A semianalytical method of mode determination for a multilayer planar optical waveguide

Abstract

A new method for mode determination of multilayer planar waveguides with complex-valued dielectric permeability is proposed. The method is based on the combination of an argument principle in complex analysis and a quasi-Newton method. The argument principle allows reliable determination of the number of modes within any finite region of the complex plane representing the propagation constants. This makes it possible to locate the propagation constants to the precision sufficient for the usage of the quasi-Newton method. The method involves 'tracking of the phase' of a complex function instead of conventional integration along a contour.