Flat-topped Beam Characterization, Simulation And Intensity-moments-based Laser Beam Quality

The flat-tapped beam has a uniform transversal profile in the near field and a Bell-shape profile in the far field. The study of such a type of beam is of practical interest in laser material processing and inertial confinement fusion (ICF). On the other hand, the intensity moments method provides a useful approach to characterizing the laser beam quality. The main advantage of this approach is that the characteristic parameters of a laser beam at the output plane can be obtained easily from the initial parameters of the laser beam at the input plane. In thas dissertation, the characterization, propagation and simulation methods of flat-topped beams, including the flattened Gaussian beams (FGBs) and super Gaussian beams(SGBs), are studied. Using the intensity moments method, the beam quality parameters such as the propagation factor (M2 factor), kurtosis parameter (K parameter) and point stability, etc. of typical laser beams, e.g., FGBs, SGBs and Hermite-cosh-Gaussian(HChG) beams, are studied. The main results obtained in this disserJt&on are summarized as follows:The propagation and simulation of flat-topped beams passing through a complicated optical system are studied. (1)Using the propagation formula of FGBs passing through a paraxial ABCD optical system, the propagation of FGBs passing through a lens series is studied. It is found that, under certain conditions, the lens series of large number lenses can be replaced by the lens series of small numberlenses and even by the free space if the lens series is composed of the same lenses and free space, and the positions of the free space and imaging-relaying system can be changed if the lens series is composed of imaging-relaying systems and free space. (2)Based on the propagation equation of FGBs passing through unapertured paraxial ABCD optical systems, the similar transformation conditions are obtained for the first time, which is expressed as that two FGBs with the same beam order have similar intensity distributions at the two positions of equal generalized Fresnel number when they propagate through two AjB,CjDi(i=l,2) systems. Furthermore, a comparison between a FOB and a SGB of the same beam A^-factor but different waist widths is performed for the first time. It is shown that the FGB and SGB passing through a paraxial ABCD system demonstrate similar irradiance profile at the positions of the equal generalized Fresnel number. But the FGB and SGB passing through a paraxial ABCD optical system having spherically aberrated lens do not demonstrate similar irradiance profile at the positions of the equal generalized Fresnel number. The nearly same irradiance profile at the positions of the equal generalized Fresnel number can be achieved if the FGB and SGB have the same A/2-factor and waist width. (3) By means of expanding the aperture function into a finite sum of complex Gaussian functions, the propagation of FGBs through a paraxial optical ABCD system with hard-edged aperture is studied, and the approximate closed-form equations of apertured FGBs are obtained for the first time. The results obtained by using the approximate closed-form equation and Collins formula are compared, and the condition under which the approximate closed-form equation is applicable is analyzed. Moreover, the similar transformation condition for the apertured FGBs is obtained. (4)The propagation of FGBs passing through a paraxial ABCD optical system including the linear gain (absorption) media is studied, and a closed-form propagation formula of FGBs through the system is derived for the first time. The condition under which the transverse field is convergent in the linear media is derived from the closed-form propagation formula. The numerical calculation simulation shows that the FGB will change its shape upon propagation. (5) Using the quasi-discrete Hankeltransform(QDHT), the fast calculation code simulating the propagation of cylindrical symmetry laser beams passing through high power laser amplifier system is built up for the first time. The code is applied to...