Beating is a simple physical phenomenon known for long in the context of sound waves but remained surprisingly unexplored for light waves. When two monochromatic optical beams of different frequencies and states of polarization interfere, the polarization state of the superposition field exhibits temporal periodic variation-polarization beating. In this work, we reveal a foundational and elegant phase structure underlying such polarization beating. We show that the phase difference over a single beating period decomposes into the Pancharatnam-Berry geometric phase and a dynamical phase of which the former depends exclusively on the intensities and polarization states of the interfering beams whereas the sum of the phases is determined solely by the beam frequencies. Varying the intensity and polarization characteristics of the beams, the relative contributions of the geometric and dynamical phases can be adjusted. The geometric phase inherent in polarization beating is governed by a compact expression containing only the Stokes parameters of the interfering waves and can alternatively be obtained from the individual beam intensities and the amplitude of the intensity beats. We demonstrate both approaches experimentally by using an interferometer with a fast detector and a specific polarimetric arrangement. Polarization beating has a unique character that the geometric and dynamical phases are entangled, i.e. variation in one unavoidably leads to a change in the other. Our work expands geometric phases into a new domain and offers important novel insight into the role of polarization in interference of electromagnetic waves.

We introduce an interferometric interpretation for the degree of polarization as a quantity characterizing the ability of a light beam to generate polarization modulation when it interferes with itself. The result is confirmed experimentally in Youngʼs interferometer with beams of controlled degree of polarization and by comparing to a standard polarimetric measurement. The new interpretation is a consequence of the electromagnetic interference law that we formulate for stationary, quasi-monochromatic, partially polarized light beams in time domain. Our work provides fundamental insight into the role of polarization in electromagnetic coherence and interference.

We show theoretically that the (spectral) electromagnetic degree of spatial coherence of a random, stationary light beam can be measured by using two dipolar nanoscatterers instead of aperture diffraction as in traditional Young's interferometer. The method is based on considering individually the correlation functions associated with the six polarization states that make up the coherence (two-point) Stokes parameters and observing separately the visibilities and the locations of the intensity fringes created by the interfering dipole fields, leading to a complete characterization of the beam's second-order spatial coherence. The novel technique, although introduced in this work for beams, paves the way toward the detection of spatial coherence in nonparaxial optical near-fields for which the use of nanoscatterers is necessary.

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