The Investigation Of Spectral Anomalies And The Longitudinal Field Effect In Laser Propagation In Free Space

The spectral analysis of radiation is one of most important analytical methods in science.During the spectral analysis of radiation,an assumption,i.e.,the spectrum does not change as the radiation propagates in free space,is used.Recently, this assumption is called into question.Researches showed that the spectrum of the radiation from the source keeps the spectrum invariance during its propagation only when the spectral degree of coherence of source satisfies the scaling law.Conversely, when the source does not satisfy the scaling law,the spectrum of the source will change during its propagation.Further studies indicate that the spectrum of partially coherent light,which satisfies the scaling law,incident upon an aperture will also experience spectral changes.And the spectrum will split into two same height peaks at critical position,a rapid transition of the spectral shift from red to blue, i.e.,spectral switches occur.On the basis of diffraction integral and the expansion of the hard-aperture function into a finite series of complex Gaussian functions,an approximate expression for spatially fully coherent polychromatic hollow Gaussian beams passing through aperture lens is obtained for the first time.With the help of the approximate expression, the propagation of polychromatic hollow Gaussian beams passing through aperture lens.Numerical results indicate that the spectrum of polychromatic hollow Gaussian beams will experimence spectrum changes when passing through aperture lens.Detailed numerical results indicate that remarkable spectral changes always occurs near the points where the field amplitude has zero value.The effects of truncation parameter,Fresnel number and the beam order on spectral shifts and spectral switches are investigated numerically.Starting from the Rayleigh diffraction integral and the expansion of the hardaperture function into a finite series of complex Gaussian functions,an approximate analytical spectrum expression for a Gaussian Schell-model(GSM)beam passing through an aperture is given.With the help of this approximate analytical spectrum expression,the propagation of Gaussian Schell-model beam passing through an aperture is well studied.Detailed numerical studies indicate the spectrum of partially coherent beams will experiment spectrum changes when passing through an aperture.The spectrum changes relate to the Fresnel number,the global coherence and the truncation parameter.By suitable choosing these parameters,we can control the position of spectrum switch,the number of spectrum switches.On the other hand,with the rapid development of the laser technology,especially the suitable description of near-field optics,tightly fbcused beams and laser beams generated by semiconductor,there has been growing interest to the description of nonparaxial propagation.In these cases,beams have large divergence angle or small spot size comparable with the wavelength,where the paraxial approximation is no longer valid.Therefbre,a suitable approxiamation is required fbr exact description.The first approach on nonparaxial propagation goes back to pioneering work of Lax et,al.Based on this power-series expansion,an analytical expression of longitudinal field fbr Hermite-Gauss beams is obtained.With the help of this expression, electron acceleration by two crossed linearly polarized Hermite-Gaussian laser beams in vacuum has been proposed and investigated in this thesis.And the necessary conditions fbr electron acceleration and energy gain expressions are also obtained.