Beam Quality Degradation During Far-field Focusing Of Laser Beams And Improvement Based On Phase Retrieval

Attention has been given to research on the focused laser beams, since the high energy concentration are required in the most applications of laser beams. Research on laser beam focusing is particularly significant for laser transmitter and beam control.We examine the beam quality degradation during far-field focusing of laser beams and improvement based on phase retrieval in this dissertation, and the relevant work is outlined as follows.1. Based on the Huygens–Fresnel diffraction integral and Bessel functions, an expression of the amplitude distribution for a Gaussian beam diffracted by a circular aperture and focused by a lens is derived. The effect of the aperture-lens separation on the focal shift and beam quality degradation is obtained, and the influence of the truncation parameter and Fresnel number on the focal shift and beam quality degradation is also presented.2. Based on the generalized Huygens–Fresnel diffraction integral(Collins’ formula), the propagation equation of Hermite–Gauss beams through a complex optical system with a limiting aperture is derived. The elements of the optical system may be all those characterized by ray-transfer matrices, as well as any kind of apertures that can be represented by complex transmittance functions. To obtain the analytical expression, we expand the aperture transmittance function into a finite sum of complex Gaussian functions. Thus the limiting aperture is expressed as a superposition of a series of Gaussian-shaped limiting apertures. The advantage of this treatment is that we can treat almost all kinds of apertures in theory. As application, we define the width of the beam and the focal plane using an encircled-energy criterion and obtain the focal shift and beam quality degradation of Hermite–Gauss beams passing through a circular aperture subsequently focused by a lens.3. The experiment to study the diffraction of a Gaussian beam passing through a circular aperture subsequently focused by a lens is carried out. The diffraction patterns in various planes perpendicular to the axis are recorded by a laser beam profile analyzer. All the experimental results are compared with theoretical predictions, and close agreement between them is obtained.4. By the use of beam width based on second-order moment and power in the bucket(PIB), the influence of atmospheric turbulence on the far-field beam quality of laser beams is investigated. Detailed calculation is also performed.5. The wavefront distortion correction system based on encircled-energy metric optimization is designed and established to improve laser beam quality at the receiver plane. In the wavefront distortion correction system, the Parallel Stochastic Perturbative Gradient Descent(SPGD) algorithm is utilized to change the phase distribution of laser beam by the use of deformable mirror. By means of encircled-energy metric optimization based on SPGD algorithm, beam quality is improved to meet the requriements of practical applications.