Coherence Properties and Intensity Distribution of a Partially Coherent Lorentz–Gauss Beam Emerging from the Axicon

Abstract

The propagation of a partially Lorentz–Gauss beam in a uniform-intensity diffractive axicon is studied according to the Huygens–Fresnel principle, the Hermite–Gaussian expansion of a Lorentz function, and using the stationary phase method. We have derived the intensity equation of a partially coherent Lorentz-Gauss beams propagating through uniform-intensity diffractive axicon, and we proved mathematically that it is the superposition of Bessel beams of various orders after emerging from axicon, using Hermite’s function series and the Bessel function integral formulas. The results show that the intensity distribution of the diffracted beam is the intensity pattern evolved from a Lorentz–Gauss shaped spot into a Gaussian-shaped spot at any position on the focal length of the axicon, and the intensity distribution of a partially Lorentz–Gauss beam generated by an axicon becomes uniform by increasing the beam width and more uniform and constant with the larger coherence width.

Propagation intensity and phase distribution of a Partially Coherent Lorentz–Gauss Vortex Beam in a Gradient-Index Medium

“…Lorentz-Gauss beams have revolutionized laser technology, opening up new possibilities in applications such as optical communications and remote sensing. These beams are generated by a single-mode diode laser and have been extensively studied in different mediums, including uniaxial crystals [1], turbulent atmospheres [2], through axicon optical system [3], and Kerr media [4]. With their unique properties, including a zero central intensity and a spiral wave-front structure, these beams have proven to be highly effective in their applications.…”