Two-Dimensional Electromagnetic Scattering of Non-Plane Incident Waves by Periodic Structures

Abstract

Abstract-This paper proposes the pseudo-periodic Fourier transform to analyze the electromagnetic scattering from periodic structures with non-plane wave incidence. The pseudo-periodic Fourier transform converts arbitrary field components into pseudo-periodic functions and the conventional grating theories based on the Floquet theorem become applicable. The inverse transform is given by integrating with respect to the transform parameter over a finite interval and the near field analysis requires numerical integration. Some application examples are numerically examined and the results show good convergence.

Complex Analysis of the Induced Currents on a Perfectly Conducting Plane Under Complex Beam Incidence

“…As a conclusion, the results suggest that it is possible to extend this complex analysis methodology to concrete scattering problems (for instance the sort of problems in [16][17][18]) including more general solutions, their interpretation in terms of complex quantities, complex scattering laws, etc. This also leads to a very important coming back to basics procedure described under the general terminology of complex signal theory currently under investigation [19].…”

Spectral-Domain Formulation of Electromagnetic Scattering From Circular Cylinders Located Near Periodic Cylinder Array

“…The spectra for the periodic cylinder array without the additional cylinder were presented in Figure 3 of Ref. [2] and they are not smooth at the Wood-Rayleigh anomalies. The additional cylinder is thought not to change the locations of the Wood-Rayleigh anomalies, and here we use the same discretization scheme with Ref.…”

“…Since the region outside the cylinders is homogeneous, the fields transformed by PPFT can be expressed in the plane-wave expansions [2]. The basis functions of plane-wave expansion are here given by column matrices f (±) (x, y; ξ), in which the nth-component is given as…”

“…The additional cylinder is thought not to change the locations of the Wood-Rayleigh anomalies, and here we use the same discretization scheme with Ref. [2], namely, the integration range is split at the Wood-Rayleigh anomalies ξ = ±0.2k d and the sample points and weights are determined by applying the GaussLegendre scheme for each subinterval. The solid and the dashed curves in Figure 2 are the results and show much improvement of the convergence.…”

“…[2] by introducing the pseudo-periodic Fourier transform (PPFT). When the incident field is not the plane-wave, the fields in the periodic structures generally have continuous spectra in the wavenumber space, and an appropriate discretization is necessary for the spectral-domain approaches.…”