The problem of a plane wave incident at an arbitrary angle on a metal strip grating of arbitrary period located at an air-dielectric interface is formulated rigorously in terms of a pair of static integral equations, from which equivalent multimode network descriptions are derived. Both aperture and obstacle approaches are treated, and both TE and TM polarizations are considered explicitly. >

Multimode network description of a planar periodic metal-strip grating at a dielectric interface. I. Rigorous network formulations

The problems of plane wave scattering by resistive- and dielectric-strip gratings are considered. The formulation involves a set of resistive-type boundary conditions that characterizes nonzero jumps in tangential field components. The method of solution is based on analytical inversion of the static part of the full-wave equations and results in a rapidly convergent numerical algorithm. The dependences of the transmitted, reflected, and absorbed power fractions on the electrical and material parameters are presented.

Plane wave scattering and absorption by resistive-strip and dielectric-strip periodic gratings

This paper presents a fully analytical model to determine the transmission and reflection properties of planar 1-D distributions of metal strips or slits made in thin metal screens. In contrast with other analytical or quasi-analytical approaches, the formulation incorporates the presence of dielectric slabs and is valid over a wide frequency band, from the long wavelength limit to the grating lobes operation. The model has been adapted to the case where two 1-D planar grids are stacked or a single grid is printed on a grounded substrate. In these cases, the model rigorously takes into account higher order mode interaction between the two stacked arrays of strips/slits or with the ground plane. Oblique incidence and both TE and TM polarizations have been considered. The analytical results show a good agreement with those computed by high-performance numerical methods, accounting for very fine details of extremely complicated transmission/reflection spectra. These results are of straightforward application to a variety of practical situations from microwaves to the terahertz regime. The present methodology can still be useful at higher frequencies provided that adequate models of the planar conductors are incorporated. In general, the model provides physical insight on the nature of the expected spectra and facilitates the design of devices based on planar metallic gratings.

Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs

This article reviews the nature and history of the discovery of high-quality natural modes existing on periodic arrays of many subwavelength scatterers; such arrays can be viewed as specific periodically structured open resonators. These grating modes (GMs), like any other natural modes, give rise to the associated resonances in electromagnetic-wave scattering and absorption. Their complex wavelengths are always located very close to (but not exactly at) the well-known Rayleigh anomalies (RAs), determined only by the period and the angle of incidence. This circumstance has long been a reason for their misinterpretation as RAs, especially in the measurements and simulations using low-resolution methods. In the frequency scans of the reflectance or transmittance, GM resonances usually develop as asymmetric Fano-shape spikes. In the optical range, if a grating is made of subwavelength-size noblemetal elements, then GMs exist together with better-known localized surface-plasmon (LSP) modes. Thanks to high tunability and considerably higher Q-factors, the GM resonances can potentially replace the LSP-mode resonances in the design of nanosensors, nanoantennas, and solar-cell nanoabsorbers.

Periodicity Matters: Grating or lattice resonances in the scattering by sparse arrays of subwavelength strips and wires.

The method of moments (MoM) is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization. Although this problem has been traditionally solved by means of the MoM in the spectral domain, this is an approach which leads to the computation of slowly convergent infinite summations. In this paper, the problem is solved by means of the mixed potential integral equation (MPIE) formulation of the MoM in the spatial domain. While applying the MoM in the spatial domain, two improvements are introduced which lead to important CPU time savings. First, the multilayered periodic Green's functions are accurately interpolated in terms of Chebyshev polynomials. Second, half the integrals involved in the computation of the MoM matrix entries are obtained in closed form. As a consequence of these two improvements, the spatial domain version of the MoM presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations.

Enhanced MoM Analysis of the Scattering by Periodic Strip Gratings in Multilayered Substrates

A new method, based on the spectral domain analysis, is presented for solving the electromagnetic wave scattering by an infinite plane metallic grating. The key point of the present method is discretization of spectral formulation in terms of the sampling theorem. Two different polarizations, transverse magnetic (TM) and transverse electric (TE) excitations, are considered here. Accuracy of the present method is examined numerically by comparison with the rigorous Wiener-Hopf solutions which are applicable only to a special case. Since the end effect of a conducting strip is taken into account analytically, final results show enough convergence to evaluate the near fields as well as the far fields with small matrix calculations. Some numerical examples are shown mainly for surface current distributions to make clear the differences between the two different polarizations.

Spectral domain analysis of electromagnetic wave scattering by an infinite plane metallic grating

A novel spectral-domain method combined with a sampling theorem is applied to the rigorous analysis of this quasi-two-dimensional problem. The accuracy and convergence of the method are examined numerically taking into account errors in comparison with extrapolated values, errors in the power relation, and the duality relationship. It is found that the numerical results exhibit good convergence. Another formulation related to Babinet's principle is discussed, and a relationship between the fields of an original and its complementary gratings is demonstrated. Numerical calculations are carried out showing that the method provides precise numerical results not only for the far fields, such as transmitted and reflected powers, but also for the near fields, such as surface current distribution on a strip and electric field intensity in a slit. Some numerical results related to the dual problem are provided. >

T. Matsunaga

Papers

Spectral domain analysis of electromagnetic wave scattering by an infinite plane metallic grating

Electromagnetic wave scattering by an infinite plane metallic grating in case of oblique incidence and arbitrary polarization