The Study Of The Ultrashort Pulsed Beams And The Spatially Induced Group Velocity Dispersion

The rapid advances of laser technology in the past few decades have made the production of extremely short laser pulses, containing only a few, even only one or nearly one, cycles of optical oscillations, which led to many new questions. In ultrashort pulsed light beams propagation, generally speaking, the spatial and the temporal parts of the wave are not separable, and the spatial evolution can affect the temporal behavior, and vice versa, even in free space. Therefore the study of the ultrashort pulsed beams has been a focus of the scientific research.In this thesis we study the propagation of the ultrashort pulsed beams by theoretical method and the numerical simulation. The thesis is composed of 5 chapters, among which are, Chapter 1 is a survey, Chapter 2, 3, 4 are the introductions of our own work, and Chapter 5 is a conclusion. The thesis is structured particularly as follows.Chapter 1: The development and applied significance of the ultrashort pulsed beam are introduced.Chapter 2: The basics equations and the complex analytical signal theory are introduced. Porras and Fu et al proposed that slowly varying envelope approximation and the complex amplitude envelope don'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. 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. If assuming the chirped parameter is equal to zero, our results deduce to that of Porras.Chapter 3: We find a family of solutions of the paraxial wave equation that represents ultrashort pulsed light beams propagation in free space. These pulsed beams have an arbitrary temporal form and a nearly elegant Hermite-Gaussian cross section, which pulsed beams we call the ultralshort pulsed elegant Hermite-Gaussian beams. The solution with a certain frequency is an elegant Hemite-Gaussian beam, and their diffractive distances are also same. In this chapter, we give some basicproperties about the pulsed beams.Chapter 4: The Spatially Induced Group Velocity Dispersion (SIGVD) of the pulsed Bessel, Bessel-Gauss beams propagating in free space is studied. The simulation results have shown that SIGVD of the temporal part is observed when the diffraction-free distance is longer than the dispersion length of SIGVD. SIGVD can be used to compensate the dispersion of medium, and a diffraction-free and quasi-dispersion-free pulsed beam, similar to a spatiotemporal soliton, can be produced in a dispersion medium.Chapter 5: summarizing the contents of the thesis.