We experimentally generate the Bessel-Gauss coherence functions using the cross-correlations between the two speckle patterns obtained using the perfect optical vortices (POV) of different orders. POV beams are generated using the Fourier transform of Bessel-Gauss beams by displaying the axicon hologram on spatial light modulator. A ground glass plate is used for scattering POV beams and the speckles are recorded. The cross-correlation function of two speckle patterns is Bessel-Gauss functions whose order is given by the difference in the orders of two POV beams used for scattering. The auto-correlation function of these speckles is Bessel-Gauss function of order zero.
We construct a orbital angular momentum (OAM) Poincar´e sphere in which we can represent 2-D superposition
states of arbitrary OAM. In addition, we represent the mixed states of OAM as non separable states inside the
sphere. We also give an experimental set up to generate all points on this sphere.
We have experimentally observed the revival of the dark core in the far field intensity distribution in optical vor tices after scattering through rotating ground glass plate. The diameter and darkness of the core is independent of the speed of the rotating ground glass plate. They depend on the spot size and azimuthal index of the beam incident on it. This shows that the spatial coherence of the scattered light is independent of the speed of the rotating ground glass plate. Our experimental results are in good agreement with the numerical results based on the theory given by Wang, Cai and Korotkova (Opt. Exp. 17, 22366 (2009)).
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