Finite gratings of many thin silver nanostrips: Optical resonances and role of periodicity

Abstract

We study numerically the optical properties of the periodic in one dimension flat gratings made of multiple thin silver nanostrips suspended in free space. Unlike other publications, we consider the gratings that are finite however made of many strips that are well thinner than the wavelength. Our analysis is based on the combined use of two techniques earlier verified by us in the scattering by a single thin strip of conventional dielectric: the generalized (effective) boundary conditions (GBCs) imposed on the strip median lines and the Nystrom-type discretization of the associated singular and hyper-singular integral equations (IEs). The first point means that in the case of the metal strip thickness being only a small fraction of the free-space wavelength (typically 5 nm to 50 nm versus 300 nm to 1 μm) we can neglect the internal field and consider only the field limit values. In its turn, this enables reduction of the integration contour in the associated IEs to the strip median lines. This brings significant simplification of the scattering analysis while preserving a reasonably adequate modeling. The second point guarantees fast convergence and controlled accuracy of computations that enables us to compute the gratings consisting of hundreds of thin strips, with total size in hundreds of wavelengths. Thanks to this, in the H-polarization case we demonstrate the build-up of sharp grating resonances (a.k.a. as collective or lattice resonances) in the scattering and absorption cross-sections of sparse multi-strip gratings, in addition to better known localized surface-plasmon resonances on each strip. The grating modes, which are responsible for these resonances, have characteristic near-field patterns that are distinctively different from the plasmons as can be seen if the strip number gets larger. In the E-polarization case, no such resonances are detectable however the build-up of Rayleigh anomalies is observed, accompanied by the reduced scattering and absorption.

Validity and Limitations of the Median-Line Integral Equation Technique in the Scattering by Material Strips of Sub-Wavelength Thickness

“…In certain cases collecting many dozens and hundreds of tiny scatterers brings new physics. If arranged periodically, they show new resonances caused by the periodicity [4], [25]. These huge collections of scatterers are absolutely out of reach if one uses either in-house MBIE algorithms or commercial software.…”

Periodicity assisted scattering and absorption of light by finite layered gratings of silver nanowires

“…In today's nanophotonics, various periodically structured scatterers, such as finite-periodic gratings, arrays or chains of particles and holes in metallic screens (in 3-D) or wires and slots (in 2-D), attract increasingly large attention of researchers [1][2][3][4][5][6][7][8][9]. This is caused by the amazing effects of extraordinarily large reflection, transmission, emission, and near-field enhancement that have been found in the scattering of light by periodic scatterers.…”

Validity of generalized boundary conditions and singular integral equation method in the scattering of light by thin dielectric strips

“…The theorems on quadratures ensure convergence of such numerical scheme with the rate of at least 1/N if N → ∞ . This enables on to study not only the scattering by single strips but also by the finite and infinite gratings of them [20][21][22][23]. All data presented below have been computed with 10 -4 accuracy that was achieved with N = 50.…”