Propagation Of Partially Coherent High Order Gaussian Beam In Inhomogeneous Atmospheric Turbulence

The atmospheric turbulence effect will reduce the beam quality and change the propagation characteristics,when laser beams propagating in the atmospheric turbulence.It seriously restricts many practical applications such as optical communications,laser ranging,atom trapping,and laser weapons.Thus,the studies of the propagation of laser beam in the atmospheric turbulence will be significant.In practical applications,the laser beam propagating along the slant path(the turbulence is named as:inhomogeneous turbulence),and the laser beam outputted by actual high power laser are high order beams and partially coherent beams.Consequently,the researches of the propagation characteristics of partially coherent high order Gaussian beam in inhomogeneous turbulence will be practical significance.The present paper have studied the propagation of partially coherent high order Gaussian beam in inhomogeneous turbulence based on the generalized extended Huygens-Fresnel principle and the second order moments of the Wigner distribution function(WDF).The main contents are list as follows:1.The propagation properties of partially coherent standard Hermite-Gaussian beam(PC-SHGB)and elegant Hermite-Gaussian beam(PC-EHGB)in inhomogeneous atmospheric turbulence have been investigated.The effect of turbulence parameters(zenith angle,inner scale of the turbulence)and beam parameters(coherence width,beam order,wave number and waist width)on the laser beams in inhomogeneous turbulence was analysed numerically.The M~2-factor,the curvature radius and the rms angular width of PC-EHGB and PC-SHGB in inhomogeneous turbulence have been explored comparatively.It is shown that the M~2-factor of PC-EHGB are smaller than that of PC-SHGB in inhomogeneous turbulence,that is to say that PC-EHGB is less affected by turbulence.2.Analytical formulae for the rms spatial width,the rms angular width and the rms M~2-factor of partially coherent standard Laguerre Gaussian beam(PC-SLGB)and partially coherent elegant Laguerre Gaussian beam(PC-ELGB)in inhomogeneous atmospheric turbulence have been derived.The effect of turbulence parameters,beam parameters and propagation distance on the propagation properties of laser beams in inhomogeneous turbulence was explored numerically and comparatively.It is shown that the PC-SLGB is less affected by the turbulence compared with PC-ELGB.3.Analytical propagation formulae for the M~2-factor,the rms spatial width,the rms angular width of Laguerre-Gaussian correlated Schell-model(LGCSM)and Hermite-Gaussian correlated Schell-model(HGCSM)beams propagating through atmospheric turbulence along a slant path are derived.The effect of zenith angle,inner scale of the turbulence,coherence width,beam order,wave number and waist width on the LGCSM and HGCSM beams in inhomogeneous turbulence was studied.It can be found that the LGCSM and HGCSM beams are less affected by inhomogeneous turbulence than a Gaussian beam or a Gaussian Schell-model(GSM)beam.The propagation of laser beam in inhomogeneous turbulence is different from that in homogeneous turbulence.