Valley photonic crystal (VPhC) slow-light waveguides can achieve robust optical transmission even in the presence of structural defects or sharp corners. However, the normalized delay bandwidth product (NDBP) of VPhC slow-light waveguides is still limited at present. Therefore, we propose a broadband low-dispersion VPhC slow-light waveguide designed by employing machine learning technique, providing references for the design of broadband low-dispersion VPhC slow-light waveguides and machine learning-based optimization of integrated photonic devices.

We take the bearded interface VPhC slow-light waveguide as the research object and adopt the machine learning method to optimize the size of equilateral triangular air holes on both sides of the interface, so as to realize the design of broadband low-dispersion VPhC slow-light waveguide. Firstly, two-dimensional plane wave expansion (PWE) is utilized to simulate the dispersion curve of the topological boundary state, with the influence of the size of air holes at different distances from the interface on the broadband low-dispersion slow-light characteristics of the topological boundary state discussed. Then, the NDBP values of the VPhC waveguides with different air hole sizes near the interface are calculated by employing the histogram of the group indices of the topological boundary states, with the database established. The samples with multi-mode and non-significant slow-light effects are marked. On this basis, a series classification regression neural network is trained to predict the NDBP of VPhC waveguides with significant slow-light characteristics (group index≥20). Finally, this forward prediction network is combined with the particle swarm optimization (PSO) algorithm, and the VPhC slow-light waveguide structure with NDBP up to 0.356 is designed by optimizing the size of the three rows of air holes near both sides of the interface.

Two-dimensional PWE is adopted to simulate the dispersion curve of the topological boundary state, and the influence of the size of air holes at different distances from the interface on the broadband low-dispersion slow-light characteristics of topological boundary state is discussed (Fig. 3). By conducting the analysis, the variation range of air holes is determined, and 1287 VPhC waveguide samples with different size of air holes near the interface are collected for the training of the sequence classification neural network (Table 1). By optimizing the neural network structure, the accuracy of neural network classification and prediction is further improved, and the mean square error is reduced (Fig. 4). Then PSO is combined with the trained neural network (Fig. 4) to optimize the structure corresponding to the maximum NDBP value of 0.3555. The optimization results are verified by two-dimensional PWE, and the calculated NDBP is 0.3654, and the full-wave simulation verifies the robust transmission of the optimized topological boundary state in the straight and Z-type waveguides, with the transmission of the pulse signal in the waveguide calculated (Fig. 5). It is improved compared with the reported VPhC slow-light waveguide NDBP (Table 2). The influence of manufacturing error on the performance of the optimized waveguide is analyzed, and the results show that the error will result in a relative small reduction of NDBP (Fig. 6).

By taking the VPhC waveguide as the main research object, we study the design method of broadband low-dispersion slow-light waveguide based on machine learning. Firstly, the dispersion curves of the boundary states of the bearded interface configuration VPhC waveguide are simulated by the two-dimensional PWE method, and the influence of the size of equilateral triangular air holes near the interface on the broadband low-dispersion slow-light characteristics of the topological boundary state is analyzed. Then, the forward prediction neural network with a series classification regression structure is trained to select the VPhC waveguide with significant slow-light characteristics (group index≥20), with the relationship between NDBP and the size of air holes near the interface modeled. Finally, the PSO algorithm is employed to drive the network, and the size of the corresponding three-row air holes on both sides near the interface is optimized. A broadband low-dispersion VPhC slow-light waveguide structure with a center wavelength of 1550 nm is designed. The group index and bandwidth of the VPhC slow waveguide are 21.89 and 25.24 nm respectively, and NDBP can reach 0.356. The robust transmission of the straight waveguide and Z-type waveguide is simulated and analyzed. Compared with the results reported in the references, NDBP and relative bandwidth are improved by 36.9% and 48.2%, respectively. Our research will contribute to the further application of VPhC slow-light waveguides in the on-chip broadband low-dispersion transmission of optical signals and can provide references for the design of high-performance photonic devices based on machine learning.