Study Of Evolution Properties Of Coherent Vortex In Atmospheric Turbulence

The research subject of singular optics is that optical vortex, wavefront dislocation and wavefront topological structure in the neighborhood of phase singularity. The research scope of singular optics has been extended from fully coherent light to partially coherent light, from single vortex beams to multiple vortex beams, and from free space to atmospheric turbulence and so on in the random mediums. Optical vortex with zero intensity not exists for partially coherent beam in general, however, there exsits the situation that the spectral degree of coherence or mutual coherence function of coherent vortex is zero. The evolution properties of coherent vortex in atmospheric turbulence are characterized by mechanism of production, evolution process and the distance for the conservation of topological charge. The thesis makes theoretical and experimental researches on the interference of vortex beam, respectively, and the evolution properties of coherent vortex in atmospheric turbulence have been studied in theory, whose major contents are as follows:The analytical expressions for the interference intensity of vortex beams with plane wave and spherical wave are derived in theory and used to study the interference of vortex beam, the corresponding relation between topological charge and interference pattern has been obtained, of which has been verified with experiments, and the experimental results and numerical results are practically consistent. It is found that vortex beams with different topological charges correspond to the unique interference pattern, hence this corresponding relation can be used to detect the topological charge of vortex beam.Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of partially coherent sin-Gaussian?Si G? vortex beams and partially coherent Si G non-vortex beams propagating through free space and atmospheric turbulence are derived, and used to study the dynamic evolution behavior of coherent vortices in free space and atmospheric turbulence. According to the creation, the coherent vortices are grouped into three classes: the first is their inherent coherent vortices of the vortex beam, the second is created by the vortex beam itself during transmission process in free space, and the third is created by the atmospheric turbulence inducing the vortex beam.Based on the non-Kolmogorov spectrum, taking the cosh-Gaussian?Ch G? vortex beams as a typical example, the distance for the conservation of topological charge of partially coherent Ch G vortex beams propagating through non-Kolmogorov atmospheric turbulence are studied. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale and the spatial correlation length, the distance for the conservation of topological charge will decrease, whereas the outer scale and the part parameters of hyperbolic cosine has no effect on the distance for the conservation of topological charge.Based on the generalized Huygens-Fresnel principle, the analytical expression for the cross-spectral density function of Gaussian Schell-model?GSM? beams with a coherent vortex dipole?CVD? propagating through atmospheric turbulence is derived, which enables us to study the evolution process of the CVD propagating through atmospheric turbulence, where the influences of the refractive index structure constant, the waist width, the spatial correlation length, the inner scale and the outer scale on the ratio of critical off-axis distance and the waist width are stressed. It shows that the evolution process of CVD depends on the off-axis distance. The larger the off-axis distance is, the larger the number of CVDs is in the far field. When the off-axis distance is zero, the coherent vortex with positive topological charge of a CVD and the coherent vortex with negative topological charge of the CVD propagating through atmospheric turbulence is always symmetrical about P_2y=P_2x When the off-axis distance is big enough, compared with the situation at source plane, the orientation of the positive coherent vortex of inherent CVD and negative coherent vortex of that rotates 180 degrees in the far field. The larger the refractive index structure constant or the waist width and the smaller the spatial correlation length or the inner scale are, the less the ratio of critical off-axis distance and the waist width is, whereas the outer scale has no effect on the ratio.In conclusion, the obtained results enrich the research content of vortex beam, and have been applied in many fields including photon counting, optical data storage, optical tweezers, optical spanner and optical communication, etc.