Improved Low Crosstalk, High Transmission and Quality Factor Eight Channel Demultiplexer Based on Photonic Crystal

Due to the importance of all-optical demultiplexers (DEMUXs) in optical communication networks, this study aims to design and simulate a novel type of DEMUX using 2D photonic crystals (2D-PhCs). The proposed structure consists of one input waveguide and eight output channels considering linear and point defects. To design this DEMUX, silicon dielectric rods with the refractive index of 3.45 are employed in the air background, the radius of which is equal to R=0.21(cid:0) ((cid:0) = 0.522µm) where (cid:0) is the lattice constant. The photonic band gap (PBG) and output spectrum of the structure are analyzed by the plane wave expansion (PWE) and nite-difference time-domain (FDTD) methods, respectively. The simulation results indicate the average quality factor and transmission eciency are 3,602 and 98%, respectively, and inter-channel crosstalk ranges from -60.5 to -25.5 dB.


Introduction
Fiber-optic communication systems transmit data with lower attenuation over long distances than radio frequency (RF) communication systems [1][2]. Recent advances in modern technologies and high speed of light are among the important factors in uencing the development of integrated optical devices. This approach gradually leads to the replacement of classical electronic systems with next-generation optical systems. In optical communication networks, light waves transmit data over very long distances with excellent speed [3][4][5][6]. In these networks, light waves travel inside optical bers which are designed in the infrared frequency range at the wavelength of 0.8-1.65 µm and transmit data across the ultra-wideband of about 1 THz [7][8][9][10].
Optical networks become easier and cheaper when they are routed through SMF for a large number of users. Wavelength division multiplexing (WDM) technology along with SMF is applied to send a number of unique light waves through the same SMF. At the receiver's end, the light emitted from the SMF is distributed to the user separately by DEMUX [11][12][13][14][15].
To construct ultra-compact optical DEMUXs, the structures should be able to control the propagation of light waves inside very small space and waveguides [16][17][18]. Due to their small size, excellent performance in optical sensors, high-speed data processing and optical networks, photonic crystals (PhCs) have provided new opportunities for designing all-optical devices required for realizing all the integrated optical circuits, communication networks and data processing systems [19][20][21][22]. Photonic crystals are composed of alternating layers of insulating materials. PBG, as one of their unique properties [23][24][25], is de ned as a speci c frequency (or wavelength) range, in which the propagation of electromagnetic waves is prohibited in any direction and can be controlled by different structural parameters such as lattice constant, dielectric constant of the material and rod radius [26][27][28][29]. Electromagnetic waves propagate inside the PBG when a defect is formed.
There are usually two types of defects, namely linear and point, for PBG. Linear defect occurs by removing or changing structural parameters (lattice constant, refractive index and rod radius) of the entire row of rods in the PhC structure. Point defect occurs by completely removing or changing structural parameters of the rod. Designing PhC structures requires the introduction of one or both types of defects [30][31][32][33][34]. These structures are applied in various optical devices such as design and fabrication of optical waveguides, optical lenses, optical lters, optical MUXs/DEMUXs, optical splitters, photonic sensors, optical converters, all-optical logic gates, optical modulators/demodulators and other types of optical devices. Various PhC-based devices have been proposed so far [35][36][37][38]. Signi cant advances in the eld of PhCs have raised hopes for having more all-optical systems and replacing electrons with photons [39][40].
PhC-based DEMUXs play a key role in WDM techniques and can be used as the basic block in realizing some other optical digital devices [41][42][43]. Hence, different methods have been presented for designing PhC-based optical DEMUXs. Nowadays, PhC-based DEMUXs have received great attention from researchers due to their intrinsic properties such as low energy consumption, very small size, low loss, better performance, etc. [44][45][46]. The number of output channels, transmission e ciency, quality factor, crosstalk and inter-channel spacing are among the most important properties of PhC-based DEMUXs [47][48]. Most of the studies have been conducted on 4-channel DEMUXs. The e ciency of DEMUX technologies depends on the number of optical channels existing inside the optical ber. To increase the number of channels inside the optical ber, it is necessary to design optical DEMUXs considering more output channels. Therefore, designing 8-channel DEMUXs is more useful than 4-channel DEMUXs. transmission coe cient of this structure were obtained as 1,319 and 98%, respectively. The crosstalk ranged from -40 to -16 dB [53]. Rakhshani (2020) presented an 8-channel DEMUX based on 2D-PhCs and reported the quality factor, transmission coe cient and average inter-channel crosstalk of 1,000, 96% and -35 dB, respectively [54]. Reviewing the reported DEMUXs, this paper aims to address the shortcomings of previous structures such as transmission e ciency, quality factor and inter-channel crosstalk. Therefore, this study presents a novel structure of PhC-based DEMUX. The rest of this paper is organized as follows: Section 2 examines PBG using PWE method and presents the nal structure of the proposed DEMUX. Section 3 presents the simulation results using FDTD method and compares results of this work with those o previous studies. Section 4 provides the conclusion.

