Introduction to the mathematical methods of the solution to the direct and inverse problems of the optical waveguide design

In English 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-wise constant permittivity.