Connection of electromagnetic degrees of coherence in space-time and space-frequency domains

Complete coherence of random, nonstationary electromagnetic fields

Despite a wide range of applications, the coherence theory of random, nonstationary (pulsed or otherwise) electromagnetic fields is far from complete. In this work, we show that full coherence of a nonstationary vectorial field at a pair of spatiospectral points is equivalent to the factorization of the cross-spectral density matrix, and full pointwise coherence over a spatial volume and spectral band leads to a factored cross-spectral density throughout the domain. We further show that in the latter case, the time-domain mutual coherence matrix factors in the spatiotemporal variables, and the field is temporally fully coherent throughout the volume. The results of this work justify that certain expressions of random pulsed electromagnetic beams appearing in the literature can be called coherent-mode representations.

Electromagnetic theory of optical coherence [Invited]

The coherence theory of random, vector-valued optical fields has been of great research interest in recent years. In this work we formulate the foundations of electromagnetic coherence theory both in the space-time and space-frequency domains, with particular emphasis on various types of optical interferometry. Analyzing statistically stationary, two-component (paraxial) electric fields in the classical and quantum-optical contexts we show fundamental connections between the conventional (polarization) Stokes parameters and the associated two-point (coherence) Stokes parameters. Measurement of the coherence and polarization properties of random vector beams by nanoparticle scattering and two-photon absorption is also addressed.