Propagation of Bessel beam in a strongly nonlocal nonlinear media

We theoretically and numerically investigated the propagation of the zeroth-order and high-order Bessel beam in a strongly nonlocal nonlinear medium. Assuming the width of nonlocal response function is much larger than the beam width, the medium, is simplified to be a linear optical system. Propagation in the system can then be described by ABCD matrix method and Collins diffraction integral formula, based on which analytical expressions of ideal Bessel beam propagation are obtained. Fourier beam propagation method is then employed to study the propagation of aperture-limited finite-energy Bessel beam in the medium. Results show that Bessel beam periodically reconstructs its intensity profile in the medium with continuously varied mainlobe size. Our work provides basic understandings of Bessel beam in a nonlocal nonlinear medium.