Extending geometrical optics: A Lagrangian theory for vector waves
Abstract
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wave spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.
- Authors:
-
[1];
- Princeton Univ., Princeton, NJ (United States)
- Princeton Univ., Princeton, NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1367374
- Alternate Identifier(s):
- OSTI ID: 1348029
- Grant/Contract Number:
- No. 32-CFR-168a; NA0002948; AC02-09CH11466
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 5; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Ruiz, D. E., and Dodin, I. Y. Extending geometrical optics: A Lagrangian theory for vector waves. United States: N. p., 2017.
Web. doi:10.1063/1.4977537.
Ruiz, D. E., & Dodin, I. Y. Extending geometrical optics: A Lagrangian theory for vector waves. United States. https://doi.org/10.1063/1.4977537
Ruiz, D. E., and Dodin, I. Y. Thu .
"Extending geometrical optics: A Lagrangian theory for vector waves". United States. https://doi.org/10.1063/1.4977537. https://www.osti.gov/servlets/purl/1367374.
@article{osti_1367374,
title = {Extending geometrical optics: A Lagrangian theory for vector waves},
author = {Ruiz, D. E. and Dodin, I. Y.},
abstractNote = {Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wave spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.},
doi = {10.1063/1.4977537},
journal = {Physics of Plasmas},
number = 5,
volume = 24,
place = {United States},
year = {Thu Mar 16 00:00:00 EDT 2017},
month = {Thu Mar 16 00:00:00 EDT 2017}
}
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Works referencing / citing this record:
Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory
journal, July 2019
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Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams
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