Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media

•The propagation of a Laguerre-Gaussian correlated Schell-model in SNNM is first reported.•The beam width, irradiance and the spectral degree of coherence change periodically.•The propagation factor of the LGCSM beam in SNNM keeps invariant.

Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.