Semiconductor Hyperbolic Metamaterials at the Quantum Limit

Inès Montaño,Salvatore Campione,Ting S Luk,Thomas E Beechem,John F Klem,Omri Wolf,Michael B Sinclair

doi:10.1038/s41598-018-35099-8

Abstract

We study semiconductor hyperbolic metamaterials (SHMs) at the quantum limit experimentally using spectroscopic ellipsometry as well as theoretically using a new microscopic theory. The theory is a combination of microscopic density matrix approach for the material response and Green’s function approach for the propagating electric field. Our approach predicts absorptivity of the full multilayer system and for the first time allows the prediction of in-plane and out-of-plane dielectric functions for every individual layer constructing the SHM as well as effective dielectric functions that can be used to describe a homogenized SHM.

Highlights

Of key importance for light-matter interaction physics and device applications of HMs is the actual determination of the effective permittivities of the hyperbolic metamaterial where the specific multilayer structure of the HMs is replaced with an effective medium with uniform properties in each direction
We have studied semiconductor hyperbolic metamaterials (SHMs) at the quantum limit experimentally using spectroscopic ellipsometry as well as theoretically using a new microscopic theory
Comparison between theory and experiments has shown that our theory correctly captures light-matter interactions in SHMs at the quantum limit

Summary

Introduction

Of key importance for light-matter interaction physics and device applications of HMs is the actual determination of the effective permittivities of the hyperbolic metamaterial where the specific multilayer structure of the HMs is replaced with an effective medium with uniform properties in each direction. For the extreme tunability was given in[35], where the crossover from confined plasmon mode (Berreman mode, isotropic Drude permittivity), to multisubband plasmon (anisotropic permittivity), to intersubband (ISB) plasmon (highly anisotropic permittivity) was achieved by decreasing the thickness of a highly doped quantum well This tunability of the light-matter coupling through bandstructure engineering is the reason why electromagnetic modeling of SHMs is not as straightforward as that of metallodielectric HMs. In SHMs the highly doped quantum well layer can have a very anisotropic electromagnetic response which has to be quantized in order to describe the SHMs through effective permittivities. We present a new theory that combines a microscopic density matrix approach for the material response and a Green’s function approach for the propagating electric field

Methods

Results

Conclusion