Topology optimal design of optical waveguides in Consideration of polarization dependence using BPM and AVM

Abstract

Topology optimization has a great potential for finding out more compact and higher performance optical waveguide devices. In past researches on topology optimization, the finite element method (FEM) or the finite difference time domain (FDTD) method has mainly been employed as a numerical analysis method [1, 2]. In the case that the longitudinal refractive index distribution varies gradually and backward wave reflections can be negligible, the beam propagation method (BPM) is very useful technique. Large size devices of being difficult to analyze with the FEM or FDTD in terms of computational cost are able to be designed using topology optimization by applying the BPM. Wavefront matching method (WFM) [3] is an design method of optical waveguide devices based on the concept of the BPM. An optimum refractive index distribution can be synthesized automatically using WFM. However, WFM is not based on a minimization problem of objective functions, and the arbitrariness of objective property has not been discussed yet. In the case of directional coupler-type devices or devices with high refractive index contrast, polarization dependence is one of the issues to be solved. In topology optimization, an optical waveguide device can be designed with consideration for TE and TM polarization. In this paper, we present a gradient-based topology optimal design of optical waveguides in consideration of polarization dependence using the BPM. We apply the adjoint variable method (AVM) for calculating sensitivities and the density method for representing refractive index distribution in design region.