An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Abstract

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and patched at these interfaces by matching the physical boundary conditions. In addition, a new technique incorporating the effective index method and the Wentzel-Kramers-Brillouin method for the a-priori determination of the scaling factor in Hermite-Gauss or Laguerre-Gauss basis functions is introduced to considerably save computational time without experimenting with it. This method shares the same desirable property of the spectral collocation method of providing a fast and accurate solution but avoids the oscillatory solutions and improves the poor convergence problem of the simple spectral collocation method with single domain where regions of discontinuous refractive index profiles exist. Applications to several two-and three-dimensional waveguide structures having exact or accurate approximate solutions are given to test the accuracy and efficiency; all the results are found to be in excellent agreement. Index Terms-Discontinuous refractive index profiles, domain decomposition, optical waveguides, orthogonal basis function, scaling factor, spectral collocation method. I. INTRODUCTION R ECENTLY, there has been growing interest in developing integrated optics devices in optical communication systems. The fundamental operating principle and optimal design of optical devices such as modulators, switches, filters, fibers, and semiconductor lasers are often based on the comprehension of optical waveguide theory [1]. Hence, solving the optical waveguide problems is an essential way to clearly realize these devices. However, only a limited number of waveguides, which have simple geometry and specific refractive index profiles (RIPs), have analytic solutions [1], [2]. Consequently, employing

Application of a discontinuous Galerkin method for waveguide analysis

“…In [43], the edge elements were explored to avoid spurious modes on waveguide analysis. Alternative methods to the FEM for waveguide analysis include the spectral ones [44], the finite-difference [45][46][47], the boundary integral equation [48][49][50], and the meshless [51] methods. On all of these methods, dealing with field singularities (due to sharp corners, for instance) is hard.…”