Integral-Equation Formulations of Plasmonic Problems in the Visible Spectrum and Beyond

Abstract

Computational modeling of nano-plasmonic structures is essential to understand their electrodynamic responses before experimental efforts in measurement setups. Similar to the other ranges of the electromagnetic spectrum, there are alternative methods for the numerical analysis of nano-plasmonic problems, while the optics literature is dominated by differential equations that require discretizations of the host media with artificial truncations. These approaches often need serious assumptions, such as periodicity, infinity, or self-similarity, in order to reduce the computational load. On the other hand, surface integral equations based on integro-differential operators can bring important advantages for accurate and efficient modeling of nano-plasmonic problems with arbitrary geometries. Electrical properties of materials, which may be obtained either experimentally or via physical modeling, can easily be inserted into integral-equation formulations, leading to accurate predictions of electromagnetic responses of complex structures. This chapter presents the implementation of such accurate, efficient, and reliable solvers based on appropriate combinations of surface integral equations, discretizations, numerical integrations, fast algorithms, and iterative techniques. As a case study, nanowire transmission lines are investigated in wide-frequency ranges, demonstrating the capabilities of the developed implementations.

A Comparative Study of Nanowire Arrays for Maximum Power Transmission

“…The developed simulation environment for the analysis of plasmonic problems, such as nanowires at optical frequencies, is extensively discussed in Ref. [36]. In this section, we consider the major components of the solver for accurate and efficient analysis of nanowires and their arrays.…”

“…are calculated on the fly using MLFMA. These matrix elements are never computed directly or stored in memory, while their multiplications with given input vectors x J and x M can still be performed with controllable accuracy, as described in [36]. Using MLFMA, a matrix equation can efficiently be solved via Krylov-subspace algorithms with OðNlogNÞ complexity per matrix-vector multiplication or iteration.…”

Solution box: SOLBOX-07

“…Both of the two problems in SOLBOX-07 were solved by using an in-house implementation of the MLFMA in the frequency domain [13,14]. The problems were formulated…”

Design and Analysis of Nanoantenna Arrays for Imaging and Sensing Applications at Optical Frequencies

“…Their sensitive responses to electromagnetic waves make nanoantennas challenging to analyze via computational methods [14]. In this work, the fast and accurate implementation to analyze nanoantenna arrays and nearby particles is based on a modified combined tangential (MCTF) formulation [15,16] in the frequency domain. The effective complex permittivity values for metals are extracted from Lorentz-Drude models or measurement results [17].…”