Theory of spatially and spectrally partially coherent pulses

Abstract

A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space-frequency domain and in the space-time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space-frequency domain is considered and their coherent-mode representation is presented.

Optical interferometry with pulsed fields

“…This result differs from other reported works [17][18][19] in that the whole train of pulses is considered rather than assuming that each pulse is incoherent with all other pulses. The spectral density [19] of the pulsed beam as a function of frequency and position is defined to be…”

“…The theoretical study of non-stationary statistical optics, applied to pulse trains, has seen a recent resurgence [17][18][19][20]. In the model presented in these references, a restricted class of non-stationary fields is considered in which a stationary field is modulated in a deterministic fashion -this is known as an intrinsically stationary model [21].…”

Statistical properties of a free-electron laser revealed by Hanbury Brown–Twiss interferometry

“…To describe FEL statistical pulse properties with a simple model we considered that the FEL beam spectral crosscorrelation function can be characterized in the framework of the Gaussian Schell model (GSM) [48] …”

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.…”