Designing scattering-free isotropic index profiles using phase-amplitude equations

TL;DR

This paper introduces a method to design two-dimensional graded-index media that are free of scattering by leveraging phase-amplitude equations, enabling reflectionless wave propagation and specific beam manipulation.

Contribution

It presents a novel approach to create scattering-free isotropic index profiles using phase-amplitude equations, with practical examples of diffraction suppression and beam shifting.

Findings

Diffraction is completely suppressed at a single frequency in a periodic grating.

A medium can laterally shift a beam without reflection at a specific frequency.

The method enables designing reflectionless, scattering-free optical media.

Abstract

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a 'beam shifter' at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.