We derive two general complementarity relations for the distinguishability and visibility of genuine vector-light quantum fields in double-pinhole photon interference involving polarization modulation. The established framework reveals an intrinsic aspect of wave-particle duality of the photon, not previously reported, thus providing deeper insights into foundational quantum interference physics.

We investigate the structure of second-order correlations in electromagnetic fields produced by statistically stationary, homogeneous, and isotropic current distributions. We show that the coherence properties of such fields within a low-loss or nondissipative medium do not depend on the source characteristics, but are solely determined by the propagation properties, and that the degree of coherence of the field is given by the sinc law. Our analysis reproduces the known results for blackbody fields, but it applies to a wider class of sources, not necessarily in thermal equilibrium. We discuss the physics behind the universal behavior of the correlations by comparing the results with those obtained by an electromagnetic plane-wave model.

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It is known that statistically stationary, homogeneous, and isotropic source distributions generate, in an unbounded low-loss medium, an electromagnetic field whose electric cross-spectral density tensor is proportional to the imaginary part of the infinite-space Green tensor. Using the recently established electromagnetic theory of coherent modes, we construct, in a finite spherical volume, the coherent-mode representation of the random electromagnetic field having this property. The analysis covers the fundamental case of blackbody radiation but is valid more generally; since a thermal equilibrium condition is not invoked, the electromagnetic field may have any spectral distribution. Within the scalar theory of coherent modes, which has been available for more than two decades, the analogous formulation results in the first explicit three-dimensional coherent-mode representation.