Introduction to the mathematical methods of the solution to the direct and inverse problems of the optical waveguide design
In this paper we give an introduction to the mathematical foundations of the optical waveguide design. A survey of the main results of the spectral theory of the Schr¨odinger operator on the line having compactly supported potential, with particular emphasis on the case of piece-wise constant potential is presented. This theory is then applied to the optical waveguide design problem of a piece-wis