UDC 621.378.325 Analysis of Planar Graded-Index Optical Waveguides with Strong Asymmetry of a Refractive Index Profile by the Beam Propagation Method A. P. Gorobets Department of Radiophysics Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, 117198, Russia In the paper application of the beam propagation method (BPM) to investigation of wave processes in regular and nonregular graded-index waveguide structures with strongly asymmetric refractive index profile is analyzed. <...> On purpose to match the BPM requirement to smoothness of the refractive index profile, the profile with strong asymmetry, at the problem solution, is approximately exchanged by a symmetrical one. <...> For exponential and Gaussian profiles of the refractive index the BPM calculations are compared to the strict and WKB solution respectively. <...> Calculation of a wave pattern of a mode field coupling into the substrate at the tapered edge of a waveguide with strongly asymmetric profile is demonstrated. <...> Key words and phrases: graded-index optical waveguide, beam propagation method. 1. <...> Among them are: i) strict analysis based on a modal field description of a waveguide, applicable to the limited number of refraction index profiles n(x) of the waveguide layer for which the strict solution of an electrodynamic problem is known; ii) approximate ray methods, in particular, the WKB method valid in cases of a smooth variation of the refractive index, if the index change at a wavelength distance is much less than n(x); iii) numerical methods, including the one based on an approximate description of the continuous refractive index distribution by a step-function with a subsequent matching of fields at the layer boundaries [3]. <...> Any waveguide components and circuits (transitions, bends, splitters, couplers, etc.) in which an energy exchange occurs are constructed on the base of nonregular waveguides with parameters being a function of the longitudinal coordinate z. <...> Application of the above methods to analysis of nonregular waveguide structures leads to remarkable difficulties, and to gain the solution is possible, as a rule, in the elementary cases [4]. <...> Along with it, throughout last years, an approximate numerical beam propagation method (BPM) first offered for study of laser light propagation in the atmosphere [5] and then in graded-index optical fibers [6] is being widely used. <...> Absence of necessity to determine eigenfunctions of waveguides, application of the Fast Fourier Transform <...>