| Inertial Confinement Fusion (ICF) is important research field of today, which has an important scientific significance and application value in developing the new energy resource in the next century. The work presented in this paper is tightly connected with ICF.In chapter 1, we retrospect the development of ICF and an introduction about the facility of ICF is given. The prameters applied to describe the beam quality and the demand of beam quality in ICF are also presented. In chapter 2, attention is focused on the intensity moments of the HChG laser beams from the zero-order to the fourth-order. The frequently used parameters such as the power in bucket (PIB), the beam width, the curvature radius, the far field divergence, the M2-factor, the Rayleigh length and the kurtosis are calculated in term of the intensity moments. In addition, the center of the gravity of the radiation field and the symmetry are discussed along with the propagation axis. Finally, the power fraction within the beam width defined by the second moments, is illustrated with numerical method. Futhermore, we have two questions about "the Propagation properties of Hermite-cosh-Gaussian laser beams" in Optics Communications 186 (2000). One is the Eq. (16) in Ref. [29] and its consequent derivation. The other is the method applied to generate the Hermite-Cosh-Gaussian (HChG) beams. Some modified equations are presented[21]. In chapter 3, The elegant Hermite-cosh-Gaussian beams as another special case in Hermite-sinusodiol-Gaussian family is introduced and its propagation properties through a first-order optical ABCD system are investigated. An analytical solution of the elegant Herimite-cosh-Gaussian beam propagating through a first-order ABCD system is derived, and correspondingly, the closed-form M2-factor, the beam width, the curvature radius and the power in bucket are presented analytically. The numerical investigations are carried out and show that the M2-factor of elegant Hermite-cosh-Gaussian beam is greater than that of elegant Hermite-Gaussian beams and less than that of Hermite-Gaussian beams approximately. In chapter 4, the algorithm of propagation and optical components are given. The construction and the interface of procedure presented.By the technique of object-oriented system analysis and design, the practical program for simulating the properties of high power laser was developed. |