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Heterostructure wavelength division demultiplexers using photonic crystal ring resonators
Optics Communications 281 (2008) 4028–4032
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Heterostructure wavelength division demultiplexers using photonic crystal ring resonators M. Djavid *, F. Monifi, A. Ghaffari, M.S. Abrishamian Department of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 January 2008 Received in revised form 19 April 2008 Accepted 19 April 2008
Keywords: Optical devices Photonic integrated circuits Ring resonators Waveguides Photonic crystals
a b s t r a c t In this paper, we demonstrate a new type of two-dimensional photonic crystal wavelength division demultiplexers based on ring resonators that can be applicable to photonic integrated circuits. The proposed structure mechanism is performed based on coupling between a waveguide and a ring resonator. Based on the calculated position, this structure is designed and verified by finite-difference time-domain computation; our simulation by using this method results over 82% output efficiency. We use a heterostructure which is constructed of three different values of dielectric constant to obtain our wavelength division demultiplexer. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Photonic crystals (PCs) have inspired great interest recently because of their potential ability to control light wave propagation. In last decade it has been demonstrated that PCs are able to modify the density of electromagnetic states inside the crystal. Several compact photonic devices based on photonic crystal waveguides (PCWs), have been demonstrated, such as Mach-Zehnder modulators, power splitters and dispersion compensators, also PC waveguides can be implemented as optical filters into wavelength division multiplexers (WDMs). Wavelength multiplexers are essential components in wavelength division multiplexing for use in point-to-point core networks. Dense-WDM (DWDM) systems require highly accurate wavelength control of the WDM light source and the wavelength multiplexer–demultiplexer [1–3]. Over the last decades, a WDM employing the conventional directional couplers has been studied, but the device size still remains very large. This is because of the weak coupling in horizontally arranged couplers. Recently, several WDM have been demonstrated such as using vertical couplers with stronger coupling; however the waveguide dispersion has been ignored. Compared with the conventional couplers the device dimensions have been improved, but are still far a way from being on the wavelength order. For improving higher drop efficiency of photonic crystal-based multi-channel drop filter, a reflection feedback system was pro* Corresponding author. E-mail address: [email protected] (M. Djavid). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.04.045
posed by Kim [4] and a wavelength-selective reflection micro-cavity system was proposed by Ren [5]. These optoelectronic devices, which are designed by photonic crystal technology, are scale in order of micrometers. The compact size optoelectronic devices in PCs base can be fabricated by semiconductor process technology and is easy to be realized by current process. Recently, in the photonic crystal based WDM, different wavelength selective filtering techniques have been used. Waveguide based filters which utilize coupling between two closely spaced waveguides [6], filters that couple two waveguides using a cavity [7,8], and negative refractive index super-prism based filters [9] are some of the examples which have recently been used to achieve PC based wavelength demultiplexing. Waveguide-coupled ring resonators are extremely useful components for filtering multiplexing/demutliplexing tasks in photonic integrated circuits. It consists of a ring resonator quickly coupled to a pair of waveguides such that power in one waveguide is transferred to the other through the resonance of the ring. In this research a numerical approach, based on the 2D FDTD has been developed and employed to analyze and optimize a new design of demultiplexer. This new design is based on the Tshaped channel-drop filter. Its operation principle is based on a resonance of the ring resonator in a specific frequency and the coupling between waveguide and ring resonator. Our structure contains three different values of dielectric constant (Heterostructure). This paper is separated into five sections: Section 2 describes a numerical analysis used in simulation. Section 3 describes a Photonic crystal T-shaped channel-drop filter based on ring resonators and the simulation results. Section 4 describes a heterostructure
M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
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WDDM using T-shaped channel-drop filters and shows the simulations results. Finally, Section 5 concludes the paper.
