Abstract

Excellent approximations to many optical fields are provided by free fields, i.e., fields in which contributions from evanescent waves are neglected. In this paper, we show that certain conservation laws hold for fields of this kind, which in some respects resemble the usual energy conservation laws. In particular we find that the field spectrum, integrated over a cross-section perpendicular to any chosen direction, is invariant on propagation. Similar results hold for the Wigner form of the cross-spectral density. These conservation laws provide insight and simple solutions to some inverse problems for partially coherent fields. As an example, we show that they may be used to determine the normalized spectrum of a planar, secondary source from the knowledge of the field spectrum in a plane parallel to the source plane. We also show that the new conservation laws make it possible to determine the cross-spectral density of a quasihomogeneous source from the knowledge of the cross-spectral density of the field at all pairs of points in any plane parallel to the source plane.

© 1991 Optical Society of America