Study On Propagation Properties Of Annular Beams

Laser beam characterization, beam propagation and beam quality control are thefundamental research subject in laser optics and laser technology. It can be shownfrom the studies that the M~2-factor and power in the bucket (PIB) are very usefulparameters for characterizing various laser beams. In some practical applications, itcan be used as a useful parameter for beam quality. On the other hand, laser beamsgenerated from high-power lasers usually result in a complex multi-mode structureand exhibit partial coherence because of the high gain, large aperture, amplificationof spontaneous emission, nonlinear optical effects, diffraction of cavity mirrors, aswell as the variation of laser control parameters. Consequently, study on thepropagation properties and beam quality of partially coherent beams would be ofboth theoretical significance and practical interest. Moreover, in many practical casesof the high-power laser, the use of the unstable cavity is an available method toobtain the output laser with high-power and good beam quality. However, the outputlaser of unstable cavity is usually an annular beam in near-field. Thus, it would be ofimportant significance to study the propagation properties of annular beams.The goal of this thesis is to study the propagation properties, the focusingproperties, the beam propagation M~2 factor and PIB of annular beams. The mainresults obtained in this thesis can be summarized as follows:1. By using the treatment of the combination of off-axial Gaussian beams, the model of the annular flattened beams under the cylindrical coordinate system wasproposed. It can be seen that the model proposed in this thesis can describefundamental Gaussian beams, annular Gaussian beams and annular flattenedbeams.2. On the basis of the theory of generalized diffraction integration and the definitionof the generalized second-order moments, the formulae for the M~2-factor and PCBof annular beam and its passing through a spherical aberrant lens, as well as thepartially coherent beam with an axial shadow were given. The effects of theFresnel number, spherical aberration coefficients and the beam orders on the beamquality were discussed in detail.3. Making use of the theory of generalized diffraction integration, the prpagationformula for the annular beams propagating through paraxial ABCD optical systemswere derived. Furthermore, the modified Fresnel number of annular beams wasdefined, and propagation properties of annular beams in free space were analyzed.4. By using the Collins formula, the focusing properties of annular beams byspherical aberrant lens were studied in detail. The effects of the beam orders, thewaist width of off-axial Gaussian beams and the spherical aberration coefficientson the position of real focal point and the maximum axial intensity were analyzedquantitatively.5. Based on the theory of interference, the transformation properties of the laserbeams passing through an axicon has been studied. The experiment was performedand the experimental results were analyzed, showing the consistent with thetheoretical analysis.