Finsler Spinoptics
arXiv:0707.0200 · doi:10.1007/s00220-008-0573-7
Abstract
The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of previous work on Riemannian spinoptics, and relying on the generic coadjoint orbits of the Euclidean group. A new presymplectic structure on the indicatrix-bundle is introduced, which gives rise to a foliation that significantly departs from that generated by the geodesic spray, and leads to a specific anomalous velocity, due to the coupling of spin and the Cartan curvature, and related to the optical Hall effect.
LaTeX, 40 pages. Introductory Sections 1 and 2 substantially shortened, conceptual rectification in Section 3, and one Reference added. To appear in Communications in Mathematical Physics
References in corpus (14)
- Hall Effect of Light
- Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of Electromagnetic Wave Packet
- Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
- Topological spin transport of photons: the optical Magnus Effect and Berry Phase
- Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
- Spin Hall effect of Photons in a Static Gravitational Field
- Fermat Principle for spinning light
- Geometrical Aspects in Optical Wavepacket Dynamics
- Fermat Principle in Finsler Spacetimes
- Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
- Geometrical Spinoptics and the Optical Hall Effect
- Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
- On the symplectic structures arising in Optics
- Presymplectic Geometry and Fermat's Principle for anisotropic media
Cited by in corpus (14)
- On the energy functional on Finsler manifolds and applications to stationary spacetimes
- Geometry of physical dispersion relations
- Covariant kinematics and gravitational bounce in Finsler space-times
- Spinoptics in a stationary spacetime
- Finsler pp-waves
- Scattering of circularly polarized light by a rotating black hole
- Maxwell equations in a curved spacetime: Spin optics approximation
- Birefringence in pseudo-Finsler spacetimes
- Pseudo-Finslerian spacetimes and multi-refringence
- Gravitational birefringence of light in Robertson-Walker cosmologies
- Gravitational birefringence of light in Schwarzschild spacetime
- From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology
- How does the photon's spin affect Gravitational Wave measurements?
- Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge