Efficient integral-equation-based method for accurate analysis of scattering from periodically arranged nanostructures

Abstract

A plethora of applications are grounded on the physics of electromagnetic interaction with a periodic arrangement of nanostructures. These range from metamaterials and negative index materials to photonic band-gap structures to surface plasmon polariton optics to nanofrequency selective surfaces. There is therefore a need for rigorous physics based methods that are both accurate and fast to enable rapid design and analysis. Difficulties that need to be overcome to realize such a simulation tool are twofold: (i) at wavelengths in the range 200-1300 nm metals behave as dielectrics with negative real permittivity. Their frequency response must be explicitly accounted for in the simulation. (ii) The computational cost to compute response over a broad band of frequencies is high. This paper develops an integral-equation-based analysis technique that addresses these challenges. This integral equation relies on a periodic layered medium formulation. The Green's dyad for this formulation is derived, and separated into a superposition of two contributions: direct and reflected components. The means to accelerate the computation of the Green's dyad and the evaluation of inner products is prescribed. The proposed technique is validated extensively against available analytical data for hypothetical materials as well as silver. It is shown that this solver can accurately predict the enhanced transmission from perforated silver films for several configurations. While the application domain in this paper is the study of enhanced transmission in perforated silver films, the method presented herein is sufficiently general and can be applied to several other application domains with little or no change.

Fast Periodic Interpolation Method for Periodic Unit Cell Problems

“…1). The PGF can be represented in the following form: (3) where and are the near-and far-field components of the PGF given by (4) Here, is given as a summation of the simple Green's functions around the zeroth unit cell, which is similar to the expression in (2) but with a finite summation over a limited range determined by ( can be chosen for most cases). The far-field component of PGF,…”

Rapidly Convergent Representations for 2D and 3D Green's Functions for a Linear Periodic Array of Dipole Sources

“…Here, the first term in the right-hand side is a summation of free-space longitudinal spectral 1D PGF, taken over 2 1 d N + sources residing at locations x nL = around the origin. The second term in the right-hand of (14), which comprises the contribution from the remaining infinite number of sources, decays exponentially fast for large , z k ρ regardless of the observation location x within the 0 n = (zeroth) unit cell (and even for 0 x = ).…”

“…The Ewald approach, in contrast, using Ewald and Poisson's transformations, leads to exponentially convergent PGF series representations. However, it requires double summations, can suffer high-frequency breakdown, and involves choosing a proper splitting parameter, which may be not straightforward to implement [1,2,[6][7][8][9][10][11][12][13][14][15][16]. Moreover, the Ewald approach has never been extended to 3D dyadic Green's functions.…”

Modelling of impedance‐loaded wire frequency‐selective surfaces with tunable reflection and transmission characteristics

“…In (C5)-(C6) functions KðÁÞ and LðÁÞ are the real and imaginary parts of Faddeeva function wðzÞ ¼ expðÀz 2 ÞerfcðÀizÞ: As noted in [22] the usage of Fadeeva function instead of error functions adopted through the literature devoted to Green's function acceleration considerably accelerates the computation. The periodic Green's function is convolved with current distribution in (4) and displays quasisingular behavior when n ¼ m ¼ 0 and s !…”