Focusing properties and focal shift of vortex Hermite-cosh- Gaussian beams

Abstract

In this work, we investigate the focusing properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a converging lens system. The analytical propagation equation as well as the beam width expression of a focused vHChGB is derived based on the Huygens-Fresnel diffraction principle. From the obtained formulae, the effects of the Gaussian Fresnel number NF and the beam parameters on the structure of the light intensity distribution and the beam spot size in the focal region are analyzed numerically. It is shown that the focal shift, which is determined from the minimum beam spot width criterion, is affected strongly by the change of the Fresnel number, the parameter b, and it is slightly altered by the vortex charge M and nearly insensitive to the beam order n. For a fixed value of NF, the focal shift is smaller when the parameter b or the vortex charge M is larger. The focal shift decreases monotonously with the increase of Fresnel number until it vanishes asymptotically for large NF. The obtained results may be useful for the applications of the vHChGBs in beam shaping and beam focusing.

Production of good quality holograms by the THz pulsed vortex beams

“…While, the well-known rectangular laser beams, which are separable inside the orthogonal direction including Four-petal Gaussian beams [41], Finite airy beams [42][43] and Hermite sinusoidal-Gaussian beams [44][45][46][47][48], are not originally vortex modes but they can be integrated by vortex phase amplitude.…”