Self-Focusing Property of Partially Coherent Beam With Non-Uniform Correlation Structure in Non-Linear Media

Coherence in a light beam has the potential to serve as a degree of freedom for manipulating the beam. In this work, the self-focusing property of a partially coherent beam with a non-uniform correlation structure propagating in a non-linear medium is investigated. The analysis of the evolution of beam width reveals that the coherence structure plays a vital role in the self-focusing formation. A threshold condition for the coherence radius is proposed for the first time, and the relation of self-focusing length and initial coherence radius is studied numerically and analytically. It is shown that a feasible approach for manipulating the self-focusing length by adjusting the initial coherence radius is achieved.

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

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.