We study the propagation of ultrashort chirped pulse beams in free space . the results show that the chirp influenced on the spatial singularity more than the width of the pulse beam 但是对于啁啾脉冲光束,啁啾导致的脉冲光谱展宽仍然会导致脉冲光束的空间奇异性,脉冲啁啾比脉冲长度对脉冲空间奇异性出现的影响更大。
During these processes , diffraction , self - phase modulation , cross - phase modulation and physical distance between the beam centers all have important effects on the beams and the pulse beams propagation 在这些过程中,衍射、自相位调制、交叉相位调制、光束之间的间距等都对光束和脉冲光束在非线性介质中的传输产生重要的影响。
Chapter 1 : the development of the investigation about the free - propagation of ultra - short pulsed beam is introduced , and the necessity of the investigation about the non - paraxial propagation of the ultra - short pulsed beam in free space is discussed 第一章:本章回顾了超短脉冲光束传输的研究进展并讨论了超短脉冲光束非傍轴传输研究的意义。
Based on the basic equation , the non - paraxial correction of pulsed beam is obtained by the spectrum analysis technic and the perturbative technic respectively . the result from the above mentioned two technics are compared to each other 基于上述方程,分别用角谱分析法和微扰法得到了脉冲光束的非傍轴修正,并对这两种方法所得结果进行了比较。
Porras and fu et al proposed that slowly varying envelope approximation and the complex amplitude envelope do n ' t fit anymore for the ultrashort pulsed beam shorter than or even near to one oscillation optical period , because they lead to a spatial singularity 结果表明,对于脉冲宽度较长(相对于一个光学周期)的超短无啁啾脉冲光束可以使用缓变包络近似和复振幅包络表达式。
For ultrashort pulsed beam propagation , to study the spatiotemporal instability . consider the time delayed response , a new instability region appeares . the position of this region and the magnitude of the gain depend on the characteristic raman response time 对于超短脉冲而言,介质的响应也不能看做瞬时的,如果考虑拉曼效应产生的响应的延迟,会产生一对增益边带,其位置和大小由响应时间决定。
Then the non - paraxial property of chirped pulsed beam and the variation of the non - paraxial correction induced by the variation of the pulse function are respectively discussed to illustrate the influence of the spectrum property on the non - paraxial property of the pulsed beam 首先分析了超短脉冲的光谱性质对其傍轴近似条件的影响,然后分别讨论了啁啾脉冲的非傍轴性质以及不同脉冲形式所导致的不同非傍轴特性。
Numerical examples illustrated the spatiotemporal properties such as spectrum redshifting , narrowing and pulse distortion , etc . it is stressed that the " antibeam " behavior of ultrashort pulsed beams can be avoided , if a suitable truncation function is introduced to the initial pulse spectrum 数值计算例说明了在色散介质中会出现谱红移、变窄、及脉冲形变等传输效应,而且对初始光谱引入截断函数可以避免“非光束”行为。
The condition , under which the paraxial approximation is valid , is given . 4 . starting from the rayleigh diffraction integral , the propagation equation of ultrashort pulsed beams in dispersive media has been derived without making the paraxial approximation and slowly varying envelope approximation ( svea ) , which allows for relatively large angles 从瑞利衍射积分公式出发,未作慢变振幅近似和近轴近似的条件下,导出了等衍射长度超短脉冲高斯光束在色散介质中非近轴传输方程,可用来处理色散介质较大角度的传输。
Chapter 3 : the influence of vectorial effect on non - paraxial propagation of pulsed beam is analysed based on the basic vectorial propagation equation of ultra - short pulsed beam in free space . on the basis of the analysis and the result of chapter 2 , the vectorial non - paraxial correction of ultra - short pulsed beam is obtained 第三章:这一章在脉冲矢量传输基本方程的基础上,分析了矢量效应对脉冲光束非傍轴修正的影响,并基于此分析以及第二章所得结果,得出了脉冲光束的矢量非傍轴修正。