Low-loss process optimization for 3D IOX waveguides fabricated by matrix electrodes using Gaussian process regression and Bayesian optimization

Three-dimensional ion-exchanged (3D IOX) waveguides show great potential for applications in co-packaged optics and high-density photonic integration. In this study, we propose what we believe to be is a novel fabrication method for 3D IOX waveguides utilizing a matrix-electrode configuration. A comprehensive multiphysics model was developed, integrating electric field, ion concentration, temperature, and refractive index distributions to accurately simulate the fabrication process. Experimental validations confirmed the model's high predictive accuracy, demonstrating an average refractive index prediction error of only 0.06%, a burial-depth prediction error of approximately 0.6 µm, and excellent agreement with measured refractive-index profiles. Furthermore, we developed an integrated optimization algorithm combining a piecewise power-law distribution with Gaussian process regression and Bayesian optimization. The proposed algorithm achieved superior prediction accuracy (<i>R</i>²=0.9996, RMSE = 0.0061), reducing the transmission loss of the optimized 3D SSC waveguide significantly from 1.52 to 0.1 dB, corresponding to a 27% improvement in transmission efficiency.