Studies On The Phase Singularities And Vortices Of Optical Fields Propagating In Turbulent Atmosphere

When a laser beam propagates through the turbulent atmosphere, the random variations will be produced in its amplitude and phase. The intensity fluctuations and phase distortions will be induced at the observation plane. In the presence of strong turbulence effect, the amplitude fluctuations are significant, and at some points where zeros in the amplitude occur, the phase of the distorted optical field will be undefined. Such points are often called phase singularities.When many phase singularities are present, they will bring great difficulties for measuring and correcting the distorted wave front in classical adaptive optics systems, which is a big challenge to the engineering application of astronomical observation, optical communication, the laser weapon and so on. So it is necessary to investigate the evolution properties of phase singularities in order to improve the performance of adaptive optics system when the laser beam propagates through the turbulent atmosphere.The optical vortex beam which possesses an intensity null and phase singularities in its core propagating through the turbulent atmosphere has become a very lively object of attention for scientific research and technical application. In general, for optical vortex beams traveling through the turbulent atmosphere, intensity fluctuations and spread of the radiation pattern will also be induced. The position wander of the optical vortex will be produced, too. In addition, the topological charge of the vortex beam is a robust quantity and can be transmitted without loss over significant distances in the atmosphere and therefore it could be used as an information carrier in optical communication. So the studies on the intensity distribution and beam spread of the optical vortex beam, and the evolution properties of optical vortices in atmospheric turbulence are necessary in optical communication.In this thesis, the contents mentioned above are investigated by four-dimension code of laser beam propagating in atmosphere and the main points and conclusions are as follow:1. The variation of phase singularities in turbulence is computed when a laser beam propagates through the turbulent atmosphere. The results indicate that, the phase singularities created close together in pairs of opposite polarity by turbulence. Phase singularities are moving with the movement of light wave in the space. Atmospherically created phase singularity pairs separate and drift apart as they propagate. The distance and the relative position between paired phase singularities will be changed. The phase singularities will also be annihilated in pairs.2. The relationships between the density of phase singularities and the characteristic parameters of turbulence effect are calculated when the laser beam propagates through the turbulence by the horizontal path. The parameters include the propagation distance,turbulence strength, wavelength, the inner scale and the outer scale of turbulence. The results show that the density of phase singularities increases with the propagation distance and strength of turbulence increase, respectively. But the density of phase singularities decreases with the inner scale of turbulence and the wavelength increase, respectively. It seems that the density of phase singularities has nothing to do with the outer scale of turbulence.3. Mainly two categories of propagation events are explored by numerical experiments about the density of phase singularities for the laser beams propagating in the atmospheric turbulence with horizontal path. In one category the laser beam propagates in weak atmospheric turbulence but long propagating length. In the other the turbulence is stronger but propagating length is shorter. The results indicate that the influence of turbulence strength on the density of phase singularities is greater than the propagation distance. Under different categories of propagation events, the relationships between the density of phase singularities and the Rytov index are different. In addition, a statistical model which is called Logistic model is found out to describe the density of phase singularities when the laser beams propagating in the atmospheric turbulence with horizontal path.4. Evolution of phase singularities density in distorted optical field is studied when laser beams propagate through turbulent atmosphere along an uplink path. Two categories of propagation events are mainly explored for the same propagation height: fixed wavelength with change of the turbulence strength and fixed turbulence strength with change of the wavelength. The results for the density of phase singularities reveal that the evolution could be divided into four interesting regions with the increase of the propagation height. When the beam propagates to a certain height, the density of phase singularities reaches its maximum and such a height changes with the turbulence strength but nearly remains constant with different wavelengths. In addition, a fitted formula describing the relationship between the density of phase singularities and propagation height with different turbulence strength and wavelength is found out. And the formula is very similar to the formula used for describing the Blackbody radiation in physics.5. The behavior of the phase singularities density in distorted optical field is investigated when laser beams propagate through turbulent atmosphere along a slant path. It is found that the behavior of the phase singularities density in a slant path is similar to that in an uplink path.Under the same propagating parameters of the refractive index structure parameter at the ground level and the propagation distance, the lager zenith angle is taken, the bigger of the phase singularities density will