Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

2007/01/31 by Konstantin Y. Bliokh, K. Yu. Bliokh, D. Yu. Frolov +1 · 2 citations
Engineering · Physics and Astronomy · #Anisotropy #Birefringence #Classical mechanics #Electromagnetic radiation #Equations of motion #Maxwell's equations #Mechanical and Optical Resonators #Photon #Photonic and Optical Devices #Physics #Polarization (electrochemistry) #Quantum #Quantum electrodynamics #Quantum mechanics #Quantum optics and atomic interactions #Stokes parameters #Zitterbewegung #cond-mat.other #physics.optics #physics.plasm-ph #quant-ph

paper · pdf · doi:10.1103/physreva.75.053821

published as Phys.Rev.A75:053821,2007 · 18 pages, 3 figures, to appear in Phys. Rev. A

arxiv created 2007/05/03 · openalex publication_date 2007/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

Citations

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
• Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field
• Fermat principle for spinning light
• Hall Effect of Light
• A review of plasma polarimetry - theory and methods
• Spin Transverse Force on Spin Current in an Electric Field
• Spin Hall effect and zitterbewegung in an electron waveguide
• Spin Hall effect and Berry phase of spinning particles
• Topological spin transport of photons: the optical Magnus effect and Berry phase
• Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
• Zitterbewegungof electrons and holes in III–V semiconductor quantum wells
• Topological spin transport of a relativistic electron
• Topological spin transport of photons: Magnetic monopole gauge field in Maxwell's equations and polarization splitting of rays in periodically inhomogeneous media

Cited by

• Spin-Orbit Coupling in Helical Waveguides: A Local Duality Perspective and Emergent Gauge Fields
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium