Silicon Nanowire-Assisted High Uniform Arrayed Waveguide Grating

Determining how to improve the non-uniformity of arrayed waveguide grating (AWG) is of great significance for dense wavelength division multiplexing (DWDM) systems. In this work, a silicon nanowire-assisted AWG structure is proposed, which can achieve high uniformity with a low insertion loss. The article compares the effect of nanowire number and shape on uniformity and insertion loss, finding that double nanowires provide the best performance. Double nanowires with a width of 230 nm and length of 3.5 μm can consist of a slot configuration between arrayed waveguides, both connecting to the star coupler and spacing 165 nm from the waveguides. Compared with conventional 8- and 16-channel AWGs with channel spacing of 200 GHz, the non-uniformity of the presented structure can be improved from 1.09 and 1.6 dB to 0.24 and 0.63 dB, respectively. The overall footprint of the device would remain identical, which is 276 × 299 or 258 × 303 μm2 for the 8- or 16-channel AWG. The present high uniformity design is simple and easy to fabricate without any additional insertion loss, which is expected to be widely applied in the highly integrated DWDM systems.

However, the non-uniformity for traditional silicon-based AWGs still needs to be improved. The insertion loss of the edge channel would be about 3 dB higher than those of the center ones when free spectral range (FSR) is fully utilized [13,21,22]. Additional light power needs to be added to maintain the same bit error rate, ultimately affecting the power budget of the entire communication system [22][23][24][25]. After long-distance transmission, the signal-to-noise ratio of the traditional AWG would decrease seriously [26]. To solve this issue, many methods have been proposed such as mode field converters [27][28][29], optical combiner structures [30], and slab waveguide configurations [31]. Mode field converters usually require careful design and fine processing. Optical combiner structures increase the overall size as well as additional insertion loss. Slab waveguide configurations require additional transition area between ridge and slab structure which would result in excess losses. Moreover, some special designs at the interface of the arrayed waveguides and the free-propagation region were proposed. For example, a cyclic 16-channel AWGR shows a non-uniformity of approximately 1.1 dB and an additional insertion loss of 2.3 dB [32]. A 12-channel AWG using multimode interference couplers can achieves a non-uniformity of 0.8 dB but greatly increases the device size [33]. Assisted waveguides have been proposed recently, which could maintain the device size and insertion loss [34]. However, it could not solve the channel non-uniformity well, and the design still needs further optimization.
In this work, a silicon nanowire-assisted AWG is proposed, which can achieve high uniformity with a low insertion loss. The article compares the effect of nanowire number and shape on uniformity and insertion loss, finding that double nanowires provide the best performance. Double nanowires are used here to consist of a slot configuration between the arrayed waveguides and connect to the star coupler, which makes it different from the traditional design. Compared with conventional 8-and 16-channel AWGs with channel spacing of 200 GHz, the non-uniformity of the presented structure can be improved from 1.09 and 1.6 dB to 0.24 and 0.63 dB, respectively. Little change happens for the device's overall size by the introduction of the nanowires into the gaps between the arrayed waveguides. The overall footprint of the device would remain identical to the conventional design, which is 276 × 299 or 258 × 303 µm 2 for the 8 or 16-channel AWG. Moreover, the present simple design has no additional insertion loss. Additionally, a commercially available CMOS-compatible manufacturing equipment can be used for device fabrication. Thus, high-volume and low-cost production can be expected. Figure 1a shows the schematic diagram of the proposed nanowire-assisted AWG. The beam diverges at the input star coupler, then propagates through the arrayed waveguide, and finally converges on the image plane of the output star coupler. Figure 1b,c show the detailed diagrams of the arrayed waveguides and star coupler, with the length difference between two adjacent arrayed waveguides of 2(∆L 1 + ∆L 2 ). Here, L 1 and L 2 are 39 and 120 µm, as well as the bending radius is 20 µm. As shown in Figure 1c, double nanowires with a width W 1 of 230 nm and length L 3 of 3.5 µm can consist of a slot configuration between arrayed waveguides, both connecting to the star coupler and spacing G 1 of 165 nm from the arrayed waveguides. The spacing G 2 between the double nanowires is 110 nm. The designed structure is based on a silicon-on-insulator (SOI) platform, with a 3-µm-thick buffering layer and a 220-nm-thick silicon core layer, as shown in Figure 1d. The silicon waveguide with a width W of 500 nm is employed, ensuring a single fundamental TE mode operation.

