Theory of partially coherent electromagnetic fields in the space–frequency domain

Abstract

We construct the coherent-mode representation for fluctuating, statistically stationary electromagnetic fields. The modes are shown to be spatially fully coherent in the sense of a recently introduced spectral degree of electromagnetic coherence. We also prove that the electric cross-spectral density tensor can be rigorously expressed as a correlation tensor averaged over an appropriate ensemble of strictly monochromatic vectorial wave functions. The formalism is demonstrated for partially polarized, partially coherent Gaussian Schell-model beams, but the theory applies to arbitrary random electromagnetic fields and can find applications in radiation and propagation and in inverse problems.

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

“…The interferometric distributions produced by each polarization component contain half of the total intensity so that q 0 / q 0 = 2 and the upper bound [Eq. (22)] leads to v Յ ͱ 2, which is fully compatible with the maximum visibility of interference fringes v =1.…”

Dimensionality of random light fields

“…The polarization properties of a random light field are in the space-frequency domain described by the spectral polarization matrix [1,2,13,14] (r, ω) = E * (r, ω)E T (r, ω) .…”

Experimental study of the relation between the degrees of coherence in space-time and space-frequency domain

“…For vectorial fields, matrices characterizing the coherence and the polarization properties simultaneously are called the beam coherence polarization (BCP) matrix [14][15][16] and the cross-spectral density (CSD) matrix [17][18][19][20] in the space-time and in the space-frequency domain, respectively. Using these matrices, several studies on various propagation dependent properties have been made in the last decade [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Though these matrices have been proposed nearly one decade back yet the equivalence condition for the elements of these matrices has not been studied till now.…”