Inverse scattering theory applied to the design of single-mode planar optical waveguides

An inverse scattering theory is used to design single-mode planar optical waveguides that have wider inhomogeneous cores than those obtained by direct scattering methods. The wave equation for the electric field in the core is transformed into a Schrödinger-type equation whose potential function q(x) is related to the refractive-index profile. The modal structure of the waveguide is characterized by the transverse reflection coefficient r(k); a single discrete propagating mode and continuous radiating modes are considered. The Gel’fand–Levitan–Marchenko inverse scattering theory is used to obtain the unique solution of q(x) from a rational-function representation of r(k).