3. Photonic crystal T-shaped channel-drop filters based on ring resonators
2. Numerical analysis
Photonic crystals have the ability to trap a particular wavelength of light around a defect. A typical ring resonator [13,14] is depicted in Fig. 1. The system under consideration is two-dimensinal and consists of an array of rods with a square lattice structure. Rods of Si, with a radius of r = 0.185a are perforated in air, where a is lattice constant. Trapping behavior is realized by this ring resonator which is obtained by removing a ring shape of columns from a square lattice of dielectric rods. In this structure, bandgap opens for the normalized frequency a/k = 0.3115–0.4601 for TM polarization (electric field parallel to the rod axis), where k is the wavelength in free space. The photonic crystal waveguides are formed by removing one row of rods. As shown in Fig. 1, by adding the four extra scatterer rods at each corner of the ring resonator at half lattice constant, which are the same as other rods, the performance of the ring resonator is improved. This work minimizes the effect of propagating mode which is resulted from back-reflections at the sharp corners of the ring. These additional rods at each corner act like a rightangled reflector reducing the back-reflection at the corresponding corner. As shown in Fig. 2, by putting a waveguide next to the ring resonator, the waveguide can couple to the ring resonator at its resonant frequency to trap the electromagnetic energy which is propagating in the waveguide and localized it in the ring resonator. In another word, the ring resonator drops the light from the horizontal waveguide and sends it to the vertical waveguide [15,16]. This structure consists of an input waveguide labeled A, and two output channels labeled as B and C. For improving the performance of the wavelength demultiplexer, end of the vertical waveguide is closed, and we improved it more, by adding the extra scatterer rod to the top of the vertical waveguide at half lattice constant. Optical power transmission characteristics of T-shaped channel-drop filter with three refractive indexes of 3.44, 3.66 and 3.82 for output ports B and C are
Plane wave expansion (PWE) method and the finite-difference time-domain (FDTD) method [10] are most popular methods for analysis of photonic crystals. First method initially is used for theoretical analysis of photonic crystal structures, which can express periodic structures as a superposition of a set of plane waves. Although this method can obtain an accurate solution for the dispersion properties of a PC structure, but due to considering propagation modes, transmission spectra and field distribution can not be extracted. FDTD is an accurate method for studying electromagnetic problems including the simulation of many PC-based devices. The FDTD method for solving Maxwell’s equations has been the workhorse of computational electromagnetic in the time domain, due to its simplicity. For a linear isotropic material in a source-free region, the time-dependent Maxwell’s equations can be written in the following form: oH 1 ¼ rE ot lðrÞ oE 1 ¼ rH ot eðrÞ
ð1Þ ð2Þ
where e(r) and l(r) are the position dependent permittivity and permeability of the material, respectively. In the two-dimensional case, the fields can be decoupled into two transversely polarized modes as the TM and TE. These equations are discretized in space and time domain using the principles of Yee algorithm [11]. The following FDTD time stepping formulas are spatial and time discretizations of Eqs. (1) and (2) on a discrete two dimensional mesh within the x–y coordinate system for the E-polarization, Where the index n denotes the discrete time step, indices i and j denote the discretized grid point in the xy planes, respectively. The FDTD mesh size and time step used in this paper are: Dx = Dy = a/21 and Dt = Dx/(2*c), where c is speed of light in free space and a is lattice constant. Berenger’s perfectly matched layers (PML) are located around the whole structure as absorbing boundary condition [12]. The number of PML is set to be 12. This structure is excited with TM polarization. An adequately broadband Gaussian pulse is launched into input port, and then we placed a detector inside each waveguide channel of the filter, measuring the time-varying electric and magnetic field. The power transmission spectra are computed by taking the fast fourier transform (FFT) of the fields that are calculated by FDTD and integrating the poynting vector over the cells of the output ports. " n # n Dt Ez ji;jþ1 Ez ji;j n1=2 Hx jnþ1=2 ð3Þ ¼ H j x i;j1=2 i;jþ1=2 l0 Dy " n # n Dt Ez jiþ1;j Ez ji;j nþ1=2 n—1=2 Hy jiþ1=2 ¼ Hy jiþ1=2;j ð4Þ l0 Dx " ! !# nþ1=2 nþ1=2 Hy jnþ1=2 Hx jnþ1=2 Dt iþ1=2;j Hy ji1=2;j i;jþ1=2 Hx ji;j—1=2 nþ1 n Ez ji;j ¼ Ez ji;j þ ei;j Dx Dy
Fig. 1. Single-ring photonic crystal ring resonator (PCRR).
ð5Þ In this paper we use mentioned method to calculate the spectrum of the power transmission, in our MATLAB code during 30,000 time step (200 min running time for final structure). The computer used in this simulation is P4 3.00 GHz and has 4 GB of RAM.
