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.
Highlights
In 2006, Gawhary and Severini [8] introduced a new kind of realizable beam named Lorentz or Lorentz–Gauss beam. ese beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions
The Lorentz beam has been provided to describe the light field of a diode lasers [9], where the diode lasers have been widely used in practical applications
The laser beams based on the Lorentz distribution have been widely investigated. e propagation properties of Lorentz and Lorentz–Gauss beams propagating through free space, optical systems, and turbulent atmosphere and oceanic have been widely investigated [10,11,12,13], but the propagation properties of a partially coherent Lorentz–Gauss beams through axicon have not been reported
Summary
The propagation properties of laser beams in axicon have been widely investigated due to their applications such as alignment and metrology, coherence tomography, atom trapping and guiding, optical pumping of plasma, and medical [1, 2], so it is considered the most important optical element [3]. e propagation properties of various laser beams through axicon have been illustrated, such as Gaussian beams [4], Laguerre-Gaussian beams [5], Gaussian Schell-model beam [6], and partially coherent flattopped beam [7]. The laser beams based on the Lorentz distribution have been widely investigated. E propagation properties of Lorentz and Lorentz–Gauss beams propagating through free space, optical systems, and turbulent atmosphere and oceanic have been widely investigated [10,11,12,13], but the propagation properties of a partially coherent Lorentz–Gauss beams through axicon have not been reported. E cross-spectral density function of a partially coherent Lorentz–Gauss beam generated by a Schell-model source propagating along the z axis at the source plane z 0 can be expressed as. En, the cross-spectral density function of a partially coherent Lorentz–Gauss beam at the source plane z 0 can be rewritten as π2 4w20xw20y
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