Propagation of Lorentz beam in strongly nonlocal nonlinear media

Based on the Collins formula in strongly nonlocal nonlinear media (SNNM), the analytical expression for Lorentz beam passing through SNNM has been derived. It is found that the propagation behavior of Lorentz beam is variable and closely related to the parameters of initial ellipticity p and input power. The beam has its own critical power in x and y directions, respectively. If the Lorentz beam with critical power in a certain direction enters in SNNM, its beam width will remain constant in that direction during propagation, otherwise its beam width varies periodically, as either broad or compressed. Moreover, when p not equal 1, the beam spot is always symmetrical in x and y directions; when p = 1, the beam spot is no longer symmetrical in x and y directions. Numerical simulations are carried out to illustrate these quintessential propagation properties.