光束在非局域非线性介质中的传输过程由非局域非线性薛定谔方程描述.1+2D非局域非线性薛定谔方程可以转化为圆柱坐标系下的变分问题.通过展开介质响应函数并合理假设试探解求解变分方程,得到光束在强非局域非线性介质中的拉盖尔-高斯解.满足一定条件时,拉盖尔-高斯光束将形成光孤子或退化为高斯光束.
The 1+2D nonlocal nonlinear Schrdinger equation can be transformed to the variational approach in a cylindrical coordinate system,and is applied to a model describing the propagation of optical beam in strongly nonlocal nonlinear media.By solving variational problems with expanding media response functions and assuming reasonable ansatz,the solution of the Laguerre-Gauss form is obtained.The Laguerre-Gaussian beams will form solitons or be reduced to Gaussian beams under certain conditions.