Transformation-optics generalization of tunnelling effects in bi-layers made of paired pseudo-epsilon-negative/mu-negative media

TL;DR

This paper introduces a complex-analytic continuation method in transformation optics to create pseudo-single-negative media, enabling new interpretations and generalizations of tunnelling effects in bi-layer structures with paired epsilon-negative and mu-negative materials.

Contribution

It presents a novel approach using complex coordinate transformations to generate pseudo-SNG media, expanding the capabilities of transformation optics beyond traditional real-valued mappings.

Findings

Pseudo-SNG media can be achieved via complex analytic continuation.

The approach provides new insights into tunnelling phenomena in bi-layers.

Extensions of tunnelling effects are possible through this generalized transformation method.

Abstract

Transformation-media designed by standard transformation-optics (TO) approaches, based on real-valued coordinate-mapping, cannot exhibit single-negative (SNG) character unless such character is already possessed by the domain that is being transformed. In this paper, we show that, for a given field polarisation, pseudo-SNG transformation media can be obtained by transforming a domain featuring double positive (or double-negative) character, via complex analytic continuation of the coordinate transformation rules. Moreover, we apply this concept to the TO-based interpretation of phenomena analogous to the tunnelling effects observable in bi-layers made of complementary epsilon-negative (ENG) and mu-negative (MNG) media, and explore their possible TO-inspired extensions and generalizations.