Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses

Abstract

The modal theory for spectrally partially coherent nonstationary plane waves is introduced. The theory is first developed in the space-frequency domain and then extended to the space-time domain. Propagation properties of the coherent modes are analyzed. The concept of the overall degree of coherence is extended to the domain of nonstationary fields, and it is shown that the overall degree of coherence of partially coherent plane-wave pulses is the same in the space-frequency and space-time domains. The theory is applied to the recently introduced concept of spectrally Gaussian Schell-model plane-wave pulses.

Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

“…The global degree of coherence for scalar waves [36][37][38][39][40] has been translated to the vectorial case in Ref. 22 in terms of the spatial weighted average of the square of the local degree of coherence for vectorial fields ͑r 1 , r 2 ͒ in Eq.…”

Temporal self-splitting of optical pulses

“…In addition to spatial domain effects, optical pulses with partial spectral or temporal coherence have recently attracted researchers' widespread attention, for their possible applications in optical telecommunication, imaging, and fiber optics [29][30][31][32][33][34][35][36][37][38][39][40][41]. Temporally partially coherent pulse trains are generated by many real sources, such as free-electron and excimer lasers, supercontinuum in microstructured fibers, or random lasers [42], although practical schemes for controlling or modulating the temporal (or spectral) coherence are scarce [43].…”

Propagation of spatial coherence in fast pulses

“…In works on nonstationary fields [6,7,20], the emphasis has been on sources that are spatially fully coherent and of infinite extent. Such sources produce polychromatic plane waves.…”

“…An analysis of such partially spatially coherent sources and the fields they produce cannot be performed by analyzing a single polychromatic plane wave. Other works [20,29] have dealt with spatial correlation functions of nonstationary fields within the context of coherent mode decompositions or the one-dimensional behavior of the twofrequency cross-spectral density function. Here, the propagation of partially spatially coherent cyclostationary statistical quantities is addressed.…”

“…Generalized spectra and cross-spectral densities for a number of classes of nonstationary fields have been defined and investigated [6,20,21]. In many of the experiments described above, the field is made up of a large number of stochastic pulses with a periodic probability density function exhibiting a fixed temporal period.…”