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Inverse scattering theory and the design of planar optical waveguides with the same propagation constants for different frequencies

Application of inverse scattering theory for designing planar optical waveguides possessing prescribed propagation constants for light with a given frequency is well known. However, waveguides designed using such a method, in general, will not be able to transmit light at other frequencies with the same propagation constant. In order to overcome this difficulty, the design problem for TE modes is transformed and reformulated to an equivalent inverse problem for Schrodinger's equation. Then using inverse scattering theory, the potential as a function of a modified spatial variable is recovered. Next the important problem of finding an explicit relation between the actual spatial variable and the modified spatial variable is solved and a systematic procedure is developed for designing waveguides which have the same propagation constant for different light frequencies. Existence and uniqueness questions are studied and some model calculations are presented.