Theory of an elliptical radial carpet beam in uniaxial crystals

It has been shown that the diffraction of a plane wave modulated by a radial amplitude grating exhibits a circular transverse carpet pattern in free space. On the other hand, due to the anisotropic diffraction, the behavior of radial carpet beams in uniaxial crystals may not be circular, and their corresponding properties have been theoretically investigated in this paper. From the diffraction theory in uniaxial crystals, the radial grating transmittance function has been derived and used to generate radial carpet beams in theory. The diffraction of the radial sinusoidal amplitude grating-modulated beams in uniaxial crystals exhibits elliptical radial carpet patterns. By varying the propagation distance and the spoke number of the gratings, the similarities and differences between the radial carpet beams in uniaxial crystals and isotropic media have been analyzed.