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Journal of Physics Conference Series

Polarization modulation in Young's interference experiment

Jani Tervo

Published Nov 1, 2008• 3 citations
Publisher

Abstract

Polarization properties at the observation screen in Young's interference experiment are examined. Several recent results on the modulation of Stokes parameters, including the minimum number of modulated parameters, are reviewed. The theory is then applied to find out the relation between the Stokes parameters at the pinholes and the Pancharatnam-Berry phase at the screen.

DOI
10.1088/1742-6596/139/1/012025

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Polarization properties at the observation screen in Young's interference experiment are examined. Several recent results on the modulation of Stokes parameters, including the minimum number of modulated parameters, are reviewed. The theory is then applied to find out the relation between the Stokes parameters at the pinholes and the Pancharatnam-Berry phase at the screen.
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.
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
Young's two-beam interference and the Pancharatnam-Berry geometric phase constitute two landmark results in optical physics. Employing the spectral interference law of electromagnetic waves, we establish a general expression for the Pancharatnam-Berry phase in Young's two-pinhole setup. We show that the phase is elegantly specified by the electric field Stokes parameters at the openings. The geometric phase can also be deduced from the interference pattern using Pancharatnam's definition of the generalized phase, as we demonstrate both numerically and experimentally. Our results imply a way to control the phase differences in two-beam electromagnetic interference by adjusting the input-field intensities and polarization states.
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.