Effects Of Turbulent Atmosphere Low-order Aberrations On The Focusing Vortex Carrying Gaussian Beam

Because of the turbulent, the merit of the laser beams has been destroyed when propagating in the atmosphere: the beam spreading rapidly, so that using of laser beams in a long distance communication has been limited. So the behaviors of the optical beams propagating in turbulent atmosphere have generated considerable interest in many researchers. We know that when we expect to improve the image resolution and meliorate the quality of the beams by means of optical adaptive technique, we need to know the property of the modulating action of every turbulent aberration on the optical beams. People are trying to find a special beam to diminish the effect of the turbulence. So, it is very significant both in theoretical and in applied to investigate the effects of the low-order turbulent aberrations on the vortex carrying Gaussian beam.In this paper, the normalized averaged intensity distributions, in image plane, of the beam under the tilt aberration, defocus aberration, astigmatism aberration, and total turbulent aberration are compared by numerical calculation, in weak and middle turbulent atmosphere respectively. Fresnel-Kirchhoff diffraction integral equation and Zernike polynomials expansion of the atmospheric aberrations have been used to deduce the theoretical expression. And numerical calculation has been used to study the roles of the three factors: turbulent intensity, propagation distance, and topological charge. The results we have got, which will have some instruction meaning and reference value to the theoretical study and practical applications in free space laser communications.The results show that:1,The effect of the tilt aberration on the intensity distribution of optical vortex beam is the most powerful effect of the three turbulent aberrations. In weak turbulent atmosphere, the tilt aberration is the main effect, the effects of the other two aberrations can be ignored; in middle turbulent atmosphere, the effect of tilt is still most significant.2,In weak turbulent atmosphere, the effects of defocus and astigmatism aberration in turbulent atmosphere on the intensity distribution of a vortex carrying Gaussian beam is so insignificant that can be ignored. However, in middle turbulent atmosphere, the effects of defocus and astigmatism on the intensity distribution in image plane, become pronounced and can't be ignored.3,In middle turbulent atmosphere, for the vortex beams with double topological charges, the modulating action of the astigmatism on the beam is even larger than tilt aberration in the center of the focal plane, eventually forming Gaussian distribution envelope. So astigmatism can be used to control and regulate beam center intensity.4,The three factors, turbulent intensity, propagation distance, and topological charge play very important roles in the influence of the three aberrations. The three factors variation results in the change of the intensity distributions of the beams. Especially for the astigmatism, the influence of the topological charge is very prominent.