Angular dependency of the polarization rotation in a coherent atomic medium

The dependency of polarization rotation with electromagnetically induced transparency (PREIT) in 87Rb vapor on the angular mismatch between the probe and the pump beams has been studied experimentally and theoretically for a V-type configuration. We have observed a nonlinear variation of the PREIT angle with the angular mismatch. The angular mismatch enhanced the residual Doppler broadening effect, as well as diminishes the two photon coherence contribution, in the medium. We have also systematically studied the effect of optical depth (OD) and the pump beam spot size variations to understand how the number of interacting atoms affect the two photon coherence contribution of the polarization rotation. The value of group velocity of the probe beam has been calculated from the experimentally observed spectrum. We have modeled a three-level V-type system to explain the experimentally observed phenomena by considering the effect of OD and spot size with angular mismatch in the medium. We have considered two-dimensional Maxwell-Boltzmann distribution to calculate the susceptibilities for all atoms of all velocity components. The characteristic variation of the angle of PREIT with the angular mismatch matches well with the experimentally observed result.