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Journal of Optics A Pure and Applied Optics

Minimum number of modulated Stokes parameters in Young’s interference experiment

Jani Tervo, Philippe Réfrégier, Antoine Roueff

Published Mar 27, 2008• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1464-4258/10/5/055002

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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 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.
In this work, we formulate a quantum-mechanical description of interference of electromagnetic fields in Young's interference experiment, thereby taking into account the polarization properties of the field and describing them in terms of quantum analogs of classical Stokes parameters.Commencing with the classical theory of interference of scalar fields, we proceed to a relatively advanced approach to electromagnetic interference, bringing into the equation cross-spectral density tensor, polarization matrix and Stokes parameters to analyze the polarization properties.Subsequently, the same phenomenon is analyzed in the domain of quantum optics, thereby expressing the fields as operators and observables as the expectation values.Firstly, an outline of the scalar approach of the operators in the interference experiment is presented to establish the foundation to base the electromagnetic approach on, followed by a full description of quantum analog of electromagnetic interference in Young's experiment.In particular, Stokes parameters are adopted to calculate the polarization effects in quantum theory. PrefaceThis report attempts to condense and present the theories related to the interference in the canonical Young's double pinhole experiment, prior to heading to investigate the phenomenon with the quantum analysis of electromagnetic fields.My interest in the realm of quantum mechanics has encouraged me to work on this thesis, wherefrom I have learnt a lot during these times.I am really grateful to my supervisors, Prof. Ari T. Friberg and Prof. Jani Tervo for guiding me and believing in me.I will always be indebted for their constant support and confidence on me.I would also like to offer my special thanks to the Faculty of Forestry and Sciences for providing the financial
The mathematical representation of each of the four interference laws of Fresnel and Arago is presented. Each of the laws is characterized by a unique Stokes vector. These vectors are arrived at by a matrix analysis of the, interference experiments of Fresnel and Arago in which only polarizers are used. The historical motivation that led Stokes to introduce the parameters that now bear his name is noted. The similarity in the approach taken by Stokes to represent the fundamental properties of the classical optical field in terms of observables is compared with Heisenberg's approach to the formulation of quantum mechanics. The mathematical statements that characterize unpolarized light are developed. These statements are then used to determine the Stokes vectors that describe each of the four interference laws of Fresnel and Arago. In a final section of the paper the mathematical apparatus developed here is used to describe Young's interference experiment with unpolarized light.