强非局域克尔介质中光束传输的变分问题

在非局域克尔介质中，光束的演化规律服从非局域非线性薛定谔方程。用变分法对此问题进行了重新表述。在强非局域的情况下，通过对介质响应函数进行泰勒展开，可以解析地表示变分问题。束宽的演化规律也可以定性地从光束束宽变分势得出。运用瑞利-里兹方法求解其变分方程，分别求出光束在自散焦和自聚焦介质中的变分解。对于自聚焦介质，当输入功率为某一特定值时，可以得到空间孤子，其束宽在传输过程中保持不变。通过与其他方法得到的解比较表明，变分法是解析讨论光束在非局域非线性介质中演化规律的方法之一。

Variational approach to beam propagation in nonlocal Kerr media

The beam propagation in nonlocal Kerr media is modeled by the nonlocal nonlinear Schrodinger equation. This problem can be re-interpreted with the variational approach. In the case of strong nonlocality, the response function can be expanded in Taylor's series, so that the variational problem can be found in a closed form. The evolution of the beam width can be obtained qualitatively by analysing the potential function. By means of a Reyleigh-Ritz optimization procedure, the closed form solutions for the evolution of beams in both defocusing and self-focusing cases can be obtained. When the beam propagates in a self-focusing material and its input power reaches a critical value, its width becomes fixed. The comparison with analytical solutions obtained by other approaches shows that the va