Reduction formula for cross-spectral purity of nonstationary light fields

We examine cross-spectral purity of random, nonstationary (pulsed), scalar light fields with arbitrary spectral bandwidth. In particular, we derive a reduction formula in terms of time-integrated coherence functions, which ensures cross-spectral purity of interfering fields having identical normalized spectra. We further introduce fields that are cross-spectrally pure in either a global or local sense. Our analysis is based on an ideal field superposition realizable with all-reflective wavefront-shearing interferometers. Such devices avoid certain problems related to Young's interferometer, which is the framework customarily employed in assessing cross-spectral purity. We show that any partially coherent beam can be transformed into a locally cross-spectrally pure beam whose cross-spectral density is specular. On the other hand, lack of space-frequency (and space-time) coupling ensures cross-spectral purity in the global sense, i.e., across an entire transverse plane, regardless of the spectral bandwidth or the temporal shape of the pulses. & COPY; 2023 Optica Publishing Group

Automated summary

This paper examines the cross-spectral purity of random and nonstationary scalar light fields with arbitrary spectral bandwidth. It introduces a reduction formula based on time-integrated coherence functions to ensure cross-spectral purity of interfering fields with identical normalized spectra. The analysis is conducted using all-reflective wavefront-shearing interferometers, which overcome problems associated with Young's interferometer commonly used to assess cross-spectral purity. The study demonstrates that any partially coherent beam can be transformed into a locally cross-spectrally pure beam with specular cross-spectral density, while lack of space-frequency coupling ensures cross-spectral purity in the global sense across an entire transverse plane, irrespective of spectral bandwidth or pulse shape.