Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays

• Verfasst von: Zhang, Yongwei [VerfasserIn]
• Verfasst von: Ma, Chupeng [VerfasserIn]
• Verfasst von: Cao, Li-qun [VerfasserIn]
• Verfasst von: Shi, Dongyang [VerfasserIn]
• Titel: Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays
• Verf.angabe: Yongwei Zhang, Chupeng Ma, Li-qun Cao, and Dongyang Shi
• E-Jahr: 2021
• Jahr: July 15, 2021
• Umfang: 30 S.
• Fussnoten: Gesehen am 03.11.2021
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on scientific computing
• Ort Quelle: Philadelphia, Pa. : SIAM, 1993
• Jahr Quelle: 2021
• Band/Heft Quelle: 43(2021), 4, Seite B907-B936
• ISSN Quelle: 1095-7197
• DOI: doi:10.1137/20M1324120
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 65F10
• Sach-SW: 65N30
• Sach-SW: 65N55
• Sach-SW: 65Y05
• Sach-SW: finite element method
• Sach-SW: metallic nanostructure arrays
• Sach-SW: multiscale asymptotic method
• Sach-SW: nonlocal optical response
• K10plus-PPN: 177600793X

Abstract

In this paper, we consider numerical simulations of the nonlocal optical response of metallic nanostructure arrays inside a dielectric host, which is of particular interest to the nanoplasmonics community due to many unusual properties and potential applications. Mathematically, it is described by Maxwell's equations with discontinuous coefficients coupled with a set of Helmholtz-type equations defined only on the domains of metallic nanostructures. To solve this challenging problem, we develop an efficient multiscale method consisting of three steps. First, we extend the system into the domain occupied by the dielectric medium in a novel way and result in a coupled system with rapidly oscillating coefficients. A rigorous analysis of the error between the solutions of the original system and the extended system is given. Second, we derive the homogenized system and define the multiscale approximate solution for the extended system by using the multiscale asymptotic method. Third, to fix the inaccuracy of the multiscale asymptotic method inside the metallic nanostructures, we solve the original system in each metallic nanostructure separately with boundary conditions given by the multiscale approximate solution. A fast algorithm based on the $LU$ decomposition is proposed for solving the resulting linear systems. By applying the multiscale method, we obtain results that are in good agreement with those obtained by solving the original system directly at a much lower computational cost. Numerical examples are provided to validate the efficiency and accuracy of the proposed method.