Fast high-order perturbation of surfaces methods for simulation of multilayer plasmonic devices and metamaterials

Monte Carlo-transformed field expansion method for simulating electromagnetic wave scattering by multilayered random media

We present an efficient numerical method for simulating the scattering of electromagnetic fields by a multilayered medium with random interfaces. The elements of this algorithm, the Monte Carlo-transformed field expansion method, are (i) an interfacial problem formulation in terms of impedance-impedance operators, (ii) simulation by a high-order perturbation of surfaces approach (the transformed field expansions method), and (iii) efficient computation of the wave field for each random sample by forward and backward substitutions. Our perturbative formulation permits us to solve a sequence of linear problems featuring an operator that is deterministic, and its LU decomposition matrices can be reused, leading to significant savings in computational effort. With an extensive set of numerical examples, we demonstrate not only the robust and high-order accuracy of our scheme for small to moderate interface deformations, but also how Padé summation can be used to address large deviations.

Stable, high-order computation of impedance-impedance operators for three-dimensional layered medium simulations

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

Launching surface plasmon waves via vanishingly small periodic gratings

The scattering of electromagnetic waves by periodic layered media plays a crucial role in many applications in optics and photonics, in particular in nanoplasmonics for topics as diverse as extraordinary optical transmission, photonic crystals, metamaterials, and surface plasmon resonance biosensing. With these applications in mind, we focus on surface plasmon resonances excited in the context of insulator-metal structures with a periodic, corrugated interface. The object of this contribution is to study the geometric limits required to generate these fundamentally important phenomena. For this we use the robust, rapid, and highly accurate field expansions method to investigate these delicate phenomena and demonstrate how very small perturbations (e.g., a 5 nm deviation on a 530 nm period grating) can generate strong (in this instance 20%) plasmonic absorption, and vanishingly small perturbations (e.g., a 1 nm deviation on a 530 nm period grating) can generate nontrivial (in this instance 1%) plasmonic absorption.

Method of field expansions for vector electromagnetic scattering by layered periodic crossed gratings

In many applications of scientific and engineering interest the accurate modeling of scattering of linear waves by periodic layered media plays a crucial role. From geophysics and oceanography to materials science and imaging, the ability to simulate such configurations numerically in a rapid and robust fashion is of paramount importance. In this contribution we focus upon the specific problem of vector electromagnetic radiation interacting with a multiply layered periodic crossed diffraction grating. While all of the classical methods for the numerical simulation of partial differential equations have been brought to bear upon this problem, we argue here that in this particular context a high-order perturbation of surfaces approach is superior. In particular, we describe how the method of field expansions can be extended to the fully vectorial and three-dimensional scattering problem in the presence of multiple layers. With specific numerical experiments we will show the remarkable efficiency, fidelity, and high-order accuracy one can achieve with an implementation of this algorithm.