The Influence Of Turbulence On The Beam Spreading And Beam Propagation Factor Of The Partially Coherent Cosh-gaussian Array Beams

The theoretical and experimental study on the laser beams propagating through atmospheric turbulence is of great significance for the applications of laser communications, laser ranging, laser radar, laser weapons, and so on. In recent years, the laser array combining technique has been paid more and more attention for its applications in high-power system, inertial confinement fusion, high-energy weapons, and so on. In practice, partially coherent beams are often encountered. Therefore, it is very meaningful to study the propagation properties of partially coherent array beams in atmospheric turbulence. The influence of turbulence on the spreading and beam propagation factor of the partially coherent and fully coherent cosh-Gaussian(ChG) array beams has been studied in this thesis. The main works are summarized as follows:1. The angular spread and directionality of ChG array beams propagating through atmospheric turbulence are studied. The closed-form expressions for the mean-squared beam width and the angular spread of ChG array beams propagating through atmospheric turbulence are derived by has the same directionality as one single Gaussian beam is given. It is shown that the angular spread of ChG array beams for the coherent combination is smaller than that for the incoherent combination. However, the angular spread of ChG array beams for the incoherent combination is less sensitive to turbulence than that for the coherent combination. In addition, The angular spread of ChG array beams for the coherent combination exists oscillatory behavior with the changes of the decentered parameter, the waist width and the relative separation distance of beams. However, the oscillatory behavior becomes weaker in turbulence. The angular spread of ChG array beams for the incoherent combination is independent of the relative separation distance of beams and the beam number.2. The influence of turbulence on the beam spreading of partially coherent ChG array beams is studied quantitatively by the turbulence distance which represents the distance at which the spreading due to the turbulence accounts for 10% of the cross-sectional area of the beam. Based on the extended Huygens-Fresnel principle, the expression for the turbulence distance of partially coherent ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov's phase structure fuction and integral transform technique. The changes of the turbulence distance versus the spatial power spectrum of the refractive index fluctuations, the beam parameters (i.e., the beam number, the beam coherence parameter, the decentered parameter, the relative separation distance of beams) and the type of the beam superposition (i.e., the superposition of the cross-spectral density function and the superposition of the intensity) are studied in detail. It is showed the turbulence distance of the partially coherent ChG array beams will increase with the the spatial power spectrum of the refractive index fluctuations, but the effect of turbulence on the spreading of partially coherent ChG array beams can be reduced by choosing the suitable beam parameters and the suitable type of the beam superposition.3. The beam propagation factor(M~2-factor)is taken as the characteristic parameter of beam quality, and the M~2-factor of ChG array beams propagating through atmospheric turbulence is studied. The analytical formula for the beam propagation factor (M~2-factor) of ChG array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov's phase structure fuction and integral transform technique, and the influence of turbulence on the M~2-factor is studied by using the relative M~2-factor. It is shown that the M~2-factor is not a propagation invariant in turbulence, and the turbulence results in an increase of the M~2-factor. For the incoherent combination, the M~2-factor of ChG array beams increases with increasing the propagation distance, the beam parameter, the relative beam separation distance and the beam number. For the coherent combination, the M~2-factor of ChG array beams increases with the oscillatory behavior as the beam parameter or the relative beam separation distance increases. For the coherent combination the M~2-factor is always smaller than that for the incoherent combination. However, for the incoherent combination the M~2-factor is always less sensitive to turbulence than that for the coherent combination. In particular, the influence of turbulence on the M~2-factor can be reduced by a suitable choice of the relative beam separation distance. In addition, with increasing the beam number, the M~2-factor is more sensitive to turbulence for the coherent combination, while for the incoherent combination the M~2-factor is less sensitive to turbulence.