| For the past few years,the requirements of laser power and beam quality increases and the high-power laser technology has developed rapidly in inertial confinement fusion and laser space-debris cleaning.However,the problem of high-power laser beam propagation through nonlinear will be encountered in generation and applications.When a high-power laser beam propagates in nonlinear media,the nonlinear Kerr effect on the beam propagation characteristics and beam quality is very significant.It is known that the nonlinear Schr?dinger（NLS）equation can be applied to describe the high-power laser beam propagation in nonlinear media,but it is difficult to obtain the analytical solution of NLS equation.On the othe hand,the twist,spatial coherence and astigmatism are also important factors affecting the beam propagation characteristics and beam quality.Therefore,it is of great theoretical and practical significance to study the influence of the twist,spatial coherence and astigmatism on the propagation characteristics and beam quality when a high-power laser beam propgates in nonlinear media.In this thesis,the effects of the twist,spatial coherence and astigmatism on the propagation characteristics and beam quality of high-power laser beams in nonlinear Kerr media are studied by applying appropriate analytical methods.The main research results are summarized as follows:1.Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model（TGSM）beams are studied.The analytical propagation formulae of TGSM beams through nonlinear Kerr media are derived by solving the NLS equation（i.e.,the mean squared beam width,the curvature radius,the spatial coherence width and the twist parameter）.Moreover,the analytical formulas for the M~2-factor,the Rayleigh range,and the far-field divergence angles of the TGSM beam in the nonlinear Kerr media are derived.In addition,we introduce a new complex parameter of the TGSM beam in the nonlinear Kerr medium,and discover the ABCD law is still valid based on the new complex parameter defned.For the beam self-focusing case（i.e.,the beam power greater than the self-focusing critical power）,the focal length analytical formula of focused TGSM beams in self-focusing media is derived,and the effect of the twist on the propagation characteristics of the laser in the nonlinear Kerr medium is studied.It is shown that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model（GSM）beam.Furthermore,the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity.On the other hand,the self-focusing effect（a nonlinear Kerr effect）enhances the beam twist,but degrades the beam spatial coherence.And it has been shown that a laser beam with twist is less affected by atmospheric turbulence than one without twist,and a partially coherent beam is less sensitive to atmospheric turbulence than a fully coherent one.Therefore,this paper draws an important conclusion that a TGSM beam has greater resistance not only to Kerr nonlinearity（i.e.,self-focusing in the atmosphere）but also to atmospheric turbulence than a GSM beam or an ideal Gaussian beam,thus a TGSM beam may have the potential to be used in laser ablation propulsion’s applications in space.2.The propagation characteristics of Gaussian–Schell model beams through optical systems in nonlinear Kerr media are studied.For the beam spreading case,the propagation formulae of Gaussian–Schell model（GSM）beams through general optical systems in Kerr media are derived,and the propagation formulae are more general,which suitable for any general optical system comprising of ideal optical elements.For an ideal thin lens,the formulae of the position and the width of the beam waist,the focal shift and the focal shift maximum of GSM beams through an ideal thin lens in nonlinear Kerr media are derived,and the propagation characteristics of GSM beams through an ideal thin lens in Kerr media are studied.It is found that the width and position of beam waist and focal shift can be controlled by the nonlinear Kerr effect,i.e.,in the self-focusing media,as the beam power increases（the self-focusing effect is stronger）or the spatial coherence increases（the beam coherence is better）,the width of the beam waist decreases,and the distance between the position of the beam waist and the focal plane of lens decreases,and the focal shift decreases.On the other hand,for the beam self-focusing case（i.e.,the beam power greater than the self-focusing critical power）,the analysis formula of the focal length of the focused GSM beam in the self-focused medium is derived.It is shown that not only the size of the focal length,but also the the number of foci can be controlled by the the self-focusing effect.3.The propagation characteristics of focused astigmatic Gaussian beams in Kerr nonlinear media are studied.For the beam spreading case,the formulae of the beam width,the position of the beam waist and the focal shift of focused astigmatic Gaussian beams in Kerr nonlinear media are derived.And the nonlinear Kerr effect on the beam astigmatism and the focal shift of focused astigmatic Gaussian beams are investigated in detail.It is shown that in the self-focusing medium,as the beam power increases（i.e.the self-focusing effect becomes stronger）,the beam astigmatism becomes stronger,but the focal shift decreases.However,in a self-defocusing medium,as the beam power increases（i.e.,the self-defocusing effect becomes stronger）,the beam astigmatism becomes weaker,but the focal shift increases.On the other hand,for the beam self-focusing case,the analytical formula of the self-focusing focal length of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived.And the self-focusing focal length and focus control of focused astigmatic Gaussian beams in the Kerr nonlinear medium are also studied.It is found that both the the size of the focal length and the number of foci can be controlled by applying beam astigmatism. |
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