Geometric phase in beating of light waves
Beating is a simple physical phenomenon known for long in the context of sound waves but remained surprisingly unexplored for light waves. When two monochromatic optical beams of different frequencies and states of polarization interfere, the polarization state of the superposition field exhibits te...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab3740 |
| _version_ | 1797750017589510144 |
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| author | Antti Hannonen Kimmo Saastamoinen Lasse-Petteri Leppänen Matias Koivurova Andriy Shevchenko Ari T Friberg Tero Setälä |
| author_facet | Antti Hannonen Kimmo Saastamoinen Lasse-Petteri Leppänen Matias Koivurova Andriy Shevchenko Ari T Friberg Tero Setälä |
| author_sort | Antti Hannonen |
| collection | DOAJ |
| description | Beating is a simple physical phenomenon known for long in the context of sound waves but remained surprisingly unexplored for light waves. When two monochromatic optical beams of different frequencies and states of polarization interfere, the polarization state of the superposition field exhibits temporal periodic variation—polarization beating. In this work, we reveal a foundational and elegant phase structure underlying such polarization beating. We show that the phase difference over a single beating period decomposes into the Pancharatnam–Berry geometric phase and a dynamical phase of which the former depends exclusively on the intensities and polarization states of the interfering beams whereas the sum of the phases is determined solely by the beam frequencies. Varying the intensity and polarization characteristics of the beams, the relative contributions of the geometric and dynamical phases can be adjusted. The geometric phase inherent in polarization beating is governed by a compact expression containing only the Stokes parameters of the interfering waves and can alternatively be obtained from the individual beam intensities and the amplitude of the intensity beats. We demonstrate both approaches experimentally by using an interferometer with a fast detector and a specific polarimetric arrangement. Polarization beating has a unique character that the geometric and dynamical phases are entangled, i.e. variation in one unavoidably leads to a change in the other. Our work expands geometric phases into a new domain and offers important novel insight into the role of polarization in interference of electromagnetic waves. |
| first_indexed | 2024-03-12T16:27:45Z |
| format | Article |
| id | doaj.art-afa1058bb4ca4dea90a29394963392ea |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:45Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-afa1058bb4ca4dea90a29394963392ea2023-08-08T15:40:07ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121808303010.1088/1367-2630/ab3740Geometric phase in beating of light wavesAntti Hannonen0Kimmo Saastamoinen1Lasse-Petteri Leppänen2Matias Koivurova3https://orcid.org/0000-0001-6100-6316Andriy Shevchenko4Ari T Friberg5Tero Setälä6Institute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandInstitute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandInstitute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandInstitute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandDepartment of Applied Physics, Aalto University , PO Box 13500, FI-00076 Aalto, FinlandInstitute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandInstitute of Photonics, University of Eastern Finland , PO Box 111, FI-80101 Joensuu, FinlandBeating is a simple physical phenomenon known for long in the context of sound waves but remained surprisingly unexplored for light waves. When two monochromatic optical beams of different frequencies and states of polarization interfere, the polarization state of the superposition field exhibits temporal periodic variation—polarization beating. In this work, we reveal a foundational and elegant phase structure underlying such polarization beating. We show that the phase difference over a single beating period decomposes into the Pancharatnam–Berry geometric phase and a dynamical phase of which the former depends exclusively on the intensities and polarization states of the interfering beams whereas the sum of the phases is determined solely by the beam frequencies. Varying the intensity and polarization characteristics of the beams, the relative contributions of the geometric and dynamical phases can be adjusted. The geometric phase inherent in polarization beating is governed by a compact expression containing only the Stokes parameters of the interfering waves and can alternatively be obtained from the individual beam intensities and the amplitude of the intensity beats. We demonstrate both approaches experimentally by using an interferometer with a fast detector and a specific polarimetric arrangement. Polarization beating has a unique character that the geometric and dynamical phases are entangled, i.e. variation in one unavoidably leads to a change in the other. Our work expands geometric phases into a new domain and offers important novel insight into the role of polarization in interference of electromagnetic waves.https://doi.org/10.1088/1367-2630/ab3740polarizationgeometric phasePancharatnam–Berry phaseinterferometry |
| spellingShingle | Antti Hannonen Kimmo Saastamoinen Lasse-Petteri Leppänen Matias Koivurova Andriy Shevchenko Ari T Friberg Tero Setälä Geometric phase in beating of light waves New Journal of Physics polarization geometric phase Pancharatnam–Berry phase interferometry |
| title | Geometric phase in beating of light waves |
| title_full | Geometric phase in beating of light waves |
| title_fullStr | Geometric phase in beating of light waves |
| title_full_unstemmed | Geometric phase in beating of light waves |
| title_short | Geometric phase in beating of light waves |
| title_sort | geometric phase in beating of light waves |
| topic | polarization geometric phase Pancharatnam–Berry phase interferometry |
| url | https://doi.org/10.1088/1367-2630/ab3740 |
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