Design and analysis of photonic crystal ring resonator based 6 £ 6 wavelength router for photonic integrated circuits

A photonic crystal ring resonator ‐ based 6 � 6 router has been designed and reported. The router is designed using silicon pillars with a refractive index of 3.47 perforated in the air background of refractive index 1 in a square lattice with a lattice constant of a ¼ 562 nm. The router is designed to operate in the third optical window wavelength which has low loss and most widely used in optical communication systems and networks. Plane ‐ wave expansion and finite difference time domain method has been used to obtain the bandgap and performance of the designed router, which exhibits acceptable performance such as low insertion loss, low propagation delay, and low crosstalk. These routers will find applications in the photonic integrated circuit that paves a path to all ‐ optical


| INTRODUCTION
Photonic integrated circuit (PIC) is the future technology in which all the optical components and devices are integrated to form a single photonic chip. These chips will satisfy the demands for signal processing and high-speed data transmission between the increasing numbers of users. These miniaturised PIC with high reliability, minimised errors, and high speed of operation will highly enhance the light wave communications [1]. This eventually entails routing of signals between different ports in the integrated circuit networks with complete connectivity and improved performance [2]. Photonic crystalbased components such as splitters [3,4], circulators [5], filters [6], decoder [7], low-power encoders [8][9][10], and routers [11][12][13] were designed and reported. Among them, routers play a vital role in transmitting signals from one user to others with low loss and high efficiency in order to deliver high-quality signals to the end-users and minimise the traffic in the data transmission.
The 3 � 3 router with two different topologies interconnecting three input and output ports was reported. Trade-off between the complexity of the structure and wavelength resource has been considered in designing the routers [2]. The 4 � 4 dynamic hitless router on Silicon on Insulator (SOI) technology using eight micro-ring resonators which were individually tuned using micro-heaters was demonstrated. The design has an extinction ratio of 20.79 dB and a bandwidth of 38.5 GHz [11]. The 4 � 4 crossbar based on micro-ring resonator add-drop filter using waveguides and ring resonators of radii as small as 1.8 µm fabricated on SOI substrate using deep UV lithography [14]. Kirman and Martínez proposed an all optical approach to construct data networks on chip that combines wavelength-based routing with high on-chip bandwidth, less power, and robust [15].
A five-port optical router based on micro-ring resonators on SOI platform using standard CMOS technology was reported. These resonators can be tuned through the thermooptic effect and extinction ratio of 21 dB was reported [16]. Calo and Petruzzelli proposed an optical 1 � 2 passive wavelength router and also analysed the behaviour of a 4 � 4 router configuration by assembling eight 1 � 2 routers which are capable of connecting four transmitters and four receivers with maximum crosstalk of À 13.9 dB between the ports [17]. Moreover, in 2014 they have proposed a 2 � 2 PhC router using two photonic crystal ring resonator (PCRR) of 3.2 µm diameter and a broadband PhC waveguide with the maximum crosstalk of À 20 dB. Analysis of 4 � 4 router using a four 2 � 2 router is also been reported [18].
Broadband PhC waveguide crossing using two 1 � 2 PhC λ-routers based on point defect micro cavities was demonstrated. High routing efficiency was achieved by engineering the rods of micro-cavity structure with gradual radii [12]. An optical switched router using 16 microrings, 14 crossrings, and 4 90°waveguide bends to construct a large photonic routing network on chips was reported [13]. Sathyadevaki et al, have demonstrated 4 � 4 wavelength routers which exhibit maximum crosstalk of À 15.1017 dB at 1567 nm and maximum insertion loss of 1.73 dB at 1520 nm [19]. The photonic crystal-based routers using different optical materials like Germanium, Gallium arsenide, and Indium phosphate was reported and the performance of the router with respect to the materials were also analysed and reported [20].
Even though considerable research has been carried out in design, size and performance of routers on different configurations from 1 � 2 router to 4 � 4 router with low crosstalk, low insertion loss, and high efficiency, the 6 � 6 routers with maximum insertion loss of 1.6115 dB and crosstalk of À 12.3553 dB with highest propagation delay of 810 ps is reported for the first time. The 6 � 6 router was designed using the 1 � 2 and 2 � 2 routers as a basic building block and the entire structure is analysed using the finite difference time domain (FDTD) method.

