Propagation Properties Of Femtosecond Pulsed Beams In Free Space, Dispersive Media, And Through Lenses

With rapid advances in femtosecond pulsed laser techniques, ultrashort few-cycle, even single-cycle pulses can be produced in laboratory. The propagation of such kind ultrashort pulsed beams has attracted much interest. The present thesis is devoted to studying the propagation of femtosecond pulsed beams in free space, linear dispersive media, and through lenses. The main results achieved in this thesis can be summarized as follows:1. By using the complex analytic signal representation and the method of stationary phase, the propagation equation of ultrashort pulses in the far-field has been derived beyond the paraxial approximation, which allows for large angles in the far-field. As compared with the solution using pulse envelope representation, the propagation equation using complex analytic signal representation reveals different spatiotemporal behaviors such as spectrum redshifting, narrowing, and pulse broadening, etc.2. Starting from the Rayleigh diffraction integral and using analytic signal complex representation, the propagation equation of ultrashort pulses in free space has been derived in the near-field beyond the paraxial approximation, which is consistent with the paraxial results in previous literatures if the paraxial approximation is made. Numerical examples show that, pulse deformation and broadening, spectrum redshifting, narrowing and distortion take place with increasing diffraction angle in the near field, and the pulse form changes with propagation distance in the near field, but is preserved in the far field.3. The propagation of ultrashort pulsed Bessel beams in free space beyond the paraxial approximation has been studied and compared with that within the paraxial approximation. The non-paraxial effect was demonstrated with numerical examples. When the spatial parameter a is small, the non-paraxial effect doesn't affect the temporal profile of the beam. However,when a becomes relatively larger, it influences the temporal profile greatly. 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. 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.5. Without making the paraxial approximation, a detailed study on the propagation of ultrashort pulsed Bessel beams in linear normal and anomalous dispersive media has been performed using the method of Fourier transform. The spatial profile of the pulsed Jn-beam remains Jn-shape unchanged upon propagation, whereas its temporal profile depends on diffraction and the material's dispersion. The pulses can be broadening and become negatively chirped while propagating in anomalous dispersive media. In normal dispersive media, the pulses can be broadening, positively or negatively chirped, or even the dispersion-free propagation can be achieved, if the beam and material parameters are suitably chosen. The condition under which higher-order dispersive effects can be neglected is also discussed with numerical examples.6. Based on the Fourier optics, the focusing of ultrashort pulses by a silica lens in both cases of constant beam waist and constant diffraction length is studied considering dispersion of first, second and higher order, respectively. For ultrashort few-cycle pulses, the group velocity dispersion should be considered, whose influence depends on the parameters of the beam and the material. In general, the lens chromatic aberration and the group velocity dispersion lead to a broadening in the temporal and spatial intensity distributions at the focal plane and a decrease o...