强非局域克尔介质中光束传输的变分问题

Variational approach to beam propagation in nonlocal Kerr media

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。

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 Rayleigh-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 variational approach is one of the efficient methods in analysing the beam evolution in nonlocal nonlinear media.