Kerr Effect On Propagation Characteristics Of Hermite-Gaussian Beams

The refractive index of Kerr media will change due to high-power laser beams,and the change of the refractive index in turn affects the beam propagation characteristics.This is called the optical Kerr effect.The Kerr effect is related to the beam field distribution.To study the optical Kerr effect of different laser beams is theoretical and practical interest.One of the high-order mode beams is a Hermit-Gaussian(H-G)beam.The previous studies were limited to the Kerr effect of H-G beams in plasma or nonlocal Kerr media.The Kerr effect of H-G beams in local Kerr media is studied firstly in this thesis.On the other hand,laser ablation propulsion technology has potential applications such as laser space debris removal and launch small satellites to low Earth orbit from the Earth.The atmosphere is a nonlinear Kerr medium.In the application of ground-based laser ablation propulsion technology,the influence of the Kerr self-focusing effect of the atmosphere should be considered.In this thesis,the influence of the Kerr effect on the propagation characteristics of H-G beams is investigated,and the main results are summarized as follows:1.The influence of Kerr effect on the propagation characteristics of H-G beams is studied.Based on the nonlinear Schr?dinger equation,the analytical propagation formulae of the beam width,the curvature radius,the self-focusing critical power,the Rayleigh range and the beam quality factor of H-G beams propagating in Kerr media are derived by using the variational approach.It is demonstrated that the ABCD law is valid if a new complex parameter is adopted,which presents a simple method to study the propagation of H-G beams through an optical system in Kerr media.It is shown that,as the beam order increases,the self-focusing critical power of H-G beams increase and H-G beams are less affected by the Kerr nonlinearity.Finally,it is found that the focus point of H-G beams never appears in self-focusing media,and the focal length is not suitable for characterizing the self-focusing effect of H-G beams.2.The influence of Kerr self-focusing effect on the propagation characteristics of Hermite-Gaussian beams in the inhomogeneous atmosphere is studied.The analytical expression of the beam width during the propagation of the H-G beam from the ground through the atmosphere to space orbit is derived.The analytical expression of beam width was modified by numerical simulation results,and the analytical expression of M~2 factor was further obtained.For the initial H-G beams with the same beam width,as the mode number m increases,the focus shift and the beam width on the target increase.The phase of H-G beams will be distorted due to self-focusing effect of the atmosphere,which results in the change of the far-field profile.It is found that the phase compensation at the initial position can maintain the profile of the H-G beam and reduce the beam width on the target.The results obtained in this thesis are useful for applications of the ground-based laser ablation propulsion technology.