Tolerance of the solution to the problem of a buried waveguide synthesis

Abstract

The problem of finding the permittivity profile of graded-index single-mode planar waveguide after the given mode parameters is considered. For solving this inverse problem a universal mathematical model of the profile is implemented. It has the form of a double truncated exponential-power function. Each set of function parameters corresponds to a particular distribution of the permittivity in the waveguide. Multiply repeated numerical solution of the direct problem by a special algorithm using the least-square method enables one to select the function parameters for a certain set of mode parameters. For solving the inverse problem a knowledge of the propagation constants is required. Exact reconstruction of the waveguide parameters can be obtained by using four criteria. Nevertheless, there are always some errors in the determination of the propagation constants. The tolerance of the solution to these errors is investigated.