We present a wafer-scale array of resonant coaxial nanoapertures as a practical platform for surface-enhanced infrared absorption spectroscopy (SEIRA). Coaxial nanoapertures with sub-10 nm gaps are fabricated via photolithography, atomic layer deposition of a sacrificial AlO layer to define the nanogaps, and planarization via glancing-angle ion milling. At the zeroth-order Fabry-Pérot resonance condition, our coaxial apertures act as a "zero-mode resonator (ZMR)", efficiently funneling as much as 34% of incident infrared (IR) light along 10 nm annular gaps. After removing AlO in the gaps and inserting silk protein, we can couple the intense optical fields of the annular nanogap into the vibrational modes of protein molecules. From 7 nm gap ZMR devices coated with a 5 nm thick silk protein film, we observe high-contrast IR absorbance signals drastically suppressing 58% of the transmitted light and infer a strong IR absorption enhancement factor of 10∼10. These single nanometer gap ZMR devices can be mass-produced via batch processing and offer promising routes for broad applications of SEIRA.

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.

Reduced basis method A posteriori error estimation Hybridizable discontinuous Galerkin method Multilevel Monte Carlo method Stochastic elliptic PDEsWe present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the highfidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.