Device Structure and Design
For the AWG design, there is a constant length difference between adjacent waveguides, which should equal an integer multiple of the central wavelength. The beam in each arrayed waveguide with the same wavelength arrives at the output star coupler with the same phase, and the light field distribution of the input star coupler will be reproduced in the output star coupler. As a result, the diverging beams in the input star coupler will converge into beams with the same amplitude and phase distribution on the image plane of the output star coupler. Due to the effect of waveguide dispersion, the focus point of the converged beam will move along the image plane of the output star coupler as the wavelength varies. Thus, the spatial separation of different wavelengths can be achieved by placing the output waveguides at an appropriate position on the image plane of the output star coupler [35]. by placing the output waveguides at an appropriate position on the image plane of the output star coupler [35]. For this AWG, the grating equation can be expressed as where ns and na are effective refractive indices of the star coupler and arrayed waveguides, da is the space between adjacent arrayed waveguides on the tangent line, α0 and α1 are the input and output angles, ∆L = 2(∆L1 + ∆L2) is the length difference between adjacent arrayed waveguides, m is an integer diffraction order, and λ is the wavelength of the beam within the waveguides [36]. For the conventional AWG, the light field distribution at the arrayed waveguides approximates a Gaussian distribution, resulting in a Gaussian envelope-distributed beam focused on the image plane of the output star coupler. Thus, this would lead to a nonuniform light intensity distribution between the central and edge channels, which could be described by a non-uniformity Lu defined as where Ie and Ic are the light intensities in the edge and center channels, respectively [21]. By introducing nanowires at the array waveguide, the field distribution at the end of the waveguide can be disturbed. Furthermore, the perturbation of the field distribution on the image plane can be calculated using Kirchhoff-Huygens formula. The parameters of nanowires are adjusted constantly so that the flat light field distribution on the image plane can be obtained. Therefore, the power difference of the output channel placed on the image plane is reduced, and the non-uniformity can be suppressed. Here, 8-and 16channel AWGs with improved non-uniformity are presented. Based on the impact of nanowires on non-uniformity, 8-and 16-channel AWGs with improved non-uniformity are designed and the main parameters are presented in Table 1. Table 1. Parameters of the nanowire-assisted AWG.
where n s and n a are effective refractive indices of the star coupler and arrayed waveguides, d a is the space between adjacent arrayed waveguides on the tangent line, α 0 and α 1 are the input and output angles, ∆L = 2(∆L 1 + ∆L 2 ) is the length difference between adjacent arrayed waveguides, m is an integer diffraction order, and λ is the wavelength of the beam within the waveguides [36]. For the conventional AWG, the light field distribution at the arrayed waveguides approximates a Gaussian distribution, resulting in a Gaussian envelope-distributed beam focused on the image plane of the output star coupler. Thus, this would lead to a nonuniform light intensity distribution between the central and edge channels, which could be described by a non-uniformity L u defined as where I e and I c are the light intensities in the edge and center channels, respectively [21]. By introducing nanowires at the array waveguide, the field distribution at the end of the waveguide can be disturbed. Furthermore, the perturbation of the field distribution on the image plane can be calculated using Kirchhoff-Huygens formula. The parameters of nanowires are adjusted constantly so that the flat light field distribution on the image plane can be obtained. Therefore, the power difference of the output channel placed on the image plane is reduced, and the non-uniformity can be suppressed. Here, 8-and 16-channel AWGs with improved non-uniformity are presented. Based on the impact of nanowires on non-uniformity, 8-and 16-channel AWGs with improved non-uniformity are designed and the main parameters are presented in Table 1.

