| Laser, as one of the most significant scientific and technological inventions of the 20th century, after 50 years of development, has been combined with multi-disciplinary fields, and greatly promoted the development of research in the interrelated basic and applied disciplines. Especially since the mid-eighties of the 20th century, the rapid development of high-power laser technology has brought wide range of applications into virtually every facet of modern life (e.g. from scientific research to industrial manufacturing and material processing, from communication to defense and medical treatment, and so on). Since the laser's invention, the investigation of beam propagation, transformation and control has always been an active area in laser science and technology.In this dissertation, taking contexts of scientific research and some practical applications of high-power lasers into consideration, from the below four aspects such as "Basic characteristics of power content beam propagation M2pc factor", "Reconstruction for dark region of annular beam of optical unstable resonator", "Wide-band beam optimization and control for high-power laser processing" and "High-repetition-rate pulse modulation for high-power continuous wave CO2 laser", the propagation, transformation and beam control of high power lasers are focused and carried out in-depth theoretical and experimental investigations. Several research achievements and contributions are summarized as follows.Firstly, the characteristics of power content beam propagation M2pc factor are exploringly investigated. It is theoretically demonstrated the "self-reproduction" beams of confocal resonator possess the minimal M2pc. The problems with M2pc for incoherent superposition of Gaussian beams are theoretically investigated. The corresponding M2pc-values can be smaller than one, depending strongly on the defined power content values. Consequently the characteristics of 86.5% power content M2pc are emphatically investigated. It is demonstrated that the M2pc-values of coherent superposition of axially shifted Gaussian beams must be larger than one. A novel set of beams with M2pc<1 is generated by the coherent superposition of Gauss-Laguerre modes with radial symmetry. Accordingly it is theoretically shown, for the first time to our knowledge, that the 86.5% values of M2pc can be smaller than one in paraxial approximation. By analyzing the influences of Fresnel number on the properties and M2pc of fundamental output beam of half-confocal resonator, it is found the M2pc-value of such beam can not be smaller than one. Starting with the scalar diffraction theory, we demonstrate the resonator withλ/2 phase-step is equivalent to a half-confocal resonator with the same geometry and dimensions. It is further shown that, in the current context of scalar diffraction theory, there is no proof that intracavityλ/2 phase-step can improve the beam quality. At last, from the theoretical and practical aspects, the relationship between the power content M2pc factor and beam quality is discussed.Secondly, the reconstruction approach for dark region of output annular beam of optical unstable resonator is theoretically investigated. The eigenmode behavior and output properties of positive branch confocal unstable resonator which is a frequently adopted cavity configuration in high-power gas laser technology are fully discussed. On the basis of these results, we investigate an annular beam shaping approach using an inner cone annular scraper and an outer cone reflector. The realization principle and optical design of the annular beam shaping system is introduced. Taking the example of a conventional unstable confocal resonator CO2 laser for industrial use, the propagation properties and beam quality of the output beam passing through such shaping system are theoretically investigated. The results show that the quality of the shaped solid circular beam is significantly improved, whose 86.5% power content beam parameter product (namely, product of beam waist and far-field divergence) is very close to diffraction-limited.Thirdly, the wide-band beam optimization and control approaches for high-power laser processing are investigated theoretically and experimentally. A novel wide-band shaping parabolic mirror for high power laser processing is presented. With such parabolic mirror the original circular beam can be effectively transformed into the narrow strip structure with uniform intensity distribution, which improves the uniformity of the hardened layer after laser heat treatment. A novel high-power wide-band laser beam shaping approach using a fan-shaped quasi-parabolic mirror is exploringly investigated theoretically and experimentally. By using such an approach, the high-power laser beam broadening with high power density, large size (can be reached to 500mm) and flexible control can be achieved.Fourthly, the high-repetition-rate pulse modulation approach based on rotating polygon for high-power continuous wave CO2 laser is investigated theoretically and experimentally. Starting with the generalized ABCD law, the focusing characteristics of a real beam through the modulating system based on the rotating polygon are investigated theoretically. The results show that, by introducing a precise defocusing, the velocity synchronization between the focal spot and the material to be processed can be realized at each pulse duration. Accordingly micro-holes of nearly circular shape can be obtained on the material surface. On the basis of above theoretical results, our laboratories carry out some experimental studies on multi-heads CO2 laser surface texturing by rotating polygon. Micro-dimples of circular shape and uniform size are obtained on the roll surface. At last, the experiments on CO2 laser perforating of tipping paper based on the optical-chopping polygon are also carried out. Permeability micro-holes of circular shape with uniform diameter are formed on the tipping paper running at high speed, which further demonstrates the correctness of our theoretical results.
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