| PHOTONIC BANDGAP STRUCTURE
The router is designed with silicon rods embedded in air background with an index difference of 2.46 in a square lattice arrangement with a lattice constant of a ¼ 562 nm. The square lattice is preferred to obtain the symmetrical structural design and well confined photonic bandgap (PBG) in this design [21]. The gap map technique was used to obtain the optimised design parameters such as lattice constant 'a', rod radius 'r'. Gap map is a plot of the PBG of crystals by varying one or more parameters of the crystals [22]. The radius of the Si rods (r ¼ 0.175*a µm) and the lattice constant 'a' were obtained from the gap map technique for the wavelength of 1550 nm. Figure 1 shows the PBG structure of the proposed router design.

| ROUTER DESIGN AND TOPOLOGY
The 6 � 6 PCRR-based router comprises of 24 ring resonators with a dense arrangement. The router is designed to operate in the third window due to its low attenuation loss and widely used optical window. Figure 2 shows the pictorial representation of 6 � 6 routers. The routing of the wavelength between the 6 inputs and output ports were achieved by using the four 1 � 2 and ten 2 � 2 routers. Table 1 shows the routing element and their respective wavelength used for the link establishment for all 30 pathways in 6 � 6 wavelength router. The proposed router requires 24 ring resonators (named from A to X) to route the four out of five wavelengths whereas the remaining one doesn't need resonators to route between the ports. Each ring resonator is designed to have specific resonant wavelengths to enhance the transmission. Four groups of six resonators have been clubbed to have one resonant wavelength for operation. Table 2 shows the resonating wavelength and rod radius of the ring resonators used in this design. The resonant wavelength of the designed ring resonators depends on the rod radius of the resonator. The value of 'r' is optimised using the Input ports Abbreviation: No R, no ring resonator.
-41 gap map technique to get a desired resonant wavelength. A gap map representing TE/TM gap locations versus the ratio of rod radius to the lattice constants, as shown in Figure 3a is used for the optimization process. From the obtained gap map plot the value of the inner rod radius is chosen accordingly to resonate the required wavelength. A curve showing the calculated resonant wavelength as a function of the rod radius is plotted as shown in Figure 3b. The wavelengths from the third window 1.49, 1.5, 1.51, and 1.52 µm were used for the routing. Resonators A, G, J, O, T, and W resonate for λ 1 ¼ 1.49 µm. B, F, K, P, Q, and V resonators form the second group resonating at λ 2 ¼ 1.5 µm. The third group of resonators C, H, I, M, S, and X resonates at λ 4 ¼ 1.51 µm and finally D, E, L, N, R, and U is designed to have a resonant wavelength of λ 5 ¼ 1.52 µm. λ 3 is been selected as 1.48 µm from the PBG range and it does not require any resonating structures to route them.
In order to have a better understanding, the routing of wavelength by considering port 2 as the input port is explained in detail with respective figures. With λ 1 as wavelength, the signal from port 2 will resonate at ring resonator G and will appear as an output signal at port 5. The wavelength λ 2 from port 2 will travel in the straight waveguide and then resonates with ring resonator F to reach output port 4.
The wavelengths λ 4 and λ 5 will resonate at the ring resonator H and E and reaches the output ports 6 and 1 respectively. Port 2 to output port 3 does not requires any resonators and λ 3 signals will propagate in the straight waveguide without encountering any ring resonator to reach the port 3. Similar to this the other wavelengths will propagate from different input ports using their respective routing path to reach the desired destination ports. The routing path depends on the input wavelength and the resonant wavelength of the resonators placed in the path. The propagation path (routing path) for the input/output ports in the structure is based on the location of the ring resonators for each wavelength. Figures 4-8 show the propagation of signal with port 2 as input to different output ports.

