Wave reflection in dielectric media obeying spatial Kramers-Kronig relations

Dipartimento di Fisica, Politecnico di Milano - Piazza L. da Vinci 32, I-20133 Milano, Italy and Istituto di Fotonica e Nanotecnlogie del Consiglio Nazionale delle Ricerche, sezione di Milano Piazza L. da Vinci 32, I-20133 Milano, Italy

Received: 5 October 2015
Accepted: 21 December 2015

Abstract

In a recent work, Horsley and coworkers (Nat. Photon., 9 (2015) 436) 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 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 loopholes. Finally, we show that instabilities might arise at the interface of KK dielectric media when the medium is not purely dissipative.