New confining optical media generated by Darboux transformations

Abstract

The parametric Darboux transformation is applied to the paraxial Helmholtz equation for graded-index media in order to generate new refractive index profiles depending also on the longitudinal coordinate. The particular case of the parabolic medium is considered, and the construction of new deformed quadratic profiles exhibiting self-focusing properties is addressed. Some examples illustrate our formalism.