Design of waveguides with prescribed propagation constants

Abstract

Inverse scattering theory is applied to the design of optical waveguides possessing refractive-index profiles that support modes with prescribed propagation constants β. When gradient terms in the refractive index are neglected, we obtain explicit expressions for the refractive index of planar guides for which all β’s may be prescribed and of circularly symmetric guides, in which all β’s corresponding to a single fixed azimuthal mode number may be prescribed. When gradient terms are retained for planar guides it is only possible to prescribe the β’s for either TE or TM modes separately. For circular guides, when the gradient terms are retained, we have been able to obtain solutions to the inverse problem for the refractive-index profile for azimuthal mode number j = 1; again, one can only solve for either TE or TM modes separately. We demonstrate that the refractive index we have obtained for planar guides can be decomposed into solitons, and the known properties of solitons can be utilized to construct indices with specific characteristics. Finally, we apply the theory to the construction of profiles that enable “perfect” transmission of spatial images.