Reconstruction of the permittivity profile using a nonlinear guided wave technique

A new method is developed to reconstruct the permittivity profile of a dielectric slab in a guided wave formulation. The propagation constants of the slab eigenmodes are used as input data for inversion of the boundary-value problem for the nonlinear differential equation representing the condition of existence of the modes. The permittivity profile is expanded into a set of special functions so that the propagation constant of a particular mode depends mainly on only one term of the set. This ensures fast convergence of an iterative procedure to find the coefficients of expansion. The method is shown to be valid for the discontinuous profiles of high contrast as well as for both symmetrical and asymmetrical profiles provided that in the last case additional measurements of the slab placed on a metal plate are performed. Several simulated and experimental examples are presented.