Study On Propagation Characteristics Of Partially Coherent Anomalous Hollow Gaussian Beam Propagating Through Turbulent Atmosphere

Laser beams propagation in the atmospheric turbulence affected by turbulence will bring about the turbulence effects of spatial spread,angle spread,beam wander and so on.The laser beams applications in fields such as laser radar,laser remote sensing,free space laser communication and laser ranging are severely restricted by turbulence.Recently,propagation characteristics of partially coherent beams propagating through atmospheric turbulence are studied deeply.The anomalous hollow Gaussian beam is a unique model system for studying the transverse instabilities,in particular,the interplay of the wake field and the lattice nonlinearity.In addition,the anomalous hollow Gaussian beam can be used as a powerful tool to study the linear and nonlinear particle dynamics in the storage ring.Consequently,it is more significant to study the propagation characteristics of partially coherent anomalous hollow Gaussian beam propagating through atmospheric turbulence.This article is specified in the following aspects:Based on the generalized extended Huygens-Fresnel principle and the Wigner distribution function(WDF),analytical formulae of the root-mean-square(rms)angular width and propagation factor(M~2-factor)of partially coherent anomalous elliptical hollow Gaussian beam(PCAEHGB)propagating through atmospheric turbulence are derived.The influence of the inner scale of turbulence,the zenith angle,the beam waist,transverse coherence length and wavelength on the rms angular width and M~2-factor are analyzed.The comparison between the propagation characteristics of PCAEHGB propagating through atmospheric turbulence along a slant path and along a horizontal path.Numerical results show that the effect of turbulence on the rms angular width and M~2-factor becomes gradually weak as the vertical height increases for PCAEHGB propagating through atmospheric turbulence along a slant path.Based on non-Kolmogorov spectrum and the theory of second moments,the general analytical expression of beam wander of PCAEHGB and partially coherent hollow Gaussian beam(PCHGB)in non-Kolmogorov turbulence is derived.The results indicate that beam wander depends on the turbulence parameters including the generalized exponent parameter,the generalized refractive index structure parameter,inner scale of turbulence,outer scale of turbulence,and the initial second moments of the laser beam at the input plane.The rms beam wander and relative beam wander are simulated numerically.The results show that PCAEHGB is less affected by turbulence than Gaussian-Schell model beam(GSMB)is.The K parameter and correlation factor(C~4-factor)of PCAEHGB propagating through atmospheric turbulence is derived based on second-order and fourth-order moments.It is shown that the K parameter and C~4-factor in turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities.Moreover,the influence of the generalized refractive index structure parameter,inner scale,the beam waist sizes and transverse coherence length on K parameter,the relative K parameter and C~4-factor of PCAHG beam in turbulent atmosphere are discussed in detail.The results show that the K parameter of PCAEHGB tends to be 2 when the propagation distance is long enough.