Fig. 2. A fundamental element of WDDM (T-shaped channel-drop filter).
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M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
Fig. 3. Optical power transmission characteristics of T-shaped channel-drop filter with three refractive indexes, 3.44 3.66 and 3.82 for output ports B and C.
puts. This WDDM contains three regions with various refractive indexes as shown in Fig. 5. The refractive index of region 1, 2 and 3 are 3.82, 3.66 and 3.44. This structure is a hybrid structure which has the optical characteristics of all three structures and overcomes single refractive index constraints. In other words, if a photonic crystal is formed from multiple refractive index structures, the newly formed structure is called a heterostructure photonic crystal. In order to avoid internal mismatches at the interface between the different refractive index structures, these structures must be matched in bandgap sizes. First we present a theoretical analysis of heterostructure photonic crystals. We examined three structures band-gaps using a two-dimensional plane-wave expansion method for TM polarization and the results are shown in Fig. 6. When photonic crystal of different refractive index structures are brought together, it is possible that discontinuity in their energy bands will occur due to structure having different band-gap. So Band-gap matching should be considered in heterostructure PCs to guide an electromagnetic wave propagating through different refractive indexes structures with minimal propagation losses. The structures of region 1, 2 and 3 have following band-gap, respectively: 8 > < 0:2903 < a=k < 0:4495; First region > :
Fig. 4. Electric field intensity of the ring resonator at (a) non resonant wavelengths of 1500 nm, (b) resonant wavelengths of 1577 nm.
shown in Fig. 3. It is obvious that when the refractive index of Tshaped channel-drop filter increases, the curves shift to right (greater wavelengths). Fig. 4 shows the time domain simulation of this T-shaped channel-drop filter with refractive index of 3.66 at (a) through wavelength (k1 = 1500 nm) and (b) drop wavelength (k2 = 1577 nm) in the communication window. The normalized transmissions of these wavelengths are over 99% and 94%, respectively. 4. Heterostructure photonic crystal wavelength division demultiplexers using T-shaped channel-drop filters In this paper we present a design for heterostructure photonic crystal WDDM that leads us to achieve a structure with four out-
0:3010 < a=k < 0:4544;
0:3170 < a=k < 0:4606;
Second region Third region
In principle, three different regions have their own band-gaps. The three band-gaps may overlap in some region which its range depends on the parameters namely r/a and dielectric constant. This means that equivalent band-gap of heterostructure WDDM is overlapping of band-gaps of its constitutive structures. According to the band-gaps of three regions the equivalent band-gap is: 0.3170 < a/k < 0.4495. In this equivalent band-gap, incident wave can be transmitted through the waveguide which is gone through all regions without any reflection. Five ports of the structure are labeled as A, B, C, D, and E, shown in Fig. 5. Fig. 7 shows the normalized transmission of the heterostructure WDDM of Fig. 5. Four different wavelengths at output ports B, C, D and E are k1 = 1513 nm, k2 = 1541 nm, k3 = 1569 nm and k4 = 1594 nm in the communication window. The normalized transmissions of these wavelengths are over 82%, 83%, 87% and 96%, respectively. As it is seen in Fig. 7, the structure is successful to separate the different incident wavelengths to different outputs. In this design, two points is most prominent. First point is the wavelength of the incident light in the dropping band of region 3 must be in the nondropping band of region 1 and 2; the wavelength of the incident light in the dropping band of region 2 must be in the non-dropping
Fig. 5. Heterostructure WDDM with ring resonators.
M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
4031
Fig. 7. Optical power transmission characteristics of four outputs WDDM with ring resonator.
Fig. 6. Band diagram of square lattice photonic crystal for (a) n = 3.82, (b) n = 3.66 and (c) n = 3.44.
band of region 1. So in this case every ring resonator drops the wavelength matched with its resonant wavelength from the bus waveguide and couples this specific wavelength into the output port.
Fig. 8. Electric field intensity of wavelength demultiplexer with ring resonator at (a) k1 = 1513 nm; (b) k2 = 1541 nm; (c) k3 = 1569 nm and (d) k4 = 1594 nm in the communication window.
