Extending geometrical optics: A Lagrangian theory for vector waves
Abstract
Even when neglecting diffraction effects, the wellknown 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 vectorwave 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 wellknown 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, lessknown polarization effect is the polarizationdriven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a firstprinciple Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarizationdriven divergence of righthand and lefthand circularly polarized electromagnetic waves in weakly magnetized plasma.
 Authors:
 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 Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1367374
 Alternate Identifier(s):
 OSTI ID: 1348029
 Grant/Contract Number:
 No. 32CFR168a; NA0002948; AC0209CH11466
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 5; Journal ID: ISSN 1070664X
 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. doi:10.1063/1.4977537.
Ruiz, D. E., and Dodin, I. Y. Thu .
"Extending geometrical optics: A Lagrangian theory for vector waves". United States.
doi: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 wellknown 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 vectorwave 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 wellknown 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, lessknown polarization effect is the polarizationdriven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a firstprinciple Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarizationdriven divergence of righthand and lefthand 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}
}
Web of Science

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Linear vector waves, both quantum and classical, experience polarizationdriven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leadingorder geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the SternGerlach Hamiltonian that is commonly known for spin1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometricaloptics rays are derived from the fundamental wave Lagrangian. The resulting EulerLagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore »Cited by 8