The relationship between the visibility of fringes and the degree of spatial coherence in electromagnetic two-pinhole interference is assessed. It is demonstrated that the customary definition of the degree of coherence of an electromagnetic field is flawed and a new quantity, free of the formal drawbacks, is introduced. The new definition, which is shown to be consistent with known results for Gaussian statistics, has some unusual properties characteristic only for electromagnetic fields. The degree of coherence is measurable by a sequence of interference experiments.
The concept of polarization freedom is employed to design diffraction gratings that are capable of transforming an electromagnetic plane wave into two or three diffraction orders with an arbitrary efficiency distribution among them, such that the combined efficiency of the signal orders is always equal to 100%. As a special case we consider paraxial-domain duplicators and triplicators with 100% efficiency, which is not possible for illumination by scalar waves: Diffractive elements that are capable of performing the required wave transformation must modulate the state of polarization of the incident field.
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.
We derive a spectral interference law that governs the behavior of the four Stokes parameters in Young's two-pinhole experiment with a random electromagnetic beam. In addition to the visibility of intensity fringes, we introduce three new contrast parameters that describe the interference-induced changes in the field's state of partial polarization. The polarization modulation depends on the electric field correlations at the pinholes and is closely related to the two-point Stokes parameters. The results are expected to be particularly useful in polarization interferometry and electromagnetic coherence theory. The formalism is demonstrated with specific examples.
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.
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