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An efficient pseudo-spectral method based on rational-Chebyshev and Chebyshev functions for optical waveguides analysis

In this paper, a novel pseudo-spectral method with domain decomposition is introduced to study the modal characteristics of optical waveguides. The approach utilizes semi-vectorial formulation in terms of transverse magnetic field components Hx and Hy. Domain decomposition is employed where the computational domain is divided into a finite number of subdomains. In each subdomain, the transverse field components are expanded in terms of Chebyshev or rational Chebyshev functions according to whether the domain is bounded or semi-infinite. Patching of subdomains is done by imposing the continuity conditions of Ez and Hz at interfaces of discontinuity.