Another important point is ring resonators must be located so far away to avoid affecting each other. Due to effect of ring resonators on each other, their resonant wavelength will be changed; this
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M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
situation makes designing rigid. Based on our simulations, distance of 6 rods leads to obtain acceptable results and no interference is occurred. Also crosstalk information from each port for the different wavelengths is written as following table:
Port Port Port Port
B C D E
1513 nm (%)
1541 nm (%)
1569 nm (%)
1594 nm (%)
82 5 9 3
8 83 4 5
0 4 87 9
0 0 3 96
Finally, snapshots of time domain simulation are depicted. The Fig. 8 shows the electric field intensity of wavelength demultiplexer with ring resonator at (a) k1 = 1513 nm of port E, (b) k2 = 1541 nm of port D, (c) k3 = 1569 nm of port C and (d) k4 = 1594 nm of port B in the communication window. 5. Conclusions In this paper, a heterostructure wavelength demultiplexer with four outputs in photonic crystal was investigated. Using this heterostructure we can demultiplex four different wavelengths within third communication window. Normalized transmission of these wavelengths is over 85%. In addition, utilizing the heterostructure in our design helps us to achieve higher power output and get a more outputs.
Acknowledgment This study was supported by Iran Telecommunication Research Center. References [1] S. Fan, P.R. Villeneuve, J.D. Joannopoulos, H.A. Haus, Channel drop tunneling through localized states, Phys. Rev. Lett. 80 (1998) 960. [2] K. Takano, K. Nakagawa, IEICE Trans. Electron. E84-C (May) (2001) 669. [3] K. Kawata, H. Nakamura, T. Sugie, Service multiplexing systems with wide pass bandWDM(WWDM) technology for access networks, IEICE Trans. Commun. E83-B (October) (2001) 2348–2354 (pp. 960–963, February 1998). [4] Sangin Kim, Ikmo park, Hanjo Lim, Chul-Sik Kee, Opt. Express 12 (2004) 5518. [5] Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, Jingyuan Wangm, Opt. Express 14 (2006) 2446. [6] J. Zimmermann, M. Kamp, A. Forchel, R. Marz, Opt. Commun. 230 (2004) 387. [7] A. Sharkawy, S. Shi, D.W. Prather, Appl. Opt. 40 (2001) 2247. [8] M.Y. Tekeste, J.M. Yarrison-Rice, Opt. Express 14 (2006) 7931. [9] B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, A. Adibi, Opt. Express 14 (2006) 2413. [10] A. Taflove, Computational Electrodynamics: The Finite-Difference TimeDomain Method, third ed., Artech House, Inc, 2005. [11] K.S. Yee, IEEE Trans. Antennas Propag. 14 (1966) 302. [12] J.P. Berenger, J. Comput. Phys. 114 (1994) 185. [13] M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, H.Y. Ryu, Opt. Express 12 (2004) 1551. [14] T. Barwicz, M. Popovic, P. Rakich, M. Watts, H. Haus, E. Ippen, H. Smith, Opt. Express 12 (2004) 1437. [15] A. Ghafari, M. Javid, F. Monifi, M.S. Abrishamian, A numeric analysis of photonic crystal tunable add-drop filters based on ring resonators, IEEE/LEOS 2007 Annual Meeting, 2007. [16] J. Romero-Vivas, D.N. Chigrin, A.V. Lavrinenko, C.M. Sotomayor Torres, Opt. Express 13 (2005) 826.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Heterostructure wavelength division demultiplexers using photonic crystal ring resonators M. Djavid *, F. Monifi, A. Ghaffari, M.S. Abrishamian Department of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 January 2008 Received in revised form 19 April 2008 Accepted 19 April 2008
Keywords: Optical devices Photonic integrated circuits Ring resonators Waveguides Photonic crystals
a b s t r a c t In this paper, we demonstrate a new type of two-dimensional photonic crystal wavelength division demultiplexers based on ring resonators that can be applicable to photonic integrated circuits. The proposed structure mechanism is performed based on coupling between a waveguide and a ring resonator. Based on the calculated position, this structure is designed and verified by finite-difference time-domain computation; our simulation by using this method results over 82% output efficiency. We use a heterostructure which is constructed of three different values of dielectric constant to obtain our wavelength division demultiplexer. