Omnidirectional wave impedance matching and Goos-Hanchen shifts in non-Hermitian balanced positive-negative index metamaterials

Abstract

Wave reflection by non-Hermitian antisymmetric parity-time (APT) photonics made of a balanced positive index material (PIM) and negative index material (NIM) is investigated. As one class of them satisfies a unitary relation, wave impedance matching (WIM) can be achieved not only for polarization independence but also for omnidirection. Remarkably, the result is independent of system sizes, material parameters, and polarization. As gain or loss is involved, any non-Hermitian systems are unable to support WIM; instead, there occurs a reflection dip, i.e., a minimum reflectance, at some system configurations, a certain incident angle, and polarization dependence. Our finding is in contrast to the parity time (PT) symmetric paradigms, in which the well-known exceptional point can be recognized as a WIM. Additionally, in the vicinity of a reflection dip, it is accompanied by a jump of reflection phase, offering an opportunity to observe a significant Goos-Hanchen (GH) beam shift in APT systems. We provide associated systems and numerically verify the GH shifts. Meanwhile, we derive a closed-form expression for a reflection dip in terms of incident angle, operating wavelengths, and material parameters. To imitate the electromagnetic responses of APT photonics for their angular dispersion, we discuss a dielectric heterostructure consisting of spatially symmetric multilayer slabs so as to have the same reflection and transmission for each APT component over a specific angular spread.