超短光脉冲在圆柱对称性共振介质中的传播特性

THE CHARACTERISTICS OF ULTRASHORT LASER PULSES PROPAGATION IN CYLINDRICAL SYMMETRY RESONANCE MEDIA

用有限差分方法求解Maxwell和Bloch的联立方程,得到圆柱对称共振介质中超短光传播的规律.计算结果表明,在考虑空间效应时,峰面积为2π的超短光脉冲不再以孤子的形式传播,光场的形状将发生变化,变形的程度和光与物质相互作用的强度有关:强度较小时,光场包络在时间和空间两方面都展宽;强度较大时,则发生分裂.光与物质相互作用的强度与光场大小、偶极矩、共振粒子浓度等因素有关.计算中解决了在圆柱中心线上Maxwell方程存在发散项1/r以及用圆柱中心线作为边界条件时,中心线上光场值难确定的问题,因而光场只需从圆柱中心计算到圆柱边界,和以圆柱的两条边作为边界条件比较,节省了将近一半的计算时间和计算机存储空间.

The spatial effect of ultrashort pulse laser propagating through the cylindrical symmetry resonance media was discussed by solving the Maxwell - Bloch equations simultaneously with the definite differential method. Results indicate that the propagating of a 2~ pulse form would no longer be a soliton when spatial effect was taken into ac- count, its profile would distort, and the degree of distortion depends on the interaction intensity of laser and materi- al： the stronger interaction, the more distortion till the profile split. The interaction intensity was decided by such elements as the laser intensity, the dipole of material, and the concentration of resonance particles. Two problems were solved in numerical calculation, one was that a term of 1/r in Maxwell was divergence in the cylindrical center where r = 0, another was that the value of optical field at the cylindrical center was difficult to be decided when the cylindrical center set as a boundary condition in the Maxwell equation. So the values of optical field need just cal- culating from the cylindrical center to the cylindrical boundary, comparing with that from one cylindrical boundary to another cylindrical boundary, nearly half CPU time and RAM are saved.