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Visibility parameters in Young's interference experiment with unpolarized light

Philippe Réfrégier, Antoine Roueff, Jani Tervo

Published Oct 1, 2007• 0 citations
OpenAlex

Abstract

We analyze the recently introduced Polarization contrast parameters and their relation to degrees of coherence in electromagnetic Young's interference experiment in the case of unpolarized illumination. We show that in the general case only two of the parameters can be made non-vanishing if suitable unitary transformations are applied to the field at pinholes. The result implies elegant relations between the contrast parameters and the intrinsic degrees of coherence in the case of unpolarized light at pinholes.

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We analyze the recently introduced Polarization contrast parameters and their relation to degrees of coherence in electromagnetic Young's interference experiment in the case of unpolarized illumination. We show that in the general case only two of the parameters can be made non-vanishing if suitable unitary transformations are applied to the field at pinholes. The result implies elegant relations between the contrast parameters and the intrinsic degrees of coherence in the case of unpolarized light at pinholes.
An electromagnetic Young's interference experiment is considered with arbitrary, spectrally partially coherent and partially polarized electric fields at the pinholes. Any correlations that exist at the openings lead to modulations of the Stokes parameters on the observation screen. The electromagnetic degree of coherence can be viewed, in direct analogy to the usual scalar case, as a measure of the modulation contrasts of not just the optical intensity but also the polarization state. The electromagnetic degree of coherence can be obtained experimentally via four visibility measurements using appropriate wave plates. If the field at the pinholes is fully polarized, a periodic variation of the polarization state appears on the observation screen, leading to a Pancharatnam–Berry phase. It is shown that this geometric phase has a straightforward but elegant relationship to the Stokes parameters at the pinholes.
The contrast parameters associated with the generalized Stokes vector in a Young's interference experiment are analyzed. It is shown that there are two unitary transformations that can be applied to the electric fields so that a partially polarized light can be described with no more than two non-zero generalized Stokes parameters. Furthermore, general conditions are derived which indicate when totally unpolarized light can be described with only one non zero generalized Stokes parameter after unitary transformations.
We study the effects of spatial unitary transformations on the complex degree of coherence and the visibility of intensity fringes in Young’s double pinhole interference setup with scalar light. We demonstrate that the degree of coherence and the visibility, in general, change in such transformations and may become zero for the output fields even when the input beams are correlated. Moreover, we explore the influence of unitary two-beam transformations on the complementarity relations associated with the degree of coherence, the intensity distinguishability, and the concurrence. We illustrate the results with the help of Gaussian Schell-model beams. Nonabsorbing beam splitters, which are key elements in optical systems, are practical realizations of spatial unitary transformations.
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.