Beam Focusing Properties And Beam Shaping

Because of the laser's extensive applications, beam transmission, quality control of the beam and research on the properties of the beam become interesting and necessary in both theory and practice. It is generally believed that the basic properties of the laser are good direction, monochromaticity, high coherence and high brightness. At one time, people attributed the laser beam's good direction to its high coherence, and therefore took series of research on the fully coherent beams. However, in recent years, it is shown that the high coherence is not a requirement for the good direction,the source with partially coherence can also produce the same far-field intensity distribution as a laser. What is more, in practical applications, the partially coherent beams are demonstrated to have advantages over the spatial completely coherent beams for their low sensitivity to speckle and their potential applications in laser fusion etc. It has been demonstrated that partially coherent beams are less affected by the atmospheric turbulence than fully coherent ones. For these reasons, more and more attention has been focused on the focusing properties of the partially coherent beam. Besides, with the developing of the laser technology, beam shaping becomes a hot topic in which people are interested.In this dissertation, the focusing properties of the fully coherent beam and the partially coherent beam are discussed in detail, and beam shaping is also investigated. The research is mainly:1. Based on the Huygens-Fresnel principle, the on-axis irradiance distribution of the axicon illuminated by the spherical wave is derived. The influence of the Fresnel number and the radii of the beam on the focused intensity distribution is analyzed.2. The effective Fresnel number is defined, and the filed behind the cylindrical lens illuminated by plane wave and the focal shifts of the field are studied in a new way. Meanwhile, the conventional numerical calculation is employed to deal with the same problem, and the comparision between these two methods is made.3. According to the generalized Huygens-Fresnel diffraction integral (Collins formula), we derive the propagation expressions of Schell model beams passing through a cylindrical lens with spherical aberration. The influencing factors of the focal shift in the focusing field, such as Fresnel number of the system, the spatial coherent degree of the beam and the spherical aberration of the lens, are also investigated.4. The lens illuminated by partially coherent beams is studied based on the concept of the effective Fresnel number. It is shown that the focal shift in the focused field can be easily expressed as the analytical formulation of the effective Fresnel number. And, we make the comparison between this new method and the conventional numerical calculation derived from Collins formula. 5. We investigate the diffraction field of the focused partially coherent beams diffracted by diffracting screen, and the generalized expression of the effective Fresnel number and the focal shift are achieved. Further more, specified cases are investigated. It is shown that the definition of the effective Fresnel number and the expression of the focal shift are simple and accurate, we can easily get the focal shift of the diffracted field by this new method.6. Based on the generalized Huygens-Fresnel principle (Collins formula), the lens illuminated by a class of partially coherent beams, with special coherent degree, is studied. The bottle beam is achieved in theory, and the influence of the spatial coherent degree, the obstruction ratio and the Fresnel number on the bottle beam is investigated.7. The partially coherent bottle beam is obtained experimentally with two systems respectively: annular diaphragm-lens system and axicon-lens system. A CCD device is employed to record the evolution of the partially coherent bottle beam. And we investigate the size of the patially coherent bottle beams influenced by the parameters of the two systems. Besides, in annular diaphragm-lens system, the partially flat-top beam is achieved, and influence of the system's parameters on the size of the partially flat-top beam is also investigated.8. We present a new approach to the Bessel beam and the system is simple and adjustable, i.e., focusing the laser beam by the lens into the capillary. Moreover, we study on the factors of the system which can affect the Bessel beam.