Efficient topology optimization of optical waveguide devices utilizing semi-vectorial finite-difference beam propagation method

An efficient gradient-based topology optimal design approach using beam propagation method (BPM) for a 3-D semi-vectorial design problem of optical waveguide devices is proposed. A semi-vectorial finite-difference BPM (SVFD-BPM) based on an alternating direction implicit method (ADIM) is employed for the wave propagation analysis in our design approach. In comparison to conventional 3-D topology optimal design approaches, it is expected that our approach can reduce its computational cost and design an optical waveguide which is too long to analyze using a finite element method or finite-difference time/frequency-domain method. In this paper, we design several waveguide devices (S-bend, power splitter, and mode converter), and it is shown that our topology optimal design approach surely works.