超短光脉冲在圆柱对称性共振介质中的传播特性

摘要：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，和以圆柱的两条边做为边界条件比较，节省了将近一半的计算时间和计算机存储空间。计算结果表明，在考虑空间效应时，峰面积为2 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。

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

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