Research On The Algorithm Of Laser Beam Propagation

The nuclear energy to be made from Inertial Confinement Fusion (ICF) is very important in the near further. The research of ICF has been carrying on several decades in several major countries for its importance both in the science and in the economics. This paper is about the numerical simulation that has some relationships with ICF in our country. It is arranged as follows.In chapter 1, a review of ICF development is given. The driver structure of ICF and the requirements for the laser beam used in ICF are listed in that following. The parameters applied to describe the beam quality are also presented.In chapter 2, the first and the second section give explicit explanations of how to use Split-Step Fourier Transformation (SSFT) algorithm and Finite-Difference Methods to solve nonlinear equation. A code table, in which a list of normalized transmission formula is included, is given to facilitate programming. In section 3, a new algorithm is given to simulate the propagation of focused beam. The traditional beam propagation algorithm based on Fast Fourier Transform fails to give right results due to the limitation of the sampling theorem. A new algorithm is then derived, in which the factor of spherical wave front is removed explicitly. Thus the propagation of a focused beam could be evaluated indirectly from propagation of an unfocused beam. The results in two cases are connected inherently by Fresnel number, which plays a key role in focused beam propagation.In chapter 3, by using theoretic analysis the focusing properties of an ideal annular beam is demonstrated. The intensity distribution near the focal point is given explicitly to show the influence of the ratio of inner to outer radius. A practical soft-edge annular beam is also studied numerically and the similar properties are obtained t6 confirm our analysis.In Chapter 4, with the help of the Fast Fourier Transform (FFT) method, a formula is given to study the pulsed spherical beams with the arbitrary cross section propagating in free space. As an application, a theoretical calculation of convergent isodiffracting pulsed spherical beam propagation with Poisson spectrum is presented. Simulation is also shown to illustrate the influence of diffraction length and focal length to spherical wave front.The results of this thesis can be generalized as following:1. A code table is given to facilitate programming, in which a list of normalized transmission formula is included.2. A new algorithm is derived to simulate the propagation of focused beam.3. The focusing properties of an annular beam are demonstrated, which give guidancefor some design in ICF driver structure.4. A formula based on FFT is given to study the pulsed spherical beams propagating in free space with the arbitrary cross section.