TWISTED GAUSSIAN SCHELL-MODEL BEAMS .2. SPECTRUM ANALYSIS AND PROPAGATION CHARACTERISTICS

Extending the work of part I of this series [J. Opt. Soc. Am. A 10, 20 08-2016 (1993)], we analyze the structure of the eigenvalue spectrum a s well as the propagation characteristics of the twisted Gaussian Sche ll-model beams. The manner in which the twist phase affects the spectr um, and hence the positivity property of the cross-spectral density, i s brought out. Propagation characteristics of these beams are simply d educed from the elementary properties of their modes. It is shown that the twist phase lifts the degeneracy in the eigenvalue spectrum on th e one hand and acts as incoherence in disguise on the other. An abstra ct Hilbert-space operator corresponding to the cross-spectral density of the twisted Gaussian Schell-model beam is explicitly constructed, b ringing out the useful similarity between these cross-spectral densiti es and quantum-mechanical thermal-state-density operators of isotropic two-dimensional oscillators, with a term proportional to the angular momentum added to the Hamiltonian.