Efficient topology optimization of optical waveguide using finite element method based on slowly varying envelope approximation

Abstract We propose a novel finite element method (FEM) for efficient optical waveguide analysis to improve the computational efficiency in inverse design of optical waveguide devices. In our formulation, applying slowly varying envelope approximation (SVEA) to FEM, an electromagnetic field expression is split into a slowly varying complex envelope amplitude and a steady-state oscillating term. Then, field profile can be obtained by just solving the slowly varying complex envelope amplitude and the number of unknown variables along the propagation direction can be greatly reduced. The proposed method can achieve efficient optical waveguide analysis. Furthermore, by employing this analysis method in the inverse design of optical waveguide devices, automatic optimization of device structure can be carried out with reasonable computational costs.