Computing parametrized solutions for plasmonic nanogap structures

• Published in: Journal of computational physics Vol. 366; pp. 89 - 106
• Main Authors: Vidal-Codina, F., Nguyen, N.C., Peraire, J.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.08.2018; Elsevier Science Ltd
• Subjects: Coaxial nanogap; Computational physics; Computer simulation; Conduction bands; Electromagnetic fields; Electromagnetic radiation; Electromagnetism; Empirical analysis; Galerkin method; Hybridizable discontinuous Galerkin method; Interpolation; Mathematical models; Maxwell's equations; Metal surfaces; Nanostructured materials; Optical properties; Parameters; Parametrized solutions; Plasmonics; Predictions; Proper Orthogonal Decomposition; Reduced order modeling; Reduced order models; Scanning electron microscopy; Sensitivity analysis; Time-harmonic Maxwell's equations; Tolerances; Wave propagation; Plasmonics; Hybridizable discontinuous Galerkin method; Reduced order modeling; Parametrized solutions; Coaxial nanogap; Time-harmonic Maxwell's equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.04.009

•Formulation of time-harmonic Maxwell's equations in reference domain for arbitrary deformation mapping.•HDG discretization to compute solution of transformed Maxwell's equations.•Combination of HDG solutions with POD and empirical interpolation for efficient model reduction.•Computation of accurate 3D electromagnetic responses for geometry deformations in real-time.•Enables computation of geometry sensitivities and design of plasmonic structures. 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.