Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

Abstract

We analyze mathematically the problem of determining refractive index proles from some desired/measured guided waves propagating in optical bers. We establish the uniqueness of the solution of this inverse spectral problem assuming that only one guided mode is known. We then propose an iterative computational procedure for solving numerically the considered inverse spectral problem. Numerical results are presented to illustrate the potential of * corresponding author: rabia.djellouli@csun.edu 1 the proposed regularized Newton algorithm to eciently and accurately retrieve the refractive index proles even when the guided mode measurements are highly noisy.