| SIMULATION RESULTS
Performance of 6 � 6 wavelength router is analysed using the FDTD method with perfectly matched layer boundary conditions. Courant condition is used to obtain stable results at each simulation with a Gaussian wave as an input signal [23]. The parameters such as propagation delay, insertion loss, and crosstalk were calculated using the standard formulae [2]. Propagation delay is obtained by using numerical analysis from FDTD simulations. Crosstalk is the phenomenon in which a signal transmitted on one channel of a transmission system creates an undesired effect in another channel. Insertion loss is the amount of light that is lost as the signal arrives at the receiving end of the link. Insertion loss is measured in decibels (dB) and each passive connection in a system increases the dB loss for the system as a whole. Transmittance at all the output ports was obtained then the crosstalk and insertion losses were calculated using the following expressions. where, T i , T t and T x are the transmittance of isolated ports, through ports and port X. Figure 9 shows the spectrum of desired signals obtained from all the output ports when each port acts as an input. Figure 10 shows the transmittance and crosstalk at output ports when input is excited at the port 2 of the router. For this proposed 6 � 6 router, a total of 36 outputs is obtained considering each port as an input port. Table 3 gives the values of insertion loss and propagation delay of the 6 � 6 wavelength router. The propagation delay for the router is in terms of nanoseconds and the highest delay of 0.81 ns is achieved for the pathway between ports 2 and port 1. In terms of crosstalk (CT), considering port 1 as input port the maximum values of CT obtained are CT 45 ¼ À 13.5044 dB, which is the CT between the through port 4 and isolated port 5. The minimum values obtained is for CT 23  The highest and lowest range of CT obtained for port 4 as input port are CT 56 ¼ À 25.8252 dB and CT 26 ¼ À 13.2951 dB. Port 5 as input port have a maximum value of CT 13 ¼ À 15.7054 dB and minimum values as CT 12 ¼ À 29.6848 dB and CT 42 ¼ À 29.9519 dB. Finally, port F I G U R E 4 Propagation of signal λ 5 ¼ 1.52 µm from port 2 to port 1 using ring resonator 'E' F I G U R E 5 Propagation of signal λ 3 ¼ 1.48 µm from port 2 to port 3 without any ring resonator F I G U R E 6 Propagation of signal λ 2 ¼ 1.5 µm from port 2 to port 4 using ring resonator 'F' F I G U R E 7 Propagation of signal λ 1 ¼ 1.49 µm from port two to port five using ring resonator 'G' F I G U R E 8 Propagation of signal λ 4 ¼ 1.51 µm from port 2 to port 6 using ring resonator 'H' THIRUMARAN ET AL.
-43 6 as an input port, the maximum and minimum values of CT obtained during the simulation is CT 51 ¼ À 17.498 dB and CT 12 ¼ À 27.9577 dB. All the values are tabulated in Table 4. The parameters of the devised structure along with the existing photonic crystal routers are shown in Table 5.
From Table 5, it is noted that different group of researchers has reported PCRR-based routers operating around the third optical window wavelength. We have designed a higher order 6 � 6 wavelength router due to the increase in demand for routing between large number of input and output F I G U R E 1 0 Transmittance and crosstalk of signals at output ports: (a) port 1 as input, (b) port 2 as input, (c) port 3 as input, (d) port 4 as input, (e) port 5 as input, and (f) port 6 as input F I G U R E 9 Transmittance of signals from output ports: (a) port 1 as input, (b) port 2 as input, (c) port 3 as input, (d) port 4 as input, (e) port 5 as input, and (f) port 6 as input ports and an increasing number of users. The parameters such as operating wavelength, crosstalk, insertion loss, delay, and area of the devised structure have been given in the table.

| CONCLUSION
In summary, photonic crystal based 6 � 6 router has been demonstrated for the first time to the best of our knowledge. The photonic router is designed based on PCRRs. The evaluation result of the designed structure based on FDTD shows that the 6 � 6 router achieves acceptable performance measures in terms of crosstalk, insertion loss, and propagation delay. The highest crosstalk, insertion loss, and -45 propagation delay obtained in this reported structure are À 12.3553 dB, 1.6115 dB, and 810 ps. In spite of the complex 6 � 6 router structure, the main advantage of the reported design is that the routing path for any input-output port configuration will encounter only one ring resonator or no resonator at all. And also the routing path between the input and output ports depends on the location of the ring resonators along the path. Thus, the routing path can be designed based on the requirement of the application. Moreover, the ultra-compact size of the router 4900 µm 2 will make it a candidate applicable for a fully integrated optical circuit in the future of telecommunication industries.