A necessary and sufficient nonnegative definiteness condition for the cross-spectral density matrix (CDM) is derived. It is also shown that this realizability condition allows the expansion of genuine CDMs in terms of recently introduced elementary fields, namely, mean-square coherent beams, and fields with position-independent stochastic behavior. The special case of uniformly polarized electromagnetic Schell-model sources is also analyzed.
© 2009 Optical Society of America
Coherence and Statistical Optics
Original Manuscript: May 14, 2009
Revised Manuscript: July 3, 2009
Manuscript Accepted: July 3, 2009
Published: July 23, 2009
Rosario Martínez-Herrero and Pedro M. Mejías, "Elementary-field expansions of genuine cross-spectral density matrices," Opt. Lett. 34, 2303-2305 (2009)