Non-reflecting permittivity profiles and the spatial Kramers-Kronig relations

TL;DR

This paper demonstrates that specific analytic permittivity profiles in complex space can eliminate reflection for waves incident from one side, using spatial Kramers-Kronig relations to design non-reflecting dielectric media.

Contribution

It establishes a theoretical link between permittivity profiles' analyticity and reflectionless behavior, extending the spatial Kramers-Kronig relations to vector wave theories.

Findings

Permittivity profiles analytic in the upper or lower complex plane are reflectionless from one side.

Spatial Kramers-Kronig relations can be used to design non-reflecting media.

The results apply to both scalar and vector wave theories.

Abstract

We show that if the permittivity profile of a planar dielectric medium is an analytic function in the upper (lower) half complex position plane then it won't reflect radiation from the left (right), whatever the angle of incidence. Consequently, using the spatial Kramers-Kronig relations one can derive a real part of a permittivity profile from some given imaginary part (or vice versa), such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories, and may have relevance for efficiently absorbing radiation, or reducing reflection from bodies.