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Optics Letters

Complex degree of coherence and fringe visibility in spatial unitary transformations of scalar fields

Atri Halder, Ari T. Friberg

Published Dec 20, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.1364/ol.45.000192

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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.
We consider two partially correlated scalar light beams in a spatially unitary interference setup. We introduce a state vector in a Poincaré-sphere-like geometrical configuration that fully specifies such an optical system and its evolution under spatial unitary transformations. We also identify three particular unitary operations together with their geometrical representations that can be optically implemented to realize an arbitrary spatial unitary transformation. Our work forms an advantageous geometrical platform to characterize distinguishability, visibility, degree of coherence, and classical entanglement, as well as their spatial unitary evolutions, in scalar two-beam light interference.
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.
The changes in the interference pattern in Young's interference experiment, produced by placing two identical narrow-band filters in front of the pinholes, are analyzed. It is shown theoretically that, in general, the fringes will not become sharp (i.e., their maximum visibility will not tend to unity) even when the filters have arbitrarily narrow passbands. The analysis brings out a relationship between the complex degree of coherence in the space-time and the space-frequency domains. When the passbands of the filters are narrow enough, the filtered light is found to be cross-spectrally pure.
All two-beam interferometry eventually reduces to quantitative measurement of the effective fringe visibility (or degree of coherence) in some form. We present generalized analytical and experimental results of visibility for the cases of two beam Poynting vectors both collinear (scanning fringe mode) and non-collinear (spatial fringe mode) with different polarizations and frequencies. This leads to a much broader and deeper understanding of the roles of material dipoles (beam splitters & detectors; both classical and quantum) in measured coherence effects that are not explicitly addressed in the traditional coherence theory. Coherence theory should be presented as correlation between sensing dipole undulations that are simultaneously induced by superposed light beams rather than as correlation between the optical fields. This generalized understanding of the physical processes behind coherence phenomenon will open up (i) better understanding of the nature of light and (ii) many more innovative approaches to quantitative interferometry.
We report a method to synthesize the complete range of arbitrary combinations of coherences independently in both the polarization and spatial degrees of freedom (DoFs) by utilizing energy conserving unitary and non-unitary transformations. We further demonstrate that starting from a fully spatially coherent and polarized field, one can achieve two light fields having any degree of mutual coherence, and remixing these fields can result in maximum visibility (unit) interference fringes irrespective of any degree of polarization of the mixed field. We believe that these results provide new insight and may contribute significantly towards the ongoing explorations on optical coherence and its applications.
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.