利用变分法研究了1+2维超高斯型光束在强非局域非线性介质中的传输特性,得到了1+2维超高斯型光束各参量的近似演化方程、一个临界功率及光束各参量的近似演化规律。一般情形下, 1+2维超高斯型光束在强非局域非线性介质中传输时, 其束宽按正弦和余弦规律作周期性振荡变化, 当初始功率等于临界功率时, 其束宽则保持不变, 可以得到稳定的1+2维超高斯型非局域空间光孤子。另外, 经过分析得到临界功率随光束阶次的增大而增大, 与相位因子的阶次无关; 光孤子的相移快慢与光束阶次、相位因子的阶次、初始功率都有关, 但随着光束阶次的升高其主要依赖于光束阶次和初始功率, 相位因子的阶次的影响可以忽略。

The propagation properties of the 1+2-dimensional super Gaussian shaped optical beam in strongly nonlocal nonlinear media are discussed by means of variational approach. A set of parameter evolution equations, a critical power and an approximate evolution law of the beam width are obtained. In the general case, the beam width of the 1+2-dimensional super Gaussian shaped optical beam in strongly nonlocal media takes periodical oscillating variation with sine and cosine shape. But the beam width remains constant and the spatial optical soliton is formed when the input power equals the critical power. The critical power increases with the order of optical beam, but is independent on the order of phase factor. The speed of phase shift of the spatial optical soliton is related with the order of optical beam, the order of phase factor and the initial power. As the order of optical beam gets higher, the order of optical beam and the initial power plays more important role, and the effect of the order of phase factor can be ignored.