Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium

2009/03/11 by Konstantin Y. Bliokh · 3 citations
Physics and Astronomy · #Angular momentum #Classical mechanics #Condensed matter physics #Electromagnetic radiation #Electron #Geometric phase #Orbital Angular Momentum in Optics #Physics #Polarization (electrochemistry) #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Quantum optics and atomic interactions #Spin Hall effect #Spin polarization #Spin–orbit interaction #cond-mat.other #hep-th #physics.optics #quant-ph

paper · pdf · doi:10.1088/1464-4258/11/9/094009

published as J. Opt. A: Pure Appl. Opt. 11, 094009 (2009) · 25 pages, 4 figures, review to appear in special issue of J. Opt. A: Pure Appl. Opt

arxiv created 2009/03/11 · openalex publication_date 2009/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i)the Berry phase responsible for trajectory-dependent polarization variations and (ii)the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometrodynamical interrelations illuminate a dual physical nature of the phenomena.

Citations

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
• Geometrodynamics of spinning light
• Fermat principle for spinning light
• Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections
• Hall Effect of Light
• Semiclassical theories of the anomalous Hall effect
• Significance of Electromagnetic Potentials in the Quantum Theory
• Spin Hall effect of photons in a static gravitational field
• Berry and Pancharatnam topological phases of atomic and optical systems
• Universal Intrinsic Spin Hall Effect
• Spin Hall effect and Berry phase of spinning particles
• Topological spin transport of photons: the optical Magnus effect and Berry phase
• Atomic Micromotion and Geometric Forces in a Triaxial Magnetic Trap
• Dissipationless Quantum Spin Current at Room Temperature
• Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
• Topological Nature of Anomalous Hall Effect in Ferromagnets
• Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
• Transverse Force on a Quantized Vortex in a Superfluid
• Role of beam propagation in Goos–Hänchen and Imbert–Fedorov shifts
• Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media
• 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
• Quantised singularities in the electromagnetic field,
• Spin gauge fields: From Berry phase to topological spin transport and Hall effects

Cited by

• Spin-Orbit Coupling in Helical Waveguides: A Local Duality Perspective and Emergent Gauge Fields
• Unified Approach towards the Dynamics of Optical and Electron Vortex Beams
• Relativistic Electron Vortex Beams in a Laser Field

Related

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
• Geometrodynamics of spinning light
• Induced Berry Connection and Photonic Spin Hall Effect in Optical Dirac Theory
• Polarized Spinoptics and Symplectic Physics
• Physical mechanism for the geometric phases in optics and angular momentum holonomy