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Photonic crystals (PCs) have inspired great interest recently because of their potential ability to control light wave propagation. In last decade it has been demonstrated that PCs are able to modify the density of electromagnetic states inside the crystal. Several compact photonic devices based on photonic crystal waveguides (PCWs), have been demonstrated, such as Mach-Zehnder modulators, power splitters and dispersion compensators, also PC waveguides can be implemented as optical filters into wavelength division multiplexers (WDMs). Wavelength multiplexers are essential components in wavelength division multiplexing for use in point-to-point core networks. Dense-WDM (DWDM) systems require highly accurate wavelength control of the WDM light source and the wavelength multiplexer–demultiplexer [1–3]. Over the last decades, a WDM employing the conventional directional couplers has been studied, but the device size still remains very large. This is because of the weak coupling in horizontally arranged couplers. Recently, several WDM have been demonstrated such as using vertical couplers with stronger coupling; however the waveguide dispersion has been ignored. Compared with the conventional couplers the device dimensions have been improved, but are still far a way from being on the wavelength order. For improving higher drop efficiency of photonic crystal-based multi-channel drop filter, a reflection feedback system was pro* Corresponding author. E-mail address: [email protected] (M. Djavid). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.04.045
posed by Kim [4] and a wavelength-selective reflection micro-cavity system was proposed by Ren [5]. These optoelectronic devices, which are designed by photonic crystal technology, are scale in order of micrometers. The compact size optoelectronic devices in PCs base can be fabricated by semiconductor process technology and is easy to be realized by current process. Recently, in the photonic crystal based WDM, different wavelength selective filtering techniques have been used. Waveguide based filters which utilize coupling between two closely spaced waveguides [6], filters that couple two waveguides using a cavity [7,8], and negative refractive index super-prism based filters [9] are some of the examples which have recently been used to achieve PC based wavelength demultiplexing. Waveguide-coupled ring resonators are extremely useful components for filtering multiplexing/demutliplexing tasks in photonic integrated circuits. It consists of a ring resonator quickly coupled to a pair of waveguides such that power in one waveguide is transferred to the other through the resonance of the ring. In this research a numerical approach, based on the 2D FDTD has been developed and employed to analyze and optimize a new design of demultiplexer. This new design is based on the Tshaped channel-drop filter. Its operation principle is based on a resonance of the ring resonator in a specific frequency and the coupling between waveguide and ring resonator. Our structure contains three different values of dielectric constant (Heterostructure). This paper is separated into five sections: Section 2 describes a numerical analysis used in simulation. Section 3 describes a Photonic crystal T-shaped channel-drop filter based on ring resonators and the simulation results. Section 4 describes a heterostructure
M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
4029
WDDM using T-shaped channel-drop filters and shows the simulations results. Finally, Section 5 concludes the paper.
3. Photonic crystal T-shaped channel-drop filters based on ring resonators
2. Numerical analysis
Photonic crystals have the ability to trap a particular wavelength of light around a defect. A typical ring resonator [13,14] is depicted in Fig. 1. The system under consideration is two-dimensinal and consists of an array of rods with a square lattice structure. Rods of Si, with a radius of r = 0.185a are perforated in air, where a is lattice constant. Trapping behavior is realized by this ring resonator which is obtained by removing a ring shape of columns from a square lattice of dielectric rods. In this structure, bandgap opens for the normalized frequency a/k = 0.3115–0.4601 for TM polarization (electric field parallel to the rod axis), where k is the wavelength in free space. The photonic crystal waveguides are formed by removing one row of rods. As shown in Fig. 1, by adding the four extra scatterer rods at each corner of the ring resonator at half lattice constant, which are the same as other rods, the performance of the ring resonator is improved. This work minimizes the effect of propagating mode which is resulted from back-reflections at the sharp corners of the ring. These additional rods at each corner act like a rightangled reflector reducing the back-reflection at the corresponding corner. As shown in Fig. 2, by putting a waveguide next to the ring resonator, the waveguide can couple to the ring resonator at its resonant frequency to trap the electromagnetic energy which is propagating in the waveguide and localized it in the ring resonator. In another word, the ring resonator drops the light from the horizontal waveguide and sends it to the vertical waveguide [15,16]. This structure consists of an input waveguide labeled A, and two output channels labeled as B and C. For improving the performance of the wavelength demultiplexer, end of the vertical waveguide is closed, and we improved it more, by adding the extra scatterer rod to the top of the vertical waveguide at half lattice constant. Optical power transmission characteristics of T-shaped channel-drop filter with three refractive indexes of 3.44, 3.66 and 3.82 for output ports B and C are
