Study On The Effective Radius Of Curvature Of Laser Beams Propagating Through Atmospheric Turbulent

Abstract:The radius of curvature of light beams is an important parameter of describing the wavefront properties. It is very difficult to study analytically the radius of curvature of light beams because non-Gaussian and nonspherical wavefronts often encounter. On the other hand, High-power laser beams are often with amplitude modulations (AMs) and phase fluctuations (PFs). The array beam has attracted a lot of attention because of the wide applications in many domains, such as high-power laser systems, inertial confinement fusion (ICF), and high energy laser weapon and so on. In this paper, the radius of curvature of the partially coherent array laser beams and laser beams with amplitude modulations and phase fluctuations propagating through atmospheric turbulence are studied analytically by using the effective radius of curvature. The main works in this thesis are summarized as follows:1、The analytical expression for the effective radius of curvature R of rectangular Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the R depends on the strength of turbulence, the beam parameters and the type of beam superposition. The R decreases due to turbulence. However, for the superposition of the intensity R is less sensitive to turbulence than that for the superposition of the cross-spectral density function. In free space R for the superposition of the cross-spectral density function is always larger than that for the superposition of the intensity. However, when the strength of turbulence increases, R for the superposition of the cross-spectral density function may be larger, equal to or even smaller than that for the superposition of the intensity. In addition, the R of GSM array beams with smaller values of the beam coherence parameter and the beam number will less affected by turbulence. The R of GSM array beams is less sensitive to turbulence than that of Gaussian array beams.2、The analytical expression for the effective radius of curvature R of partially coherent Hermite-Gaussian (H-G) array beams propagating through atmospheric turbulence is derived, which can be reduced to several typical cases. In free space, R of Gaussian array beams and Gaussian Schell-model array beams are larger than that of partially coherent H-G array beams, but are more affected by turbulence. In free space, R of a single partially coherent H-G beam is smaller than that of the partially coherent H-G array beam, but is less affected by turbulence. For the superposition of the intensity, the R of fully coherent H-G array beams is larger than that of partially coherent H-G array beams, but is more affected by turbulence. In general, the R is more sensitive to turbulence, if the R is larger in free space. Therefore, the R of laser beams with larger R in free space will become smaller than the R of those with smaller R in free space after a certain propagation distance in turbulence.3、The analytic formula of the effective radius R of curvature of truncated laser beams with AMs and PFs propagating through atmospheric turbulence is derived by using the statistical optics method. It is shown that the R in free space increases with increasing the phase fluctuation parameter, the intensity modulation parameter and the truncated parameter. But the influence of turbulence on the R also increases with increasing the three parameters. The R of Gaussian beams is largest in free space, but it is most affected by turbulence. Therefore, in turbulence the R of truncated laser beams with amplitude modulations and phase fluctuations is even larger than that of Gaussian beams when the propagation distance is large enough. In particular, the relative effective radius Rr of curvature is non-monotonic versus the propagation distance, and there exists a minimum at a propagation distance where the influence of turbulence on the R is largest. In addition, the position where the Rr reaches its minimum increases with increasing the intensity modulation and the phase fluctuation.