Generation of Mathieu Beams in Millimeter Wave Band using Diffractive Elements

Abstract

The nondiffracting Mathieu beams have highly localized distribution along the angular direction and sharply peak quasiperiodic structure along the radial direction.The beams can propagate a long distance without changing their transverse intensity distribution. The dielectric diffractive elements, which can convert plane wave and Gaussian beam to nondiffracting Mathieu beams at millimeter wavelength, are designed. The transverse intensity patterns of Mathieu beam generated by the proposed diffractive elements are in good agreements with the theoretical distributions, and the propagation distance of generated Mathieu beam is larger than the Gaussian beam.

Complex Point Source for the 3d Laplace Operator

“…Some authors proposed replacing a real point source with a complex placed one to obtain Gaussian beams as a paraxial approximation to certain solutions of the Helmholtz wave equation [2][3][4][5]. Radiation and scattering problems have been constructed within the framework of these solutions, with special attention to paraxial approximations as Gaussian beams [6][7][8][9][10][11]. A more general description of the exact complex beams and the complex polar and spherical coordinates resulting from the complex extension of the coordinates has been studied in [12][13][14][15][16].…”