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Differences between the geometric phase and propagation phase: clarifying the boundedness problem

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Abstract

We show white light interferometer experiments that clearly demonstrate the basic differences between geometric and propagation phases. These experimental results also suggest a way to answer the “boundedness problem” in geometric phase—whether geometric phase is unbounded (i.e., can take on any values without limit) or bounded (i.e., limited to values between ${-}\pi$ and ${+}\pi$). We show why the answer to this question is not as easy as it seems, from both a theoretical and an experimental perspective, and explain how the answer depends on one’s choice of phase convention. We also hope that the videos provided will be pedagogically useful for explaining geometric phase.

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Supplementary Material (6)

NameDescription
Visualization 1       The pattern of geometric phase produced for all states on the Poincaré sphere, generated by a waveplate with fast axis at 0° whose retardance varies from 0 (at the beginning of the video) to p (at the end of the video). Note that all polarization sta
Visualization 2       The fringe pattern produced in the Mach-Zehnder interferometer as the propagation phase is slowly shifted by about 8 waves. The measured interferograms are shown above, and the plots underneath are derived from summing down the columns of the interfe
Visualization 3       The fringe pattern produced in the Mach-Zehnder interferometer as the propagation phase is slowly shifted by about 8 waves. The measured interferograms are shown above, and the plots underneath are derived from summing down the columns of the interfe
Visualization 4       The raw line-imaging spectrometer video obtained from the Michelson interferometer while the propagation phase is shifted, by pushing the adjustable fold mirror from its original position. As the video proceeds, and the angle of the fold mirror incre
Visualization 5       The raw line-imaging spectrometer video obtained from the Michelson interferometer while the half-wave plate inside the QHQ is rotated through five full turns. As the video proceeds, we see that the slant angle of the spectral fringes does not change
Visualization 6       This visualization is an attempt to show, in as simple terms as possible, the differences in behavior between geometric and propagation phase shifting. In both the left and right simulations, there are three waves of different wavelengths shown: 450n

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon request.

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Figures (11)

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Equations (1)

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