We introduce three-dimensional (3D) stationary, electromagnetic Gaussian Schell-model (GSM) sources in the space-frequency domain and derive the realizability conditions that the source parameters must obey. In particular, we extend to 3D GSM sources two approaches to the realizability conditions presented previously for beam-like GSM sources. The results are of interest in the analysis and synthesis of tunable non-paraxial, partially coherent, partially polarized light fields.

A model for the coherence properties of free-electron lasers (FELs) in time and frequency domains is introduced within the framework of classical second-order coherence theory of nonstationary light. An iterative phase-retrieval algorithm is applied to construct an ensemble of field realizations in both domains, based on single-pulse spectra measured at the Linac Coherent Light Source (LCLS) in self-amplified spontaneous emission mode. Such an ensemble describes the specific FEL pulse train in a statistically averaged sense. Two-time and two-frequency correlation functions are constructed, demonstrating that the hard X-ray free-electron laser at LCLS in this case behaves as a quasistationary source with low spectral and temporal coherence. We also show that the Gaussian Schell model provides a good description of this FEL.

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We investigate the temporal coherence of random, pulsed, quasi-stationary scalar light fields and introduce a new type of expansion for the mutual coherence function in terms of fully coherent frequency-shifted quasi-monochromatic modes of identical shape. The mode representation is valid provided the pulse length is shorter and the coherence time is much shorter than the width of the time window in which the field is considered. The construction of the expansion is particularly straightforward since information is required only on the average spectrum and the average temporal intensity. The method enables us to assess the coherence properties of quasi-stationary light by analyzing the behavior of deterministic quasi-monochromatic fields. The frequency-domain counterpart of the representation is also given. The method is illustrated by application to a pulsed free-electron laser source.

We present a novel time-domain coherent-mode representation for random, stationary electromagnetic beams. We subsequently introduce random, quasistationary pulsed electromagnetic beams and develop an analogous (pseudo) mode decomposition for them as well. The former decomposition is valid provided the time window in which the field is considered is much longer than the coherence time, while the latter requires the field to vanish outside the window. For stationary beams, the theory is demonstrated by an example illustrating the role of polarization in the representation. In both cases, the data needed for the construction of the mode decomposition are straightforward to measure. The formalisms enable us to treat random vector-light beams in the time domain in terms of deterministic fields. We expect that the modal representations will find a wide range of applications in problems involving spatiotemporal propagation of temporally partially coherent light in optical systems.