An Efficient Numerical Full-Vectorial Mode Solver Based on Fourier Series Expansion Method

A new algorithm of full-vectorial eigenmode solver is presented, which is utilized to determine the modal index of dielectric optical waveguides. The approach is based on the Fourier cosine and sine series expansions of the magnetic field distributions and the refractive index profile. By substituting these series expansions in the wave equation, a pair of second-order differential matrix equations is obtained by collecting all the terms with the same spatial frequency. With boundary conditions used, a matrix equation with a dimension of (N+1) by (N+1), where N is the number of terms for truncated series, is obtained, which can be easily solved by using the Newton-Raphson root-shooting algorithm. The presented scheme requires considerably less computational time and memory storage by only considering the finite terms of the Fourier cosine/sinusoidal series. Calculated results by our proposed method are in good agreement with those obtained by BeamPROP and COMSOL and compare well with other available methods, demonstrating the accuracy and efficiency and also the applicability of our proposed method.