超短脉冲光束传输缓变包络近似理论的失效和空间奇异性的形成与消除

研究了单周期或更短的超短脉冲光束在真空中的传输.结果显示,在此情况下缓变包络近似理论已不再有效,其失效的原因是,该理论导致了脉冲光束解的空间奇异性,并使脉冲光束不再具有符合物理意义的光束行为,而通过复解析信号的分析方法可以消除这种空间奇异性.给出了时间波形为Gauss,Hyperbolic Secant和Lorentz的脉冲光束奇异性的计算模拟,并给出了解决这些奇异性的复解析信号解.同样,会发现在脉冲光束超过一定的长度后两种解是一致的.

INVALIDATION OF THE SLOWLY-VARYING ENVELOPE APPROXIMATION AND PRODUCING AND ELIMINATING OF THE SPATIAL SINGULARITY FOR ULTRASHORT PULSED-BEAM PROPAGATION IN FREE SPACE

In this paper we study the propagation of the single cycle or much shorter pulsed-beam in free space. We show the invalidation of the slowly-varying envelope approximation (SVEA) theory because it leads to the spatial singularity of the ultrashort pulsed-beam solution and is inconsistent with the physical significance of the beam propagation. We eliminate the spatial singularity by making use of the complex analytical signal theory (CAS), and then give the solution and simulation of the Gauss, hyperbolic secant and Lorentz pulse beam for SVEA and CAS. The SVEA and CAS solutions are consistent if the pulsed beam becomes long enough.