Modeling and observation of mid-infrared nonlocality in effective epsilon-near-zero ultranarrow coaxial apertures

Daehan Yoo,Cristian Ciracì,Ngoc-Cuong Nguyen,Sang-Hyun Oh,Ferran Vidal-Codina,Jaime Peraire,David R Smith

doi:10.1038/s41467-019-12038-3

Abstract

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1–2 nm have been realized. Plasmons in such ultranarrow gaps can exhibit nonlocal response, which was previously shown to limit the field enhancement and cause optical properties to deviate from the local description. Using atomic layer lithography, we create mid-infrared-resonant coaxial apertures with gap sizes as small as 1 nm and observe strong evidence of nonlocality, including spectral shifts and boosted transmittance of the cutoff epsilon-near-zero mode. Experiments are supported by full-wave 3-D nonlocal simulations performed with the hybridizable discontinuous Galerkin method. This numerical method captures atomic-scale variations of the electromagnetic fields while efficiently handling extreme-scale size mismatch. Combining atomic-layer-based fabrication techniques with fast and accurate numerical simulations provides practical routes to design and fabricate highly-efficient large-area mid-infrared sensors, antennas, and metasurfaces.

Highlights

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1–2 nm have been realized
In the local response approximation (LRA), the wavelength is assumed to be much larger than the characteristic dimensions, the dielectric tensor is invariant with respect to the wavevector, that is εðr; tÞ 1⁄4 εðtÞδðrÞ in real space, with δ being the Dirac delta function
ENZ photonics has provided a convenient framework to describe a wide range of phenomena such as electromagnetic tunneling through ultranarrow channels operating at the cutoff condition, uniform phase accumulation, large field enhancement, supercoupling, optical nonlinearity, and nonlocality[35,36,37,38]

Summary

Introduction

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1–2 nm have been realized Plasmons in such ultranarrow gaps can exhibit nonlocal response, which was previously shown to limit the field enhancement and cause optical properties to deviate from the local description. While a full quantum mechanical description of optical response is not yet possible for structures other than small clusters[26,27], a semi-empirical hydrodynamic model has been successfully applied to describe electron–electron interactions in the limit of the Thomas–Fermi approximation in film-coupled nanoparticle systems at optical frequencies[12,28] To extend this method toward the longer-wavelength regime, in particular the mid-IR regime, it is necessary to address the increased size mismatch between the minimum feature dimensions and the free-space wavelength, that is over ten times larger than in the visible regime, presenting both simulation and fabrication challenges. It should be noted that most existing works studied nonlocality in simplified two-dimensional (2-D) geometries or in specific (spherically or axially) symmetric threedimensional (3-D) structures due to the computational burden

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Results

Conclusion