Maxwell-Schrödinger Equation for Polarized Light and Evolution of the Stokes Parameters
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By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schr\"odinger-like equation for two levels (or states) representing polarization. By using the quantum mechanical technique, the density matrix, and path integral, the evolution of the Stokes parameters results in the equation of motion for a pseudospin representing a point on the Poincar\'e sphere. Two typical examples relevant to actual experiments are considered; the one gives the generalized Faraday effect, and the other realizes an optical analog of magnetic resonance.
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The conservation of total angular momentum, Eq. (3.42), links the spin Hall effect of light to the transverse Imbert-Fedorov shift.
“The conservation of the total angular momentum, Eq. (3.42), links the spin Hall effect of light to another remarkable phenomenon - the transverse Imbert-Fedorov shift [24,27,99 -118].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [103]
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- [10]To consider the partially polarized state means that one should treat the time-varying function of the polarization. This implies that the polarization is distributed over a certain range of frequency, which is denoted by some parameter ξ . Thus we treat the partially polarized state by using the statistical distribution P ξ , ¯ ρ = ∑ ξ ψ ξ P ξ ψ ξ † . (Note that the wave function is also paramtetrized by the parameter ξ ). See L. Landau and E. Lifschitz, Classical Fields , Course of Theoretical Physics Vol.5 (Pergamon, Oxford, 1968).
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Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Bliokh, K. Y. (2009) · Journal of Optics A: Pure and Applied Optics · doi:10.1088/1464-4258/11/9/094009 · Cited by 217 · see citing works
Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
Kravtsov, Y. A., Bieg, B., & Bliokh, K. Y. (2007) · Journal of the Optical Society of America A · doi:10.1364/josaa.24.003388 · Cited by 40 · see citing works
Spin-orbit interactions of light in isotropic media
Bliokh, K. Y., Aiello, A., & Alonso, M. A. (2012) · The Angular Momentum of Light · doi:10.1017/cbo9780511795213.009 · Cited by 20 · see citing works
- Authors
- Kuratsuji, H., & Kakigi, S.
- Affiliations
- Ritsumeikan University (JP)
- ORCID
- Kuratsuji, Hiroshi
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-03-02
- Volume
- 80
- Issue
- 9
- Pages
- 1888-1891
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2056121154
- Cited by
- 65
- References
- 13
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 3 · 2023: 4 · 2022: 2 · 2021: 2 · 2020: 4 · 2019: 3 · 2018: 3 · 2017: 3 · 2016: 3 · 2015: 2 · 2013: 4 · 2012: 5
- FWCI
- 0.73
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Keywords
- Maxwell-Schrödinger equations, polarization evolution, Stokes parameters, Poincaré sphere, pseudospin, Faraday rotation, density matrix, path integral, two-level system
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