Modeling instances of partially coherent fields with an arbitrary Wigner distribution function

We introduce a general-purpose numerical algorithm for simulating single-shot realizations of partially coherent electromagnetic radiation, based solely on its known statistical correlations. The algorithm operates by shaping complex Gaussian noise using an arbitrary Wigner distribution function, without assuming factorability in the corresponding Fourier domains. This enables the generation of field realizations for a broad class of sources, including thermal light, synchrotron radiation, and, notably, free-electron laser (FEL) pulses in the linear regime. Compared to Monte Carlo particle-based methods, our approach circumvents the need for detailed modeling of emission mechanisms and offers a substantially more efficient means of generating large ensembles of stochastic fields. As a case study, we simulate FEL pulses with spectrally nontrivial coherence properties (e.g., frequency chirps), thereby demonstrating the versatility of the algorithm. We analytically confirm that ensemble-averaged intensity and correlation properties are correctly reproduced. The algorithm provides a computationally lightweight framework for modeling partially coherent radiation with an arbitrary Wigner distribution function and can serve both as a theoretical tool and as a practical simulation resource for users’ experiments at FELs.