In this wavelength, a little part of input power is transmitted to port C, while most of it is
PT
transferred to port B.
CC E
3.3 λ=1.8 μm
For the last simulation, the behavior of the structure at 1.8μm which is exactly at the
A
boundary of the TE PBG region is being investigated.
6
IP T M
A
N
U
SC R
(a)
(b)
ED
Fig. 5. a) schematic of pulse propagation in CD filter in λ=1.8μm, b) schematic of transmitted powers in different ports.
In this section, all the input power would be transferred to port B, showing the
PT
wavelength is out of the TE PBG region. Therefore, it is occluded from Fig. 5, that CD filter
CC E
would act as a straight waveguide in λ=1.8μm.
4. Conclusion
A
In this paper, a novel channel drop filter based on 2D photonic crystal with octagonal
shaped structure has been proposed. The proposed structure consists of 19*18 silicon rods in the air background with the refractive index of 3.5 and rod radius of 0.16a; where a is a lattice constant and equals 0.6μm. The simulations has been conducted with PWE and FDTD methods. The structure indicated wide TE PBG regions in 1.27μm < λ < 1.8μm and 1.84μm < 7
λ < 1.93μm. As a result, the proposed CDF has appropriate characteristics and could be used
A
CC E
PT
ED
M
A
N
U
SC R
IP T
in future wavelength division multiplexing (WDM) communication systems.
8
REFERENCES
[1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton : NJ, USA, 1995. [2] H.Z. Wang, W.M. Zhou, J.P. Zheng, "A 2D rods-in-air square-lattice photonic crystal optical
IP T
switch", Optik, (2010), Vol. 121, pp. 1988–1993. [3] M. Mehrabi, J. Barvestani, "Localized photonic modes in photonic crystal heterostructures", Opt. Commu., (2011), Vol. 284, pp. 5444-5447.
SC R
[4] A. Rostami, H. Alipour Banaei, F. Nazari, A. Bahrami, "An ultra compact photonic crystal
wavelength division demultiplexer using resonance cavities in a modified Y-branch structure", Optik, (2011), Vol. 122, pp. 1481–1485.
[5] A. Taher Rahmati, N. Granpayeh, "Kerr nonlinear switch based on ultra-compact photonic crystal
U
directional coupler", Optik, (2011), Vol. 122, pp. 502–505.
[6] Y. Wan, M. Yun, L. Xia, X. Zhao, "1 × 3 Beam splitter based on self-collimation effect in two-
N
dimensional photonic crystals", Optik, (2011), Vol. 122, pp. 337–339.
A
[7] M.R. Rakhshani, M.A. Mansouri-Birjandi, "Heterostructure four channel wave-length demultiplexer using square photonic crystals ring resonators", J. Electromagn. Waves Appl., (2012),
M
Vol. 26, pp. 1700–1707.
[8] M. Djavid, M.S. Abrishamian, "Multi-channel drop filters using photonic crystal ring resonators",
ED
Optik, (2010), Vol. 123, pp. 167–170.
[9] H. Guan, P. Han, Y. Li, X. Zhang, W. Zhang, "Analysis and optimization of a new photonic crystal filters in near ultraviolet band", Optik, (2012), Vol. 123, pp. 1874–1878.
PT
[10] M. A. Mansouri-Birjandi, M. Ghadrdan, "All-optical ultra compact photonic crystal switch based on nonlinear micro ring resonators", Int. Res. J. Appl. Basic Sci., (2013), Vol. 4, pp. 972–975.
CC E
[11] N. Zhu, L. Xu, "Research on slow light for slotted photonic crystal waveguide with mixed dielectric constant", Optik, (2013), Vol. 124, pp. 2817-2820. [12] T. Uthayakumar, R. Vasantha Jayakantha Raja, "Designing a class of asymmetric twin core photonic crystal fibers for switching and multi-frequency generation", Opt. Fiber Tech., (2013), Vol.
A
19, pp. 556-564.
[13] Z. Hu, H. Wu, "Temporal response and reflective behaviors in all-optical switch based on InAs/GaAs one-dimensional quantum-dot resonant photonic crystal", Opt. Commun., (2013), Vol. 288, pp. 76-81. [14] L. Li, G.Q. Liu, "Photonic crystal ring resonator channel drop filter", Optik, (2013), Vol. 124, pp. 2966-2968.
9
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