Waveguide mode-solving techniques using finite difference method with coordinate stretching

Abstract

Dielectric waveguides are commonly used in photonic integrated circuits and their accurate modeling is essential for the development of new, higher performance optical components required by high-bandwidth communications system. Modal analysis is a critical part of the waveguide design process, providing information on the modes that may propagate, such as propagation constants and mode shapes. In brief, by reformulating the Maxwell equation, the problem is deducted to an eigenvalue equation and it can be discretized by a finite difference method. The full-vector waveguide equation is solved by the classic inverse iteration method and the alternating-direction-implicit (ADI). In addition, coordinate stretching technique is employed, which effectively removes the sensitivity of the calculated results to the size of the computational domain.