Intersubband plasmons induced negative refraction at mid-IR frequency in heterostructured semiconductor metamaterials

IntroductionIn this paper we report theoretical and experimental results on negative refraction in highly doped layered semiconductor materials. We reveal that intersubband (ISBT) transitions induce a hyperbolic metamaterial... [ view full abstract ]

Introduction

In this paper we report theoretical and experimental results on negative refraction in highly doped layered semiconductor materials. We reveal that intersubband (ISBT) transitions induce a hyperbolic metamaterial behaviour in the quantum wells (QW).

Methods

The proposed system consists of a stack of alternated layer of doped ZnO and undoped MgZnO forming an array of quantum wells grown on native ZnO substrate. The choice of ZnO is mainly related to the possibility of reaching very high doping level. Moreover, for non-polar growth conditions, i.e. c-axis along the plane, we avoid detrimental quantum confined Stark effect which would otherwise increase the complexity of the QW design. A scheme of the system is reported in Fig.1.

To obtain realistic material permittivity, the photonic response of the entire stack was calculated using Maxwell-Garnett theory, in the presence of QW, the barrier and the phononic response of the semiconductor. Details on the model accounting for phonon contribution, and anisotropic ISBT response will be presented.

Results

The main results are summarized in Fig.2, showing both in- and out-of-plane components of the real part of the effective medium permittivity. The optical properties range from pure metal to pure dielectric passing through HMM type 1 and 2. We show that T1 HMM originates from the intersubband plasmon response of the material.

The theoretical prediction were tested experimentally with two samples of 4 and 35 nm thickness ZnO quantum wells that, according to the model, should exhibits positive and respectively negative refractions as presented in Fig.3. In presence of negative refraction a maximum (minimum) in transmission is expected for θ<0 (θ>0). These results are confirmed by experimental spectra.

Discussion

Experimental demonstration of negative refraction due to intersubband transition are in agreement with the theoretical model. Intersubband response is essentially due to both electronic confinement in subwavelength semiconductor layers and electronic doping, but as we show in this work, these materials generally exhibit -as well- inherent hyperbolic metamaterials response. Highlighting this connection between the more conventional concepts of intersubband plasmons in doped multiple quantum wells and its hyperbolic photonic response, opens avenues for designing new sources and emitters.