Non-Paraxial Wave Analysis of 3D Airy Beams

The 3D Airy beam (AiB) is thoroughly explored from a wave-theory point of view. We utilize the exact spectral integral for the AiB to derive local ray-based solutions that do not suffer from the limitations of the conventional parabolic equation (PE) solution, and are valid far beyond the paraxial zone and for longer ranges. The ray topology near the main lobe of the AiB delineates a hyperbolic umilic diffraction catastrophe, consisting of a cusped double-layered caustic, but this caustic is deformed in the far range where the field loses its beam shape. The field in the vicinity of this caustic is described uniformly by a hyperbolic umilic canonical integral which is structured explicitly on the local geometry of the caustic as obtained from the initial field distribution. In order to accommodate the finite-energy AiB we also modify the canonical integral by adding a complex loss parameter. The canonical integral is calculated using a series expansion and the results are used to identify the validity zone of the conventional PE solution. The analysis is performed within the framework of the non-dispersive AiB where the aperture field is scaled with frequency such that the ray skeleton is frequency-independent. This scaling enables an extension of the theory to the ultra wide band (UWB) regime and ensures that the pulsed field propagates along the curved beam trajectory without dispersion, as will be demonstrated in a subsequent publication

Analysis of Electromagnetic Scattering Using Arrays of Fictitious Sources

The use of models of fictitious elemental current sources, located inside the scatterer, to simulate the scattered field, has proved to be an efficient computational technique for analyzing scattering by metallic bodies. This paper presents a novel modification of the technique in which the omnidirectional elemental sources are arranged in groups of array-sources with directional radiation patterns, and the boundary testing points are arranged in groups of testing arrays with directional receiving patterns. This modification, which is motivated by physical understanding, is equivalent to mathematical basis transformations. It renders the system matrix more localized and thereby enables the analysis of larger bodies. The new approach is applied to the case of TM scattering by a perfectly conducting square cylinder with side-length of 20. Reduction of 50% in the number of the non-zero elements of the system matrix is achieved with virtually no degradation in the accuracy of the RCS calcu..