We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) applications such as multi-wavelength and multi-angle optimizations, demultiplexers. To optimize surfaces that can be thousands wavelengths in diameter, with (or millions) parameters, the key is fast approximate solver scattered field. employ "locally periodic" approximation which scattering problem approximated by composition periodic...

This paper introduces a new windowed Green function (WGF) method for the numerical integral-equation solution of problems electromagnetic scattering by obstacles in presence dielectric or conducting half-planes. The WGF method, which is based on use smooth windowing functions and integral kernels that can be expressed directly terms free-space function, does not require evaluation expensive Sommerfeld integrals. proposed approach fast, accurate, flexible, easy to implement. In particular,...

This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and cavities on perfectly conducting or half-planes. In detail, the algorithms introduced in this apply to eight classical problems, namely: a bump half-plane, filled, overfilled void cavity half-plane. all cases field representations based single-layer potentials appropriately chosen Green functions are used. The numerical far fields near exhibit excellent...

Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are modeled an approximation akin to ray optics: the reflection or transmission of incident wave at each point is computed as if were "locally uniform," and then total field obtained summing all these local scattered fields via a Huygens principle. (Similar approximations found in scalar diffraction theory optics for curved surfaces.) In this paper, we develop precise such...

This paper presents a new methodology for the solution of problems two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles defects presence an arbitrary number penetrable layers. Relying on use certain slow-rise windowing functions, proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to highly expensive Sommerfeld that have...

This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly hypersingular, and nearly singular integral kernels present in 3D Helmholtz surface layer potentials associated operators. Relying on Green's third identity pointwise functions form planewaves, these allow operators to be expressed terms integrand that remain bounded or even more regular regardless location target point relative sources. Common challenging integrals arise both...

This paper presents a study of the absorption electromagnetic power that results from interaction waves and cylindrical bumps or trenches on flat conducting surfaces. Configurations are characterized by means adequately selected dimensionless variables parameters so applicability to mathematically equivalent (but physically diverse) systems can be achieved easily. Electromagnetic fields increments caused such surface defects evaluated high-order integral equation method which resolves fine...

This contribution presents a novel Windowed Green Function (WGF) method for the solution of problems wave propagation, scattering, and radiation structures that include open (dielectric) waveguides, waveguide junctions, as well launching and/or termination sites other nonuniformities. Based on use “slow-rise” smooth-windowing technique in conjunction with free-space functions associated integral representations, proposed approach produces numerical solutions errors decrease faster than any...

This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated Poisson and Helmholtz equations in two dimensions. Following ideas density interpolation boundary proposed methodology leverages Green's third identity local polynomial interpolant function to recast potential as sum single- double-layer potentials regularized (bounded or smoother) integrand. The layer can be accurately...

This paper presents a class of boundary integral equation methods for the numerical solution acoustic and electromagnetic time-domain scattering problems in presence unbounded penetrable interfaces two spatial dimensions. The proposed methodology relies on convolution quadrature (CQ) schemes recently introduced windowed Green function (WGF) method. As standard from bounded obstacles, CQ method user's choice is used to transform problem into finite number (complex) frequency-domain posed, our...

This article presents an extension of the recently introduced planewave density interpolation method to electric-field integral equation (EFIE) for problems scattering and radiation by perfect electric conducting objects. Relying on Kirchhoff formula local interpolations surface currents that regularize kernel singularities, technique enables off- on-surface EFIE operators be reexpressed in terms integrands are globally bounded (or even more regular) over domain integration, regardless...

We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency spectrum, including cutoff (or Wood) frequencies. overcome obstacle non-convergent quasi-periodic Green functions at these frequencies incorporating newly introduced shifted functions. Using latter in definition operators leads to rigorously stable...

We present non-overlapping Domain Decomposition Methods (DDM) based on quasi-optimal transmission operators for the solution of Helmholtz problems with piece-wise constant material properties. The boundary conditions incorporate readily available approximations Dirichlet-to-Neumann operators. These consist either complexified hypersingular integral equation or square root Fourier multipliers complex wavenumbers. show that under certain regularity assumptions closed interface discontinuity,...

We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting observations that (1) three components scattered electric field and (2) scalar quantity are radiative solutions Helmholtz equation, we see novel equation formulations obstacles can be derived using Green’s identities applied to aforementioned quantities conditions on surface scatterer. The unknowns these normal...