Determination of wavelengths which correspond to taken propagation constant of planar waveguide by wave equation Fourier transform method

Abstract

The paper describes a numerical method based on the Fourier transform application for studying propagating optical waves in dielectric planar waveguides. The inverse problem to known direct one in waveguide investigation is proposed, namely a search of light wavelengths according to taken values of propagation constants. For each constant a set of wavelengths is obtained, among which an input value of wavelength in direct problem exists necessarily. A high accuracy of the method proposed is confirmed by exact values obtained by solution of transcendental dispersion equation. This method is tested on many examples, in particular, for waveguides of different permittivity profiles or modes of TE- and TM-polarization.