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 [Formula: see text] and input power. The beam has its own critical power in [Formula: see text] and [Formula: see text] 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 [Formula: see text], the beam spot is always symmetrical in [Formula: see text] and [Formula: see text] directions; when [Formula: see text], the beam spot is no longer symmetrical in [Formula: see text] and [Formula: see text] directions. Numerical simulations are carried out to illustrate these quintessential propagation properties.

中文翻译：

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洛伦兹光束在强非局部非线性介质中的传播

基于强非局部非线性介质（SNNM）中的柯林斯公式，推导了洛伦兹光束通过SNNM的解析表达式。研究发现，洛伦兹光束的传播行为是可变的，与初始椭圆率[公式：见正文]和输入功率等参数密切相关。光束在[公式：见文字]和[公式：见文字]方向上分别具有自己的临界力量。如果在某个方向具有临界功率的洛伦兹光束进入 SNNM，则其光束宽度在传播过程中将在该方向上保持恒定，否则其光束宽度会周期性地变化，要么是宽的，要么是压缩的。而且，当【公式：见文】时，光斑在【公式：见文】和【公式：见文】方向上总是对称的；当[公式：见正文]，束斑在[公式：见正文]和[公式：见正文]方向上不再对称。进行数值模拟以说明这些典型的传播特性。