Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene.

Dong Zhao,Shaolin Ke,Peixiang Lu,Bing Wang,Qingjie Liu

doi:10.1364/oe.26.002817

Abstract

We theoretically investigate the Goos-Hänchen (GH) shifts of optical beam in a defective photonic crystal composed of dielectric multilayers and graphene. The system is non-Hermitian and possesses exceptional points (EPs) as the scattering matrix becomes defective at the zero points of reflection. The reflective wave at EPs experiences an abrupt phase change and there the eigenvalues of scattering matrix coalesce. The GH shifts are extremely large near EPs in parametric space composed of dielectric refractive index and incident angle. The positive and negative maxima of GH shifts could be as high as 103 times of the incident wavelength. The direction of GH shifts switches at EPs and the EPs position can be readily controlled by the chemical potential of graphene. Moreover, the GH shifts should remarkably change as the incident waves impinge on the structure from opposite directions. The study of GH shifts in the graphene incorporated multilayers may find great applications in highly sensitive sensors.

Highlights

Since the Goos-Hänchen (GH) shift was first observed experimentally by Goos and Hänchen in 1947 [1], many efforts have been devoted into the theoretical and experimental studies of the effect [2,3,4,5,6,7,8,9,10]
The exceptional points (EPs) position can be controlled by the graphene chemical potential
In conclusion, we construct a non-Hermitian system by dielectric multilayers and graphene, which is lossy and asymmetric

Summary

Introduction

Since the Goos-Hänchen (GH) shift was first observed experimentally by Goos and Hänchen in 1947 [1], many efforts have been devoted into the theoretical and experimental studies of the effect [2,3,4,5,6,7,8,9,10]. Very large GH shifts may exist in periodic dielectric multilayers with PT-symmetry where the lateral shifts are tightly independent on the incident direction [28]. Since giant GH shifts are present in PT-symmetry and notable at EPs [24, 27, 28], it is necessary to explore the behavior of GH shifts in non-Hermitian systems. Through the unique characteristic of EPs including unidirectional zero reflection and abrupt phase change, we could in turn find EPs in non-Hermitian systems [35]. As a result, incorporating the graphene into metamaterials can constitute a non-Hermitian system [40, 41], in which EPs locate at the zero points of reflection [24, 42] and the EPs positions in parametric space can be tuned by the chemical potential of graphene. We illustrate the application of GH shifts in dielectric refractive index sensing

Non-Hermitian dielectric multilayers

GH shifts for sensing

Conclusion