Fig. 1. Detail of the principle of the PS algorithm. (a) Schematic of the second step: search process of the first vertex. (b) Flow chart of the PS algorithm.

Fig. 2. Design process of the integrated DCMC-CW module. (a)–(d) Outline of the design process, where the right figures of (a)–(d) are the corresponding polygons of the structures in the left figures of (a)–(d), respectively.

Fig. 3. Two prediction methods of the second step. (a)–(c) Using the approximate gradient to predict a better vertex position. (a), (b) Linear and quadratic function fittings. (c) Predict β by the approximate gradient. The FOM corresponding to each x-y coordinate represents the FOM when the vertex searching for the best position is at that x-y coordinate, while the positions of other vertices are unchanged. (d)–(f) Using a neural network to predict a better vertex position. (d) Sampling in the prediction region. (e) Schematic of a neural network. (f) Predict β by a neural network.

Fig. 4. Simulation and experimental testing results of the integrated DCMC-CW module(s). (a) Scanning electron microscopy (SEM) image of an integrated DCMC-CW module. (b), (c) Electromagnetic field distribution in a single integrated module when TE0 is input in the left and top ports. (d) SEM image of two integrated DCMC-CW modules connected for the interconversion between TE1 and TE2. (e) Electromagnetic field distribution in two integrated modules. (f) Simulated and experimental tested transmission when TE0 is input in different ports of a single integrated module. (g) Simulated and experimental tested transmission when two integrated modules are used for interconversion between TE1 and TE2.

Fig. 5. Four-channel CMDM system and its performance. (a) Four-channel CMDM system applied in optical computing. (b) SEM image of a kind of configuration of the four-channel CMDM system. (c) Electromagnetic field distribution in the system in (b) when all the channels have signal input. (d) ILs and CTs of every channel in the working bandwidth.

Fig. 6. Contrast experiment of the PS algorithm and some mainstream inverse design algorithms. (a)–(f) Initial structures of the best examples shown in Table 1. (g)–(l) Final structures with an optimal performance. (m) Comparison of the optimization processes of the best examples.

Fig. 7. Multi-channel CMDM systems composed by the integrated DCMC-CW modules. (a) Three-channel CMDM system. (b) Four-channel CMDM system. (c) Five-channel CMDM system. (d) Six-channel CMDM system.

Fig. 8. Specific simulation results of the four-channel CMDM systems. (a)–(d) Electromagnetic field distributions in the crossing-mode-conversion region when the signal is transmitted in channels 1–4. (e)–(h) Transmission at the output port when the signal is transmitted in channels 1–4.

Fig. 9. Detailed initial structures in the contrast experiment. (a)–(c) Three kinds of initial structure 1 with different number of vertices. (a) Initial structure of PS 1, PS 2, GA 1, and GA 2. (b) Initial structure of PS 3, GA 3, and GA 4. (c) Initial structure of PS 4 and GA 5. (d) Initial structure of PS 5, PS 6, and GA 6. (e) Initial structure of PS 7, GA 7, and GA 8. (f) Initial structure of PS 10 and GA 10. (g) Initial structure of PS 8, PS 9, and GA 9. The width of the waveguides is 1.8 μm. (h) Random structure of DBS 10.

Fig. 10. Robustness of the PS-designed devices to fabricating deformations in small regions. (a), (b) Initial and final structures of the integrated module in PS 3. (c) Fabricating result of the integrated module in PS 3. (d) Contrast experiment results of the final structures before (solid line) and after (dashed line) removing the small absences (the black solid line and black dashed line are very close). (e) Comparison of experimental testing and simulation results of the fabricating result in (c).