运用变分法研究了1+1维双曲正割型光束在强非局域非线性介质中的传输特性,得到了光束各参量的近似演化方程以及束宽的近似演化规律和一个临界功率。当初始功率大于临界功率时,双曲正割型光束在强非局域非线性介质中传输时,束宽按雅可比椭圆正弦函数和椭圆余弦函数作周期性压缩变化;反之,当初始功率小于临界功率时,其束宽按雅可比椭圆正弦函数和椭圆余弦函数作周期性展宽变化;当初始功率等于临界功率时,可以近似得到双曲正割型空间孤子。在束宽远小于强非局域非线性介质响应函数的响应宽度(束宽比α<0.300)的前提下,得到的结果与数值解基本一致。

The variational approach is used in discussing the propagation properties of 1+1 dimensional hyperbolic secant shaped optical beam in strongly nonlocal nonlinear media, a set of optical beam approximate evolution equations, the beam width approximate evolution law and a critical power are obtained. When the initial power is bigger than the critical power, the beam width compresses periodically and obeys the Jacobian elliptical sinusoid function and elliptical cosine function, with hyperbolic secant shaped optical beam propagating in strongly nonlocal nonlinear media; otherwise, when the initial power is smaller than the critical power, the beam width broadens periodically and obeys the above function laws. When the initial power equals the critical power, the hyperbolic secant shaped spatial soliton can be obtained approximately. In the case that beam width is far smaller than the response function width of the strongly nonlocal nonlinear media, namely, the above width ratio is smaller than 0.300, the analytical solution basically tends to the numerical solution in this paper.