Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media

Abstract

Based on the Snyder and Mitchell model, a closed-form propagation expression of astigmatic sin-Gaussian beams through strongly nonlocal nonlinear media (SNNM) is derived. The evolutions of the intensity distributions and the corresponding wave front dislocations are discussed analytically and numerically. It is generally proved that the light field distribution varies periodically with the propagation distance. Furthermore, it is demonstrated that the astigmatism and edge dislocation nested in the initial sin-Gaussian beams greatly influence the pattern configurations and phase singularities during propagation. In particular, it is found that, when the beam parameters are properly selected, a vortex beam with perfect doughnut-shaped profile can be obtained for astigmatic sin-Gaussian beams with two-lobe pattern propagating in SNNM.

An astigmatic transform of a fractional-order edge dislocation

“…The extra dislocation closest to the center on the right is found on the horizontal axis and is 'being prepared' to become the sixth dislocation as soon as the fractional part gets close to 1. Figure 2(c) depicts the field amplitude in (7), with its phase presented in figure 2(a). Here, just three central intensity nulls can be seen on the horizontal axis and although the rest nulls are not seen but their position can be extracted from the phase distribution in figure 2 wavelength of light was λ = 532 nm, and the Gaussian beam radius was w = 500 µm.…”

“…A significant conclusion that can be made from the numerical simulation results is as follows: considering that the fractional number ν enters equation ( 7) only as a term of the constant before the exponential function and the first parameter of the Tricomi function, it is the latter which is responsible for the birth of extra dislocations and their evolution with varying fractional part of ν. From equation (7), the OVs are seen to be born at Tricomi function zeros lying on the horizontal axis because the Tricomi function argument becomes real at y = 0. For the case of an integer-order edge dislocation, ν = n, the Tricomi function zeros coincide with real zeros of the Hermite polynomial H n (x), lying on the horizontal axis at the crosssection of beam (8).…”

“…For instance, the propagation of a HG beam in a 4 × 4 optical system, including an astigmatic one, was investigated in [2,3], whereas [4] was concerned with a Hermite-LG beam traveling in an astigmatic mode converter. Also, focusing of a high-order optical vortex (OV) with an astigmatic lens [5,6], conversion of an astigmatic sin-Gaussian beam in a nonlinear medium [7], and an astigmatic mode conversion in a laser cavity [8,9] have been reported. Elliptic optical Gaussian beams with astigmatic phase were investigated in [10,11], at first with the conversion of an HG beam (0, n) by means of a tilted cylindrical lens and later by studying a mode beam in which a conventional OV with the charge n. In the last case, the charge embedded into an elliptic astigmatic Gaussian beam remains unchanged upon propagation, not splitting into a bunch of simple OVs.…”

Astigmatic transformation of a fractional-order edge dislocation

“…Асимптотика функции Трикоми (5), которая входит как сомножитель в амплитуду поля (7), имеет вид [26]:…”

“…В [5,6] исследовалась фокусировка астигматической линзой оптического вихря высокого порядка. Преобразования астигматического sin-Гауссова пучка в нелинейной среде рассматривались в [7]. В [8,9] исследовалось астигматическое модовое преобразование внутри лазерного резонатора.…”