Very good approximations to many optical fields are provided by free fields, i.e., fields that do not contain any evanescent waves. New conservation laws are derived for partially coherent fields of this kind, propagating into a half-space. It is found that the cross-spectral density, integrated over either the average or the difference of spatial coordinates in any cross section of the field, is invariant on propagation. It is also shown that, as a consequence of these conservation laws, both the spectrum and the so-called antispectrum of the field, integrated over cross-sectional planes, are conserved. The new conservation laws are illustrated by application to Gaussian Schell-model beams.
© 1993 Optical Society of America
Original Manuscript: March 27, 1992
Manuscript Accepted: July 23, 1992
Published: January 1, 1993
Marek W. Kowarz and Emil Wolf, "Conservation laws for partially coherent free fields," J. Opt. Soc. Am. A 10, 88-94 (1993)