Device Performance and Discussion
In order to simulate the performance of the nanowire-assisted high uniform AWG, 2.5D-FDTD (Lumerical FDTD Solutions of 8.9.1584) method was used [37]. Perfectly matched layers (PML) were used to simulate boundary conditions. The mesh size of the simulation area was set to ∆x = ∆y = 50 nm and ∆z = 20 nm. The refractive indices were 1.444 and 3.476 for SiO 2 and Si, respectively. When the wavelength was 1556 nm, the dispersion was about 1.4227 × 10 3 ps/nm/km. The light source was set to TE mode with a center wavelength of 1556 nm. Additionally, the simulation areas of the 8 or 16-channel AWG were 310 × 290 or 450 × 350 µm 2 . Light intensity field distribution along the image plane of AWG with different values of G 1 , W 1 and L 3 were compared with the other two parameters unchanged as in Figure 2d It should be emphasized that double nanowires configuration is optimum for the non-uniformity improvement. Tapered nanowire may not help to improve the insertion loss and non-uniformity but greatly increase the complexity of the design [21]. Figure 3 shows the simulated non-uniformity and insertion loss for all output channels with the variation of nanowire number N 1 . The optimal parameters of nanowires vary with the nanowire number N 1 . When N 1 is 1, the optimal parameters of nanowires are G 1 = 110 nm, W 1 = 440 nm and L 3 = 5 µm. When N 1 is 2, the optimal parameters of nanowires are G 1 = 165 nm, W 1 = 230 nm and L 3 = 3.5 µm. When N 1 is 3, the optimal parameters of nanowires are G 1 = 140 nm, W 1 = 160 nm and L 3 = 3.4 µm. For both, the non-uniformity decreases first and then increases with the nanowire number N 1 . When N 1 is 2, the channel's non-uniformity can be minimized to 0.24 and 0.63 dB with a minimum insertion loss for the 8-and 16-channel AWGs. The additional nanowires can improve the coupling efficiency of arrayed waveguides and star couplers, reducing insertion loss. Too few nanowires can not make the light intensity flat, while too many ones will deteriorate the performance.
It is important to investigate the influence of diffraction order (m) on non-uniformity and insertion loss. Figure 4 demonstrates the non-uniformity and insertion loss of all output channels with change of diffraction order. The non-uniformity for an 8-channel AWG initially decreases and then increases when the diffraction order increases gradually from 35 to 45, as shown in Figure 4a. When m is 40, the non-uniformity can be minimized to 0.24 dB. For a 16-channel AWG, the non-uniformity gradually reduces as the diffraction order increases from 28 to 36 as in Figure 4b. The free spectral range of 25.99 nm in this AWG can be fully utilized at m = 36, and the minimum non-uniformity may be achieved at 0.63 dB. It should be emphasized that double nanowires configuration is optimum for the non-uniformity improvement. Tapered nanowire may not help to improve the insertion loss and non-uniformity but greatly increase the complexity of the design [21]. Figure 3 shows the simulated non-uniformity and insertion loss for all output channels with the variation of nanowire number N1. The optimal parameters of nanowires vary with the nanowire number N1. When N1 is 1, the optimal parameters of nanowires are G1 = 110 nm, W1 = 440 nm and L3 = 5 μm. When N1 is 2, the optimal parameters of nanowires are G1 = 165 nm, W1 = 230 nm and L3 = 3.5 μm. When N1 is 3, the optimal parameters of nanowires are G1 = 140 nm, W1 = 160 nm and L3 = 3.4 μm. For both, the non-uniformity decreases first and then increases with the nanowire number N1. When N1 is 2, the channel's non-uniformity can be minimized to 0.24 and 0.63 dB with a minimum insertion loss for the 8and 16-channel AWGs. The additional nanowires can improve the coupling efficiency of arrayed waveguides and star couplers, reducing insertion loss. Too few nanowires can not make the light intensity flat, while too many ones will deteriorate the performance. It is important to investigate the influence of diffraction order (m) on non-uniformity and insertion loss. Figure 4 demonstrates the non-uniformity and insertion loss of all output channels with change of diffraction order. The non-uniformity for an 8-channel AWG initially decreases and then increases when the diffraction order increases gradually from 35 to 45, as shown in Figure 4a. When m is 40, the non-uniformity can be minimized to 0.24 dB. For a 16-channel AWG, the non-uniformity gradually reduces as the diffraction order increases from 28 to 36 as in Figure 4b. The free spectral range of 25.99 nm in this put channels with change of diffraction order. The non-uniformity for an 8-channel AWG initially decreases and then increases when the diffraction order increases gradually from 35 to 45, as shown in Figure 4a. When m is 40, the non-uniformity can be minimized to 0.24 dB. For a 16-channel AWG, the non-uniformity gradually reduces as the diffraction order increases from 28 to 36 as in Figure 4b. The free spectral range of 25.99 nm in this AWG can be fully utilized at m = 36, and the minimum non-uniformity may be achieved at 0.63 dB.  