Vortex optical field is widely used in optical communication, particle control, quantum information and other fields due to its special physical structure. Coherence is an important inherent property of the beam, with unique advantages in resistance to speckle noise and atmospheric turbulence disturbance. In this paper, taking the cosine-Gaussian correlation function as an typical example, a mathematical model of the cosine-Gaussian-correlated Schell model vortex (CGCSMV) source is established. Using the extended Huygens-Fresnel integral, and the generalized anisotropic turbulence spectral model, we derive an analytical expression for the far-field cross spectral density function of a CGCSMV beam propagating in anisotropic turbulence. Lastly, we perform numerical simulations of the behaviors of the far-field spectrum of our beam. The results of this paper have some practical reference value for the new optical field regulation, optical communication and lidar system.
Changes in the polarization properties of a spatially and spectrally partially coherent stochastic electromagnetic Gaussian Schell-model (EGSM) ultrashort pulse laser beam propagating through the atmospheric turbulence are investigated. We derive analytic equations for the spectral degree of polarization and the polarization angle in terms of the extended Huygens-Fresnel principle and elements of the 2×2 cross-spectral density function matrix of the electric field. Within the framework of the Tatarskii model of the turbulent atmosphere, which taking the inner scale of the turbulent eddies into consideration, the dependence of along the z-axis and off the z-axis the spectral degree of polarization and the polarization angle of a stochastic EGSM ultrashort pulse laser beam on the parameters of the source including spatial coherence length and temporal coherence length are stressed and illustrated numerically. Results show that the spectral degree of polarization and the polarization angle of the EGSM ultrashort pulse laser beam propagating through the atmospheric turbulence are determined by the parameters of the source. Our results have potential applications in atmospheric remote sensing and ground-to-satellite optical communications.
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