Study On The Partially Coherent Array Beams Propagating Through Atmospheric Turbulence

Laser array beams have been attracted much attention because of their wide applications in high-power system, inertial confinement fusion and high-energy weapons, and so on. On the other hand, the propagation of laser beams in atmospheric turbulence is a topic that has been of considerable theoretical and practical interest. In practice, a partially coherent and high order mode laser beams is often encountered. In practice, partially coherent and high order mode laser beams are often encountered. Therefore, it is very important to study the propagation properties of partially coherent and high order mode laser beams through atmospheric turbulence. The main works in this thesis are summarized as follows:(1) The Rayleigh range and the M2-factor are taken as the characteristic parameters of beam quality, and the beam quality of radial Gaussian Schell-model (GSM) array beams is studied in detail. The analytical expressions for the Rayleigh range and the M2-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function the radial GSM array beam has zR that is longer and has the M2-factor that is lower than that for the superposition of the intensity. As compared to a single GSM beam centered at the origin, the radial GSM array beam has the longer non-spreading distance, but has the higher M2-factor.(2) The influence of atmospheric turbulence on the propagation of superimposed partially coherent Hermite-Gaussian (H-G) beams is studied in detail. The closed-form propagation equation of superimposed partially coherent H-G beams through atmospheric turbulence is derived. It is shown that the turbulence results in a beam spreading and a decrease of the maximum intensity. However, the larger the beam number, the beam order, the separate distance, and the smaller the beam correlation length are, the less the power focusability of superimposed partially coherent H-G beams is affected by the turbulence.(3) The angular spread(θsp) and directionality of array beams propagating through atmospheric turbulence are studied in detail. The analytical expressions for the mean-squared beam width and the angular spread of the GSM array beam and partially coherent H-G array beam in turbulence are derived. It is shown that for superposition of the cross-spectral density function,θsp of the array beams with smaller coherence length, waist width, beam number and larger separation distances is less sensitive to the effects of turbulence than those with larger coherence length, waist width, beam number and smaller radial radius. On the other hand, under certain conditions, partially coherent H-G array beams may generate the same directionality as a Gaussian laser beam in free space and also in turbulence. However, the directionality of H-G array beams in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but both may be consistent in atmospheric turbulence.(4) The effect of turbulence on the spreading of radial Gaussian Schell-model (GSM) array beams is studied quantitatively by the turbulence distance zT. The analytical expression for the turbulence distance zT of radial GSM array beams is derived. The results obtained in this paper will be useful for choosing the suitable array beam parameters and the type of the superposition in order to reduce the effect of turbulence on the spreading of radial GSM array beams in practice.