Search of mode wavelengths in planar waveguides
by using Fourier transform of wave equation
V.M. Fitio^{1}, V.V. Romakh^{1}, Ya.V. Bobitski^{1,2}

^{1}Lviv Polytechnic National University, Department of Photonics,
12, Bandery str. 79013 Lviv, Ukraine
^{2}University of Rzeszów, Faculty of Mathematics and Natural Sciences,
1, Pigonia str., 35959 Rzeszów, Poland
Phone/fax: +38(032)-258-25-81; e-mail: polyana@polynet.lviv.ua, vladykv@gmail.com, bobitski@polynet.lviv.ua

Abstract. The article describes a numerical method based on Fourier transform for studying propagating optical waves in dielectric planar waveguides. The inverse problem to the 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 from 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 for TE and TM modes propagate there.