Spectral invariance and scaling law for nonstationary optical fields

Abstract

We develop a scaling law for a class of statistically nonstationary scalar optical fields, which ensures spectral invariance on their propagation into the far zone of a planar source. The invariance involves the constraint that the normalized far-zone spectrum must be the same in every direction of observation, as well as equal to the normalized area-averaged source spectrum. Thus, it additionally represents an extension of the earlier work by Wolf on stationary fields [Phys. Rev. Lett. 56, 1370 (1986)] that assumed the normalized source spectrum as independent of position. We present examples of both nonstationary and stationary fields that satisfy the scaling law and extended spectral invariance.