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中文摘要：
基于非线性薛定谔方程和热扩散的泊松方程,采用分步傅里叶算法以及多重网格法对厄米-高斯光束在不同形状的热非局域介质铅玻璃中的传输进行了数值模拟研究.结果表明,低阶厄米-高斯光束可以较为稳定地在铅玻璃中传输.高阶厄米-高斯光束在铅玻璃中传输变得不稳定,并且阶数越高,稳定性越差.样品的形状对于厄米-高斯光束的影响很大.在正方形样品中,厄米-高斯光束的传输与Snyder-Mitchell模型符合得相对较好.在矩形样品中厄米-高斯光束在传输过程中的强度分布将发生较大的变化.
英文摘要：
Based on the nonlocal nonlinear Schrdinger equation and Poisson equation of thermal diffusion,using the slip-step Fourier algorithm and multi-grid method,we numerically investigated the propagation properties of Hermite-Guassian beams in the nonlocal thermal media. The results show that low-order Hermite-Gaussian beams can propagate stably,in contrast with the unstable propagation of high-order Hermite-Gaussian beams. The worse the stability is,the higher the order is. The effect of the boundary of the sample with different cross sections on the propagation properties of Hermite-Guassian beam is also discussed in detail. We found that propagation properties in square geometry are in agreement with those in Snyder-Mitchell model. However,in rectangular sample,the evolution of intensity distribution of Hermite-Gaussian beams differs seriously from that in the square sample.
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