Plane wave expansion (PWE) method and the finite-difference time-domain (FDTD) method [10] are most popular methods for analysis of photonic crystals. First method initially is used for theoretical analysis of photonic crystal structures, which can express periodic structures as a superposition of a set of plane waves. Although this method can obtain an accurate solution for the dispersion properties of a PC structure, but due to considering propagation modes, transmission spectra and field distribution can not be extracted. FDTD is an accurate method for studying electromagnetic problems including the simulation of many PC-based devices. The FDTD method for solving Maxwell’s equations has been the workhorse of computational electromagnetic in the time domain, due to its simplicity. For a linear isotropic material in a source-free region, the time-dependent Maxwell’s equations can be written in the following form: oH 1 ¼ rE ot lðrÞ oE 1 ¼ rH ot eðrÞ
ð1Þ ð2Þ
where e(r) and l(r) are the position dependent permittivity and permeability of the material, respectively. In the two-dimensional case, the fields can be decoupled into two transversely polarized modes as the TM and TE. These equations are discretized in space and time domain using the principles of Yee algorithm [11]. The following FDTD time stepping formulas are spatial and time discretizations of Eqs. (1) and (2) on a discrete two dimensional mesh within the x–y coordinate system for the E-polarization, Where the index n denotes the discrete time step, indices i and j denote the discretized grid point in the xy planes, respectively. The FDTD mesh size and time step used in this paper are: Dx = Dy = a/21 and Dt = Dx/(2*c), where c is speed of light in free space and a is lattice constant. Berenger’s perfectly matched layers (PML) are located around the whole structure as absorbing boundary condition [12]. The number of PML is set to be 12. This structure is excited with TM polarization. An adequately broadband Gaussian pulse is launched into input port, and then we placed a detector inside each waveguide channel of the filter, measuring the time-varying electric and magnetic field. The power transmission spectra are computed by taking the fast fourier transform (FFT) of the fields that are calculated by FDTD and integrating the poynting vector over the cells of the output ports. " n # n Dt Ez ji;jþ1 Ez ji;j n1=2 Hx jnþ1=2 ð3Þ ¼ H j x i;j1=2 i;jþ1=2 l0 Dy " n # n Dt Ez jiþ1;j Ez ji;j nþ1=2 n—1=2 Hy jiþ1=2 ¼ Hy jiþ1=2;j ð4Þ l0 Dx " ! !# nþ1=2 nþ1=2 Hy jnþ1=2 Hx jnþ1=2 Dt iþ1=2;j Hy ji1=2;j i;jþ1=2 Hx ji;j—1=2 nþ1 n Ez ji;j ¼ Ez ji;j þ ei;j Dx Dy
Fig. 1. Single-ring photonic crystal ring resonator (PCRR).
ð5Þ In this paper we use mentioned method to calculate the spectrum of the power transmission, in our MATLAB code during 30,000 time step (200 min running time for final structure). The computer used in this simulation is P4 3.00 GHz and has 4 GB of RAM.
Fig. 2. A fundamental element of WDDM (T-shaped channel-drop filter).
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Fig. 3. Optical power transmission characteristics of T-shaped channel-drop filter with three refractive indexes, 3.44 3.66 and 3.82 for output ports B and C.
puts. This WDDM contains three regions with various refractive indexes as shown in Fig. 5. The refractive index of region 1, 2 and 3 are 3.82, 3.66 and 3.44. This structure is a hybrid structure which has the optical characteristics of all three structures and overcomes single refractive index constraints. In other words, if a photonic crystal is formed from multiple refractive index structures, the newly formed structure is called a heterostructure photonic crystal. In order to avoid internal mismatches at the interface between the different refractive index structures, these structures must be matched in bandgap sizes. First we present a theoretical analysis of heterostructure photonic crystals. We examined three structures band-gaps using a two-dimensional plane-wave expansion method for TM polarization and the results are shown in Fig. 6. When photonic crystal of different refractive index structures are brought together, it is possible that discontinuity in their energy bands will occur due to structure having different band-gap. So Band-gap matching should be considered in heterostructure PCs to guide an electromagnetic wave propagating through different refractive indexes structures with minimal propagation losses. The structures of region 1, 2 and 3 have following band-gap, respectively: 8 > < 0:2903 < a=k < 0:4495; First region > :
Fig. 4. Electric field intensity of the ring resonator at (a) non resonant wavelengths of 1500 nm, (b) resonant wavelengths of 1577 nm.
