Vortices of light and their interaction with matter

Optical vortices are singularities in the phase distribution of a light field. At the phase singularity, real and imaginary parts of the field vanish simultaneously and associated wavefront becomes helical. For an optical vortex of topological charge l, there are l number of helical windings in a given wavelength of light and it carries an orbital angular momentum of l~ per photon. This dissertation concerns with the study of interaction of optical vortices with matter namely nonlinear optical crystal -Barium Borate (BBO) and Bose-Einstein condensate. A new method to determine the order of optical vortex from just the intensity distribution of a vortex has been discussed. We show that the number of dark rings in the Fourier transform (FT) of the intensity can provide us the order. To magnify the effect of FT, we have used the orthogonality of Laguerre polynomials. We have studied the interaction of optical vortices with BBO crystal. The spatial-distribution of degenerate spontaneous parametric down-converted (SPDC) photon pairs produced by pumping type-I BBO crystal with optical vortices has been discussed. For a Gaussian pump beam, we observe a linear increase in thickness of the SPDC ring with pump size. On the other hand, the SPDC ring due to optical vortex forms two concentric bright rings with an intensity minimum in the middle. We also observe that if the beam size is lower than a particular value for a given topological charge l of the vortex, then there will be no change in full-width at half maximum of the rings formed by down-converted photons. We have experimentally varied the quantum inspired optical entanglement for classical optical vortex beams. The extent of violation of Bell's inequality or continuous variables written in terms of the WDF increases with the increase in their topological charge. To obtain this, we have used the FT of two-point correlation function that provides us the WDF of such beams. Quantum elliptic vortex (QEV) is generated by coupling two squeezed vacuum modes with a beam splitter (BS). The Wigner distribution function (WDF) has been used to study the properties of this quantum state. We also study how this coupling could be used to generate controlled entanglement for the application towards quantum computation and quantum information. We observe a critical point above which the increase in vortices decreases the entanglement. We have also studied the annihilation of vortex dipoles in Bose-Einstein condensates. To analyze this, we consider a model system where the vortexantivortex pair and gray soliton generated by annihilation of vortex dipoles are static and the system could be studied within Thomas-Fermi (TF) approximation. It is observed that the vortex dipole annihilation is critically dependent on the initial conditions for their nucleation. Noise, thermal actuations and dissipation destroy the superflow reflection symmetry around the vortex and antivortex pair. It is note worthy that some of our theoretical results have already been verified experimentally.by Shashi PrabhakarPh.D