Figure 5a shows the comparison of the light intensity distribution on the image plane between the conventional and optimized designs. By introducing nanowires between the arrayed waveguides, the variation of light intensity on the image plane of the output star coupler can be reduced, which ensures that each output waveguide can be obtained the same optical power and the non-uniformity can be dramatically reduced. As shown in Figure 5b, the calculated electric field distribution shows that the beam diverges in the input star coupler, then enters the arrayed waveguides homogeneously. In Figure 5c, the beam from the end of arrayed waveguides can pass through the output star coupler and converge on the image plane at a wavelength of 1556 nm.  Figure 5a shows the comparison of the light intensity distribution on the image plane between the conventional and optimized designs. By introducing nanowires between the arrayed waveguides, the variation of light intensity on the image plane of the output star coupler can be reduced, which ensures that each output waveguide can be obtained the same optical power and the non-uniformity can be dramatically reduced. As shown in Figure 5b, the calculated electric field distribution shows that the beam diverges in the input star coupler, then enters the arrayed waveguides homogeneously. In Figure 5c, the beam from the end of arrayed waveguides can pass through the output star coupler and converge on the image plane at a wavelength of 1556 nm.  Figure 6 shows the spectral response of the 8-and 16-channel AWGs with the conventional and the nanowire-assisted design, respectively. The double nanowires with G1 = 165 nm, W1 = 230 nm and L3 = 3.5 μm can be chosen as the best parameters for subsequent simulations. For the 8-channel AWG as in Figure 6a,b, the non-uniformity is reduced from 1.09 to 0.24 dB as the insertion loss of the center channel is reduced from 6.78 to 6.26 dB. Meanwhile, the non-uniformity of the 16-channel AWG is reduced from 1.6 to 0.63 dB and the insertion loss of the center channel is reduced from 10.58 to 10.1 dB as in Figure 6c,d.   Figure 6a,b, the non-uniformity is reduced from 1.09 to 0.24 dB as the insertion loss of the center channel is reduced from 6.78 to 6.26 dB. Meanwhile, the non-uniformity of the 16-channel AWG is reduced from 1.6 to 0.63 dB and the insertion loss of the center channel is reduced from 10.58 to 10.1 dB as in Figure 6c,d. The coupler loss between the waveguide and the star coupler and furthermore the excitation loss of the adjacent grating make up the majority of the insertion loss of the AWG. For 8-and 16-channel AWG, the excitation loss of adjacent gratings are 3.18 and 3.95 dB, respectively, and the coupling loss are 3.08 and 6.15 dB. The AWG has little scattering and absorption loss. When the bending radius of the waveguide is greater than 5 µm, the bending loss is negligible [38]. Hence, the nanowire-assisted AWG can greatly improve the non-uniformity of the channel and reduce the insertion loss, which is beneficial for the development of WDM systems. 0 to 1 rad, the simulated noise floor of the 8-and 16-channel AWG would increase 4.16 and 6.14 dB, respectively. Thus, an optimized fabrication process is crucial for the device production. We also compare the presented design with other reported results as in Table 2. The proposed AWG can perform better in improving the non-uniformity without introducing any additional insertion loss. At the same time, the waveguide size enables its fabrication by commercially available manufacturing facilities, which could facilitate its low-cost applications. The proposal of this scheme is quite simple for improving AWG performance, which is expected to be applied in other multi-parameter uniformity optimization.  It is crucial to perform a sensitivity analysis of the device and demonstrate its robust. For the sensitivity analysis, the above constraint for parameters optimization should also be met. As shown in Figure 7, the sensitivities of 8-and 16-channel AWGs were simulated. Variations in non-uniformity were simulated by applying offsets to the AWG parameters W 1 , G 2 , and L 3 . For a 8-channel AWG, when ∆W 1 is between −11 and 11 nm, ∆G 1 is varying from −15 to 10 nm, and ∆L 3 is between −130 and 130 nm, the non-uniformity lies in the range from 0.24 to 0.34 dB, as shown in Figure 7a. For a 16-channel AWG, when ∆W 1 is between −6 and 9 nm, ∆G 1 is varying from −20 to 14 nm, and ∆L 3 is between −60 and 80 nm, the non-uniformity lies in the range from 0.63 to 0.73 dB, as shown in Figure 7b. Thus, for the 8-channel AWG, with the fabrication tolerance for W 1 , G 2 , and L 3 of 22, 25, and 260 nm, respectively, the maximum variation of non-uniformity is 0.1 dB. For the 16-channel AWG, with the fabrication tolerance for W 1 , G 2 , and L 3 of 15, 34, and 140 nm, respectively, the same non-uniformity change can be obtained. It should be mentioned that some phase noise would be introduced during the lithography. When the phase noise increases from 0 to 1 rad, the simulated noise floor of the 8-and 16-channel AWG would increase 4.16 and 6.14 dB, respectively. Thus, an optimized fabrication process is crucial for the device production.

