Permittivity profile synthesis of planar buried waveguides

The method of finding the permittivity profile of a graded-index single-mode planar waveguide from the given mode parameters is described. For solving this inverse problem the universal mathematical model of the profile is proposed. It has the shape of a double truncated exponential-power function. Each set of function parameters corresponds to a particular distribution of permittivity in the waveguide. The solution of the direct problem by the shift formula method yields the mode parameters of the waveguide. Multiply repeated numerical solution of the direct problem by a special algorithm using the least-square method enables us to select the function parameters for a certain set of mode parameters. As a result of the procedure, the profile function in question is synthesized