Investigation And Measurement Of The Spatiotemporal Evolutions Of Broad Bandwidth Laser Pulses In The Kerr Medium

With the development needs of ultrashort pulses laser technology, the pulse width of a laser has entered the field of attosecond, so that the spectrum width of the laser becomes more and more wide. Beam quality (spatiotemporal characteristics) is an important parameter, which is usually used to evaluate the laser system performance. Because broadband laser pulses have "sharp" time characteristics (femtosecond or less), small beam diameter, and high peak power and so on, leading to generate lots of nonlinear effects when they propagates in a nonlinear medium. The self-focusing, especially the small-scale self-focusing, is one of the most important nonlinear effects, which affects the beam quality and leads the output beam serious distortion. In order to control output beam quality better, real-time monitoring and precision measuring the spatiotemporal evolutions of broadband laser pulses during nonlinear propagation is necessary. Therefore, investigation and precision measurement of the the spatiotemporal evolution regularities of broadband laser pulses in the process of nonlinear propagation is very great significance both in theory and practical application. In this dissertation, we investigated both theoretically and experimentally the spatiotemporal evolution laws of broadband laser pulses during nonlinear propagation, and obtained the main results as follows:Firstly, based on the exact solutions of the (3+1)-dimensional generalized nonlinear Schrodinger equation (GNLSE), we theoretically study the spatiotemporal propagation characteristics when a laser propagates in an inhomogeneous nonlinear medium, and obtained a condition of stable propagation. These results are helpful to the extendable investigation of nonlinear propagation and control of a laser pulse.The (3+1)-dimensional generalized nonlinear Schrodinger equation with distributed coefficients is solved analytically by an improved homogeneous balance principle and F-expansion technique. A number of exact periodic traveling wave and spatiotemporal soliton solutions are obtained. The different order intensity moment can describe the characteristics of a laser, so the spatiotemporal propagation characteristics are investigated by intensity moments when a laser propagates in an inhomogeneous nonlinear medium, and the beam width (BW), the pulse width (PW), the skewness and the kurtosis parameter are calculated. The spatiotemporal propagation stability of the analytical solutions is analyzed detailedly by the second-order intensity moment.(1) When the diffraction and dispersion coefficients are the identical distributed functions, the BW and PW of the soliton solution with chirp or without chirp are constants; the BW and PW of the chirped or unchirped periodic traveling wave solution vary periodically during nonlinear propagation. So the spatiotemporal propagation of the analytical solutions is stable.(2) When the diffraction and dispersion coefficients are other coefficients, the BW and PW of the unchirped soliton solution is a constant, but the BW and PW of chirped soliton solution and chirped or unchirped periodic traveling wave solution vary irregularly due to the effect of a chirp. Therefore, the spatiotemporal propagation of the analytical solutions is unstable.Secondly, we propose a method of precision measuring the fine structure of laser pulse in time domain during nonlinear propagation. This method has advantages of simple operation, convenient and high resolution. The temporal evolutions of a laser pulse are obtained during self-focusing in experiment. This method has a certain reference value for measuring the temporal evolutions of a mid-IR laser pulse in the process of nonlinear propagation.When the initial pulse with a distortion propagates and amplifies in the large-scale Nd:glass laser system, the distortion degree will be accumulated and enhanced. So a corresponding measurement technique to characterize the fine structure of pulse is necessary. We propose a method of measuring the spatiotemporal evolutions of picosecond laser pulse by synchronized femtosecond laser pulse. Firstly, the feasibility and corretness of this method are analyzed theoretically. It is shown that the fine structure and pulse width of a complex picosecond pulse can be measured by this method. When the pulse width of the femtosecond pulse is shorter, the resolution is high and the measurement error is small. Then, the fine structure of a picosecond Nd:YLF laser pulse with pulse width of about75ps is characterized by a synchronized femtosecond pulse with pulse width of about100fs experimentally. The result of pulse width of picoseond pulse is the same with that by autocorrelation method. Finally, the spatiotemporal evolutions of a picosecond laser pulse propagating through different lengths of CS2medium are measured. We find that the the pulse width has a trend of slight narrow because picosecond laser generates slight self-focusing effect in space with increment of the length of CS2medium.Thirdly, we propose a method of precision measuring the temporal evoluitons of ultrashort laser pulse at different spatial positions during nonlinear propagation. The pulse width evolutions affected by partial spatial intensities is revealed experimentally during small-scale self-focusing, which is referred to as spatiotemporal coupling effect.Small-scale self-focusing (SF) causes rapid increase in the partial spatial intensity, breaking up the spatial profile of the beam into an intensity increasing zone (IZ) and a non-increasing zone (NIZ). We investigate experimentally the spatiotemporal evolutions at the IZ and NIZ. The pulses widths of ultrashort laser pulse are difference due to the distributions of initial spatial intensities are non-uniform. A modified cross-correlation method is proposed, which can precision measure the pulse widths of femtosecond laser pulse at different spatial positions. Then we measure the pulse width evluitons at IZ and NIZ in the process of SF. It is shown that the spatial peak intensity increases rapidly with increasing laser power, which shows the SF becomes more and more strong. Therefore, the pulse width at the IZ is compressed with increasing partial spatial peak intensity. The pulse width will become narrowest when the spatial peak intensity reaches maximum. However, the spatial peak intensity is almost unchanged with increasing laser power, which shows the SF is very weak, so the pulse width remains almost constant. Before the formation of filaments in the partial spatial zones of a beam, we believe an understanding of the detailed process of temporal evolutions at different partial spatial zones can help us to obtain a better understanding of the filaments of high power lasers.