Proposed Demux
This study aims to present a PhC-based 8-channel DEMUX. For this purpose, the 63×31 array of dielectric rods was used in X and Z directions in the air background. The structure lengths were 33 µm and 16 µm in X and Z directions, respectively. The area of the proposed structure was considered to be 528 µm 2 .
The design of PhC structures depends on parameters such as lattice constant ( ), radius of dielectric rods (R), refractive index of dielectric rods (n) and material of dielectric rods. The desired PBG could be achieved by changing these parameters. The radius of dielectric rods (R) was considered as R=0.21 ( = 0.522µm), where is the lattice constant, i.e., all the four dielectric rods were located at square corners, the side length of which was equal to 0.522 µm. The dielectric rods were made of silicon with the refractive index of 3.45 (n si = 3.45).
The structure should have the appropriate PBG within the desired wavelength range in order to conduct light waves in photonic crystals. For this purpose, PBG was calculated by PWE method. The PWE method follows Maxwell's equations, and calculates TE and TM band gaps as follows [8,52]: where ε(r) is the dielectric constant, E(r) is the frequency-dependent electric eld vector, ω is the angular frequency and c is the light speed in vacuum. Fig. 1 indicates PBG diagram of the proposed structure. The PBG was in the range of 1.29µm < λ < 1.86µm, which was suitable for optical communications in the third telecommunication window.
Choosing the structure wavelength was the most important part in designing the PhC-based DEMUX. The input waveguide was created by removing 55 dielectric rods from the central row of the structure. Then, four output waveguides were created both at the top and bottom of the structure by removing and changing the radius of dielectric rods. At each output, several dielectric rods were removed and the radius of the dielectric rod was changed. Using different radii for the eight outputs provided different wavelengths for them. Table 1 presents the defect rod radius related to the proposed DEMUX structure. Fig. 2 indicates the nal structure of the proposed DEMUX. Simulation Results The simulation was performed using FDTD method in order to investigate the optical behavior of the proposed DEMUX and the output spectrum was plotted in terms of wavelength. To use this method, accurate meshing and time calculations were required. The following equation was applied [55]: where Δx and Δz denote mesh sizes of the structure, Δt represents time steps of the structure and c is the light speed in open space.
The 8-channel DEMUX is a key process in data transmission. In this study, the main goal was to design an optical DEMUX with 8 output channels at very low bandwidth in the third telecommunication window due to low losses. The lattice constant ( ) had to be changed in order to place the output channels in the range of 1.55 µm in the proposed structure. The output spectrum of the structure tended toward lower wavelengths by reducing the lattice constant, so that the output spectrum of the structure was in the wavelength range of C-band at the lattice constant of 0.522 µm. Then, the appropriate output spectrum was obtained for the eight output channels in terms of quality factor, transmission e ciency and crosstalk by managing the refractive index and radius of dielectric rods of the structure and performing the trial and error of defect rods in the output path. As shown in Fig. 3, the average overall e ciency and channel spacing were 98% and 5 nm, respectively.
Quality factor (QF) is another important parameter in DEMUX. The quality factor of DEMUX for each channel was calculated as follows: where QF is the quality factor, λ 0 is the central wavelength and ∆λ is the channel bandwidth. According to the above equation, lower bandwidth was associated with a higher quality factor. Therefore, in the proposed structure, the minimum and maximum quality factors were 2,739 and 4,277, respectively. Table  2 presents details of the output spectrum of each channel such as central wavelength, bandwidth, quality factor and transmission e ciency.  The degree of interference between adjacent channels (crosstalk) is another important indicator for evaluating the performance of the PhC-based DEMUX. The effect of crosstalk on optical communications is serious because the signal sent to a channel can create an adverse effect on another channel. In designing DEMUXs, there is less effort to achieve crosstalk. According to the output spectrum of the structure (dB) shown in Fig. 5, Table 3 presents the crosstalk. The inter-channel crosstalk ranged from -60.5 to -25.5 dB, which was very lower than previous similar works.  Table 4 compares the obtained results with those of previous works in order to value the present paper. The proposed structure had higher quality factor and transmission e ciency as well as lower crosstalk than previous works.

Conclusion
This study designed and simulated an 8-channel DEMUX based on 2D-PhCs with a square structure using linear and point defects. This structure consisted of one input waveguide and eight output waveguides. The wavelength of the output channels was in the range of the third telecommunication window by setting the lattice constant. The appropriate output spectrum was obtained in terms of quality factor, transmission e ciency and crosstalk via managing the refractive index and radius of dielectric rods of the structure, and changing the radius of defect rods in the path of the output channels. One of the important properties of our proposed structure was that a very regular output spectrum could be achieved without moving the rods, which was very effective in the manufacturing process. The transmission e ciency, inter-channel spacing, bandwidth and quality factor of the proposed DEMUX were 98%, 5 nm, 0.44 nm and 3,602. Moreover, inter-channel crosstalk ranged from -60.5 to -25.5 dB, which improved compared to previous similar works. The functional properties of the proposed DEMUX could meet the expectations of CWDM systems. Furthermore, the area of the proposed structure was about 528 µm 2 , which was very small. Therefore, it could be implemented for photonic integrated circuits. Figure 1 The band structure diagram of the proposed photonic crystal The schematic diagram of the proposed 8-channel PhC DEMUX Figure 3 Output spectrum of the proposed 8-channel DEMUX Figure 4 Electric eld distribution of the proposed DEMUX in channels 1 (a), channel 2 (b), channel 3 (c), channel 4 (d), channel 5 (e), channel 6 (f), channel 7 (g) and channel 8 (h) Figure 5 Output spectrum of the proposed 8-channel DEMUX (dB)