Propagation of perfect optical vortex beams in a strongly nonlocal nonlinear medium

The unique spatial characteristics of perfect optical vortex (POV) beams make them ideal candidates for a wide range of applications, from microparticle trapping and manipulation to optical communication. In this work, we investigate the propagation of POV beams in a strongly nonlocal nonlinear (SNNL) medium. An analytical expression for the complex field amplitude is derived using the ray transfer matrix formalism and the Huygens–Fresnel integral. We numerically study how various beam and medium parameters — such as the topological charge (TC), the ratio of the beam’s ring radius ($R$) to its half-ring width ($w_0$), and the nonlocal parameter ($\eta$) — affect the longitudinal intensity distribution of the POV beam. Both non-diffracting and self-focusing effects are clearly observed, accompanied by a periodic intensity distribution along the propagation axis. Increasing the TC has minimal impact on the beam profile size and intensity distribution during the non-diffracting stage. However, in the self-focusing stage, the central dark core expands monotonically with the TC. Additionally, the self-focusing effects diminish and eventually disappear as $\frac{R}{w_0}$ approaches unity. For a fixed beam wavelength and waist size, the nonlocal parameter exclusively determines the periodicity of the intensity distribution, revealing an inverse relationship between periodicity and nonlocality. These findings may contribute to improved techniques in microparticle trapping and manipulation using POV beams.