Computing parametrized solutions for plasmonic nanogap structures

Abstract

The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the confinement of light to small regions, typically several orders of magnitude smaller than the incident wavelength. The accurate prediction of these resonances entails several challenges. Small geometric variations in the plasmonic structure may lead to large variations in the electromagnetic field responses. Furthermore, the material parameters that characterize the optical behavior of metals at the nanoscale need to be determined experimentally and are consequently subject to measurement errors. It then becomes essential that any predictive tool for the simulation and design of plasmonic structures accounts for fabrication tolerances and measurement uncertainties.In this paper, we develop a reduced order modeling framework that is capable of real-time accurate electromagnetic responses of plasmonic nanogap structures for a wide range of geometry and material parameters. The main ingredients of the proposed method are: (i) the hybridizable discontinuous Galerkin method to numerically solve the equations governing electromagnetic wave propagation in dielectric and metallic media, (ii) a reference domain formulation of the time-harmonic Maxwell's equations to account for arbitrary geometry variations; and (iii) proper orthogonal decomposition and empirical interpolation techniques to construct an efficient reduced model. To demonstrate effectiveness of the models developed, we analyze geometry sensitivities and explore optimal designs of a 3D periodic coaxial nanogap structure.

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

“…Starting from the work in [203], research on timeharmonic Maxwell's equations tackled the analysis and development of HDG formulations [186], including methods suitable for simulations at large wave numbers [189] and Schwarz-type domain decomposition (DD) strategies designed for HDG [18,185]. Recent applications of HDG to time-harmonic Maxwell's equations focus on wave propagation in heterogeneous media modelling photovoltaic cells [41], coupling with nonlocal hydrodynamic Drude and generalised nonlocal optical response models [184] and with hydrodynamic models for metals [257][258][259]271] to simulate plasmonic nanostructures. In the context of timedomain Maxwell's equations, HDG methods are presented and analysed in [55,59,122], whereas implicit hybridised DG discretisations are proposed in [67].…”

“…In [260,261], a reduced order model to accelerate the Monte-Carlo simulation of stochastic elliptic PDEs is constructed coupling a high-order HDG method with a reduced basis and empirical interpolation approach. The combination of an HDG solver for time-harmonic Maxwell's equations and a proper orthogonal decomposition (POD) strategy to design parametrised plasmonic nanogap structures is proposed in [259]. An HGD-POD reduced order model (ROM) is also discussed in [249] for the fast simulation of the unsteady heat equation.…”

An accurate triangular spectral element method-based numerical simulation for acoustic problems in complex geometries

“…was first proposed by Berenger 27 in 1994 for electromagnetic problems. In recent years, PML has been extended to applications in wider range [28][29][30] including CAA, and considerable improvements were made to promote the computational efficiency. 31,32 In this paper, an improved split-PML developed by Komasitsch and Tromp 33 is applied.…”

POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations

“…We will consider the parametrized time-dependent problems in the near future. Some related contributions please refer to [26,50,51].…”