The propagation of hypergeometric beams through an annular apertured paraxial ABCD optical system

Abstract

By means of expanding the hard aperture function into a finite sum of complex Gaussian functions and based on the generalized Huygens-Fresnel diffraction integral, a novel approximate analytical expression of hypergeometric (HyG) beams passing through a paraxial ABCD optical system with an annular aperture is derived. The results could be reduced to the case of a circular aperture or a circular black screen. Some numerical simulations are also performed and illustrated for the propagation characteristics and focusing properties of a HyG beam through a paraxial ABCD optical system with an annular aperture. The results obtained from the approximate analytical formula provide more efficiency than the usual way of using diffraction integral formula directly.

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

“…) where z R is the Rayleigh distance, p gc = 1/γ 2 z 2 R is the critical power with which Gaussian and higher-order Gaussian beams come into solitons in SNNM under the on-waist incidence. The HyGG beams passing through an ABCD optical system obeys the well-known Collins integral formula [16]:…”

“…Gaussian beams, modified Bessel-Gaussian beams and Laguerre-Gaussian beams can be regarded as the special cases of HyGG beams when the optical parameters are taken as proper values [8]. In recent years, the propagation of HyGG beams in various media and optical systems, for instance in plasma [9], uniaxial crystal [10], hyperbolic-index medium [11], parabolic refractive index medium [12], turbulent atmosphere [13,14], apertured optical system and fractional Fourier transform optical system [15,16], have been extensively studied.…”

Design of LCPG-type polarization-independent shutter with diffractive efficiency and high contrast at wavelength 532 nm

“…The partial recognition of structures, called diffractive elements (gratings) and sometimes anisotropic and vectoral grating(s), dates back to 1970 when some generalities were posited about holograms polarization [1]. Later, it was known that polarization gratings (PGs) could have the potential for control and handling of non-polarized light only at their multiple-order diffraction element [2,3]. PGs are transparent and thin elements that diffract incident light through great angles with high efficiency.…”