Conclusions
In summary, a silicon nanowire-assisted AWG is proposed, which can achieve a high uniformity with a low insertion loss. In comparison with conventional 8-and 16-channel AWGs for channel spacing of 200 GHz, the non-uniformity of the presented structure can be improved from 1.09 and 1.6 dB to 0.24 and 0.63 dB, respectively. The overall footprint of the device could remain identical, which is 276 × 299 or 258 × 303 μm 2 for the 8 or 16channel AWG. Moreover, the proposed AWG has the advantages of moderate wire size, which can be fabricated by a commercial CMOS foundry in high volumes at a low cost. The present nanowire-assisted highly uniform silicon-based AWG is of great significance for the development of integrated DWDM systems.

Data Availability Statement:
The data that support the findings of this study have not been made available but can be obtained from the author upon request.

Conflicts of Interest:
The authors declare no conflicts of interest. We also compare the presented design with other reported results as in Table 2. The proposed AWG can perform better in improving the non-uniformity without introducing any additional insertion loss. At the same time, the waveguide size enables its fabrication by commercially available manufacturing facilities, which could facilitate its low-cost applications. The proposal of this scheme is quite simple for improving AWG performance, which is expected to be applied in other multi-parameter uniformity optimization.

Conclusions
In summary, a silicon nanowire-assisted AWG is proposed, which can achieve a high uniformity with a low insertion loss. In comparison with conventional 8-and 16-channel AWGs for channel spacing of 200 GHz, the non-uniformity of the presented structure can be improved from 1.09 and 1.6 dB to 0.24 and 0.63 dB, respectively. The overall footprint of the device could remain identical, which is 276 × 299 or 258 × 303 µm 2 for the 8 or 16-channel AWG. Moreover, the proposed AWG has the advantages of moderate wire size, which can be fabricated by a commercial CMOS foundry in high volumes at a low cost. The present nanowire-assisted highly uniform silicon-based AWG is of great significance for the development of integrated DWDM systems.

Data Availability Statement:
The data that support the findings of this study have not been made available but can be obtained from the author upon request.

Conflicts of Interest:
The authors declare no conflict of interest.