Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material.

S Dai,T Andersen,F Keilmann,M K Liu,K Watanabe,A S Mcleod,T Taniguchi,P Jarillo-Herrero,M M Fogler,Z Fei,Q Ma,D N Basov,M Thiemens,M Wagner

doi:10.1038/ncomms7963

Abstract

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials, light propagation is unusual leading to novel and often non-intuitive optical phenomena. Here we report infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride, a natural mid-infrared hyperbolic material, can act as a ‘hyper-focusing lens' and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon–polaritons launched by metallic disks underneath the hexagonal boron nitride crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization.

Highlights

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media
In our previous work[33], we used for this purpose a sharp tip of an atomic force microscope (AFM) incorporated in our scattering-type scanning near-field optical microscopy (s-SNOM) apparatus (Methods)
We show that the observed dependence of the near-field images on the frequency and hexagonal boron nitride (hBN) thickness is the result of directional propagation of the polaritons along conical surfaces with frequency-tunable apex angle given by Equation (2)

Summary

Introduction

Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials, light propagation is unusual leading to novel and often non-intuitive optical phenomena. The largest characteristic momentum that can pass through a superlens of thickness d can be found from the relation Im e $ e À ktd In this regard, hyperbolic media (HM)[8,9] promise a significant advantage as they support large-k hyperbolic polaritons that remain propagating rather than evanescent, so that the condition on damping is much softer (see below). Directional propagation of hyperbolic polaritons along ‘resonance cones’ of apex angle y has been observed in a

Methods

Results

Conclusion