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.
Highlights
Localized surface-plasmon resonances on the standalone and coupled noble-metal wires are an area of active research in nanophotonics since the 2000s,1–4 more recently the emphasis has been shifted to the analysis of three-dimensional plasmonic particles.[5,6,7,8] Periodic arrays or gratings made of noblemetal nanosize elements are attracting even greater attention of research community
Summarizing, we have presented accurate numerical analysis of the resonance phenomena caused by the periodicity in the scattering and absorption of the H- and E-polarized light by freestanding sparse finite flat gratings of large number of thin silver nanostrips
Our modelling has been based on the elimination of the internal fields inside strip grating with the aid of generalized boundary conditions imposed on the strip median lines
Summary
It was not observed for a metal-strip grating on a thin substrate. In many publications they were regarded as specific plasmons. The small thickness suggests that the analysis can be simplified by neglecting the internal field of the strip and considering only the external field limiting values.[28,29,30] This enables reduction of the integration contours in the associated IEs to the corresponding median lines at the expense of introduction of certain “effective” or generalized boundary conditions Such an approach leads to very economic and rapidly convergent algorithms, whose results agree very well with full boundary[2,3,4] and volume IE results.[1,31,32] It has been used earlier in the analysis of the wave scattering by the infinite gratings of thin material strips[20,21,22] using the method of analytical regularization, and more recently by a dielectric strip using the Nystrom method.[33].
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