Point Interactions, Metamaterials, and PT-Symmetry

TL;DR

This paper models boundary conditions in metamaterials as point interactions to analyze wave reflection, symmetry, and PT-symmetry, revealing new insights into Veselago's slab and phase-conjugation phenomena.

Contribution

It introduces a novel point interaction framework for metamaterials, enabling analysis of reflectionless propagation, symmetry properties, and PT-symmetric quantum analogies.

Findings

Veselago's slab is omnidirectionally reflectionless for all wavelengths.

The slab exhibits translational and reflection symmetry.

Connections between metamaterials and PT-symmetric quantum systems are established.

Abstract

We express the boundary conditions for TE and TM waves at the interfaces of an infinite planar slab of homogeneous metamaterial as certain point interactions and use them to compute the transfer matrix of the system. This allows us to demonstrate the omnidirectional reflectionlessness of Veselago's slab for waves of arbitrary wavelength, reveal the translational and reflection symmetry of this slab, explore the laser threshold condition and coherent perfect absorption for active negative-index metamaterials, introduce a point interaction modeling phase-conjugation, determine the corresponding antilinear transfer matrix, and offer a simple proof of the equivalence of Veselago's slab with a pair of parallel phase-conjugating plates. We also study the connection between certain optical setups involving metamaterials and a class of PT-symmetric quantum systems defined on wedge-shape contours in the complex plane. This provides a physical interpretation for the latter.