运用变分法,对任意实对称响应函数泰勒级数展开取至二阶,得到了1+1维强非局域非线性介质中光束传输的超高斯光束的近似分析解,提出了超高斯空间光孤子族模型。分析结果表明：束宽解是三角函数型,相移、空间啁啾以及临界输入功率都正比于超高斯光束的阶数,束宽振荡周期不仅与介质材料有关,而且还与光束和相位因子的阶有关。提出了准方波形空间光孤子的可能性。

Presented is the family of super-Gaussian spatial optical solitons in non-local nonlinear media modelled by 1+1 dimensional non-local nonlinear Schrdinger equation (NNLSE), in the strongly non-local case, an approximate analytical solution is obtained for an arbitrary response function by a variational approach. The solution with a sine beams width shows that the shift of phase, the spatial chirp and the critical input power are proportional to the order of the super-Gaussian optical beams, the period of the beam width is related not only to the material, but also to the orders of both the beams and the phase. The probability of quasi-square wave spatial solitons is also involved.