Time-dependent physical spectra of Gaussian Schell-model pulses

The time-dependent physical spectra introduced by Eberly and Wódkiewicz J. Opt. Soc. Am. 67 (1977) 1252], observable with a photon-counting detector placed behind a Fabry-Perot filter, are evaluated for a class of temporally partially coherent non-stationary fields known as Gaussian Schell-model plane-wave pulses. Numerical comparisons between source spectra and observed spectra are provided and discussed, and several general features such as initial spectral broadening at the arrival of the pulse and a temporal pulse tail are illustrated. Closed-form approximations are obtained for the time evolution of the observable spectrum by evaluating the leading terms in an appropriate series expansion.