Wave reflection in dielectric media obeying spatial Kramers-Kronig relations

TL;DR

This paper investigates the reflection properties of dielectric media obeying spatial Kramers-Kronig relations, providing conditions for proper scattering states and confirming their one-way reflectionless nature, while also discussing potential instabilities.

Contribution

It offers a rigorous proof of one-way reflectionless behavior in KK dielectric media and addresses issues related to complex permittivity profiles.

Findings

KK dielectric media are one-way reflectionless for all angles of incidence.

Proper scattering states exist under certain conditions on the imaginary part of the dielectric profile.

Instabilities can occur at interfaces when the medium is not purely dissipative.

Abstract

In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric permittivity are related by spatial Kramers-Kronig (KK) relations, are one-way reflectionless, whatever the angle of incidence. Such a fascinating property, besides of extending our comprehension of the fundamental phenomenon of reflection, may offer new ways for the design of antireflection surfaces and thin materials with efficient light absorption. However, KK dielectric media are generally described by slowly-decaying complex permittivity profiles which may introduce some subtle issues in the study of the scattering problem. Here we provide a condition on the imaginary part of the dielectric profile that ensures the existence of proper scattering states and present a proof of the one-way reflectionless property in KK dielectric media which is free from loophole. Finally, we show that instabilities might arise at the interface of KK dielectric media when the medium is not purely dissipative.