shown in Fig. 3. It is obvious that when the refractive index of Tshaped channel-drop filter increases, the curves shift to right (greater wavelengths). Fig. 4 shows the time domain simulation of this T-shaped channel-drop filter with refractive index of 3.66 at (a) through wavelength (k1 = 1500 nm) and (b) drop wavelength (k2 = 1577 nm) in the communication window. The normalized transmissions of these wavelengths are over 99% and 94%, respectively. 4. Heterostructure photonic crystal wavelength division demultiplexers using T-shaped channel-drop filters In this paper we present a design for heterostructure photonic crystal WDDM that leads us to achieve a structure with four out-
0:3010 < a=k < 0:4544;
0:3170 < a=k < 0:4606;
Second region Third region
In principle, three different regions have their own band-gaps. The three band-gaps may overlap in some region which its range depends on the parameters namely r/a and dielectric constant. This means that equivalent band-gap of heterostructure WDDM is overlapping of band-gaps of its constitutive structures. According to the band-gaps of three regions the equivalent band-gap is: 0.3170 < a/k < 0.4495. In this equivalent band-gap, incident wave can be transmitted through the waveguide which is gone through all regions without any reflection. Five ports of the structure are labeled as A, B, C, D, and E, shown in Fig. 5. Fig. 7 shows the normalized transmission of the heterostructure WDDM of Fig. 5. Four different wavelengths at output ports B, C, D and E are k1 = 1513 nm, k2 = 1541 nm, k3 = 1569 nm and k4 = 1594 nm in the communication window. The normalized transmissions of these wavelengths are over 82%, 83%, 87% and 96%, respectively. As it is seen in Fig. 7, the structure is successful to separate the different incident wavelengths to different outputs. In this design, two points is most prominent. First point is the wavelength of the incident light in the dropping band of region 3 must be in the nondropping band of region 1 and 2; the wavelength of the incident light in the dropping band of region 2 must be in the non-dropping
Fig. 5. Heterostructure WDDM with ring resonators.
M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
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Fig. 7. Optical power transmission characteristics of four outputs WDDM with ring resonator.
Fig. 6. Band diagram of square lattice photonic crystal for (a) n = 3.82, (b) n = 3.66 and (c) n = 3.44.
band of region 1. So in this case every ring resonator drops the wavelength matched with its resonant wavelength from the bus waveguide and couples this specific wavelength into the output port.
Fig. 8. Electric field intensity of wavelength demultiplexer with ring resonator at (a) k1 = 1513 nm; (b) k2 = 1541 nm; (c) k3 = 1569 nm and (d) k4 = 1594 nm in the communication window.
Another important point is ring resonators must be located so far away to avoid affecting each other. Due to effect of ring resonators on each other, their resonant wavelength will be changed; this
4032
M. Djavid et al. / Optics Communications 281 (2008) 4028–4032
situation makes designing rigid. Based on our simulations, distance of 6 rods leads to obtain acceptable results and no interference is occurred. Also crosstalk information from each port for the different wavelengths is written as following table:
Port Port Port Port
B C D E
1513 nm (%)
1541 nm (%)
1569 nm (%)
1594 nm (%)
82 5 9 3
8 83 4 5
0 4 87 9
0 0 3 96
Finally, snapshots of time domain simulation are depicted. The Fig. 8 shows the electric field intensity of wavelength demultiplexer with ring resonator at (a) k1 = 1513 nm of port E, (b) k2 = 1541 nm of port D, (c) k3 = 1569 nm of port C and (d) k4 = 1594 nm of port B in the communication window. 5. Conclusions In this paper, a heterostructure wavelength demultiplexer with four outputs in photonic crystal was investigated. Using this heterostructure we can demultiplex four different wavelengths within third communication window. Normalized transmission of these wavelengths is over 85%. In addition, utilizing the heterostructure in our design helps us to achieve higher power output and get a more outputs.
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