Twisted Gaussian Schell-model beams II Spectrum analysis and propagation characteristics

Abstract

Extending the work of part I of this series [ J. Opt. Soc. Am. A10, 2008– 2016 ( 1993)], we analyze the structure of the eigenvalue spectrum as well as the propagation characteristics of the twisted Gaussian Schell-model beams. The manner in which the twist phase affects the spectrum, and hence the positivity property of the cross-spectral density, is brought out. Propagation characteristics of these beams are simply deduced from the elementary properties of their modes. It is shown that the twist phase lifts the degeneracy in the eigenvalue spectrum on the one hand and acts as incoherence in disguise on the other. An abstract Hilbert-space operator corresponding to the cross-spectral density of the twisted Gaussian Schell-modelbeam is explicitly constructed, bringing out the useful similarity between these cross-spectral densities and quantum-mechanical thermal-state-density operators of isotropic two-dimensional oscillators, with a term proportional to the angular momentum added to the Hamiltonian.