be generated. When the beam propagates to a certain distance, the density of phase singularities reaches its maximum and such a distance changes with the zenith angle. The smaller the zenith angle is taken, the shorter of the propagation distance where the density of phase singularities reaches its maximum will be.Under the same zenith angle and the propagation distance, the stronger refractive index structure parameter at the ground level is taken, the bigger of the phase singularities density will be generated and the maximum of the density of phase singularities will be larger.6. The evolution of phase singularities density in distorted optical field is studied when laser beams propagate through turbulent atmosphere along a downlink path. It is shown that if the light source is higher above the ground level, the phase singularities begin to create at a higher altitude and the density of phase singularities in distorted optical field is bigger near the ground. The functional form of the phase singularities density has a shape of monotone increasing cure with the decrease of the propagation height and reaches its maximum near the ground.7. The spatial distribution of the mean intensity in a cross-section normal to the optical radiation propagation of a Laguerre-Gaussian(LG) vortex beam in turbulent atmosphere is simulated. The computational results indicate that the beam profile successively changes from an annular structure to a flattened-top profile and finally to a Gaussian profile with the propagation. The process is closely relate with the propagation distance, the turbulence strength, the outer scale of turbulence, the topological charge, the width of beam’s waist and the wavelength of the vortex beam. However, the process of intensity variation has nothing to do with the inner scale of turbulence. Calculations also show that the shape stability decreases with the propagation distance, turbulence strength, and the outer scale of turbulence increase for a fixed LG vortex beam propagating in the turbulent atmosphere.With an increase in the topological charge, the narrow width of beam’s waist, and the long wavelength, the shape stability increases for different vortex beams propagating in the fixed turbulent atmosphere.8. Some results about the vortex beams broadening obtained by numerical modeling using four-dimension code when the vortex beams propagating through the turbulent atmosphere under different conditions. The results indicate that if the propagation distance is longer or the turbulence is stronger, the beam broadened by the turbulence will be more severe. And if the topological charge is higher, or the beam’s waist width is narrower, or the wavelength is longer, the beam broadened by the turbulence will be smaller. Though the inner scale and the outer scale of turbulence have an effect on the beam broadening, the influence of them is relatively weak. In addition, the broadening of vortex beams and fundamental Gauss beam through the turbulent atmosphere are studied numerically and comparatively. The result demonstrates that the beam broadening for a fundamental Gauss beam is always more than for vortex beams.9. Analyze the properties of the algebraic sum of the topological charges of all the phase singularities(abbreviated AS-PS) on a transverse plane and found that the AS-PS is approximately equal to the topological charges of the input beam. Propose a method for determining the topological charges of the vortex beam propagating through the atmospheric turbulence based on the AS-PS. The method could be able to eliminate the influence of the local turbulence more effectively and thus diminish the fluctuation of the determined topological charge values. Investigate the influence of the propagation distance,the turbulence strength, the topological charge of the input beam and the testing size of the receiver aperture on the AS-PS determination. The results indicate that, the shorter propagation distance, the weaker turbulence strength, the lower topological charge, the moderate source size for the input vortex beam, the suitable testing size which is approximately equal to the spot size of the vortex beam at receiver plane may be a good choice for the purpose of a low increase of the tested deviation with propagation. The result of the testing size provides a quantitative guideline for the design of an optimal detector of topological charge.10. The wandering behavior of optical vortices with the topological charge +1 or-1 on propagation through atmospheric turbulence is studied. The occurrence number of the optical vortex position on a transverse plane in the atmosphere is formulated. The results shown that the occurrence number on the receiver plane is Gaussian random variables,which means that the probability of vortex position on receiver plane center is the maximum. As the propagation distance, turbulence strength, or the topological charges increase, Gaussian fitting curves become broader, and the statistics of vortex position becomes to random distribution. In addition, choosing the suitable width of the input beam could induce the wander of the optical vortex. The results maybe have potential application in optical vortex communication.11. The propagation characteristics of nondiffracting Bessel beams travelling in turbulent atmosphere are preliminarily investigated. The beam-width spreadings and the densities of phase singularities of zero-order Bessel beam, zero-order Bessel-Gaussian beam and higher-order Bessel-Gaussian beam(Bessel-Gaussian vortex beam) are studied comparatively. The results indicate that the higher-order Bessel-Gaussian beam broadened is slighter by turbulence and optical vortices from the input vortex beam are not impacted under some conditions. So the nondiffracting Bessel vortex beams are more applicable in free space communication.