Vacuum Laser Far-field Optical Problems, The Electron Acceleration Mechanism

Due to the rapid development of solid lasers and chirped-pulse amplification technique, peta-watt (PW) short-pulse lasers with intensity of 10²² W/cm² is available in laboratories. Because of the high intensity of the laser field, there has been much interest in the study of making use of the laser field to accelerate electrons in order to develop new type of small size, high energy laser-driven accelerator. The properties of the ultra-short pulsed beam need to be investigated in particular when it is applied to accelerate electrons, because of the high intensity, the ultra-short interacting time, and the spatiotemporal coupling. In this thesis, we investigated some optical problems aimed to the far field vacuum electron acceleration (especially the capture and acceleration scenario (CAS)), which includes: i) the vectorial nonparaxial propagation of the ultrashort pulsed beam; ii) influence of the spatiotemporal coupling on the CAS; and iii) validation and detecting of the nonuniform distribution of the phase velocity in focused beams. We hope the investigation is of interest in designing and optimizing the new type of small size, high energy laser-driven accelerator which is based on the far-field vacuum electron acceleration mechanism (especially the CAS). Our work mainly follows:I. The vectorial nonparaxial propagation of the ultrashort pulsed beam is investigated. The vectorial non-paraxial correction of ultra-short pulsed beam is obtained. And the influence of the spectrum property on the non-paraxial property of the pulsed beam is discussed.The longitudinal component of the laser field plays a key role in the far-field vacuum electron acceleration. And the paraxial approximation is not satisfied in the strongly focused beam. We investigated the vectorial nonparaxial propagation of the ultrashort pulsed beam. Firstly we discussed the relationship between i) the transverse and the longitudinal components; ii) the vecotorial component and the nonparaxial correction of the transverse component. Then the vectorial nonparaxial correction of the ultra-short pulsed beam is obtained based on the angular spectrum analysis and the perturbation method. And then the influence of the spectrum property on the non-paraxial property of the pulsed beam is discussed. This work may be useful in the designing and theoretical investigation of the pulsed beam used in the far-field vacuum electron acceleration.II. Study the properties of the ultrashort pulsed beam aimed to the far-field vacuum electron acceleration, especially the CAS vacuum electron acceleration.The spatiotemporal coupling in the propagation makes the investigation of the pulsed beam much more complicated than that of the continuous-wave (CW) beam. It has been proved that even in free space propagation the spatial and temporal dynamics cannot be analyzed separately. Because the acceleration relies much on the propagation of the pulsed beam, the CAS acceleration may be influenced by the spatiotemporal coupling. We investigate the properties of the pulsed beam that is related to the CAS acceleration. It shows that the spatiotemporal distribution of the phase velocity, the longitudinal component of the electric field, and the acceleration quality factor are qualitatively similar to that of the CW Gaussian beam, and are quantitatively influenced by the spatiotemporal coupling of the pulsed beam. When the full-width-at-half-maximum (FWHM) pulse duration T_FWHM > 5T₀ (where T₀ is the oscillation period of the carrier frequency), the spatiotemporal coupling as were as the above influence is very weak and can be neglected. In that case, the long pulse approximation can be adopted, i.e., the pulsed beam can be simply written as a product of a beam expression and a common temporal shape factor, in the investigation of the CAS acceleration process.Furthermore, although the high peak power of the ultrashort pulsed beam greatly benefit the CAS acceleration, the influence of the carrier-envelope phase (CEP) on the maximum net energy gain is a critical disadvantage when the FWHM pulse duration is shorter than 5 optical cycle. Therefore, if we want to introduce these ultrashort pulsed beam into the CAS acceleration process, the technique of CEP control, besides the technique of large-band-width pulse amplification and pulse compression, is very important.III. Propose that the nonuniform distribution of the phase velocity in focused beams can be validated and detected by quadratic nonlinear processes.The phase velocity, which is the speed with which each of the cophasal surfaces advances, is an oldest problem in optical science. The phase velocity is very important for the electron acceleration, especially the CAS far field electron acceleration. Previous investigation shows theoretically that there are subluminal and superluminal regions in focused beams. But it is difficult to directly measure the phase velocity by using traditional methods, because the phase velocity in the focused beam is distributed non-uniformly and the difference is very small (e.g., the difference is only of the order of 10^-4c when the beam waist is 10 times of the wavelength). To validate and detect the nonuniformly distributed phase velocity of the focused beam, new and effective methods are required.We propose that the nonuniform distribution of the phase velocity in focused beams can be validated and detected by quadratic nonlinear processes, which include: i)the second harmonic generation between off-axis Gaussian beams; ii) the difference frequency generation between a planar pump wave and a focused signal wave.In the investigation of the second-harmonic generation from the type-II phase-matched off-axis two focused Gaussian beams. We find that the optimal phase mismatch is influenced by the off-axis distance, and the influence comes of the phase velocity distribution of the Gaussian beam. Based on this property, an approach to measure the phase velocity distribution of the Gaussian beam is presented.Furthermore, the difference frequency generation between a planar pump wave and a focused signal beam is investigated. The numerical results have shown that the DF waves present interesting beam patterns related to the nonuniform phase velocity distribution of the focused signal beam. The resulted beam patterns can conversely reflect the relationship among the phase velocities of the interacting waves and is useful in detecting the slightly nonuniform distribution of the phase velocity in focused beams. This property may be of interest in designing and selecting the beam structure aimed to the far-field vacuum electron acceleration.