The Propagation Of Spinning Light In An Inhomogeneous Medium

When the polarized light propagating in inhomogeneous medium, thereare two important observable effects which induced by the spin-orbitinteraction:one is the spin Hall effect which displays polarization-dependenttransverse deflection of ray trajectory perpendicular to the momentum ofphotonand inhomogeneity gradient n, the other is the Berry phase which is anonintegrable phase and displays the rotation of the polarization plane of thelinearly polarized light propagating along asingle-mode helical optical fiber. Thespin Hall effect and the Berry phase of light pave a new way for the control ofoptics information, and have applications in nano-optics, information optics andthe development of photonic devices.The evolution of the polarized light in inhomogeneous medium is similarto the evolution of spinning charged particle in external field. This offers a goodopportunity to investigate the evolution of the polarized light using thegeometrodynamicsmethod. The traditional geometrical optics describes theparticle-like features of light without the intrinsic degree of freedom, but can’tdescribe the propagation of spinning light in inhomogeneous medium.In thispaper, we investigate the polarization transport of light in inhomogeneousmedium using the generalized geometrical optical optics which taking intoaccount the spin-orbit interaction and the spin-spin interaction of photons. Themain research method and innovation finding are presented as follows:(1) Using the dynamical method of photons,we investigate the influence ofspin-orbit interaction on the propagation of the polarized light ininhomogeneous medium by means of the opticalmetric and the Maxwellequations in curved space, and investigate the spin-spin interaction ofphotons firstly. We obtain the Hamiltonian ofphotons including thespin-orbit interaction and the spin-spin interactioncorrections, whichcorrespond to the first-order and second-ordercorrections in the geometricaloptics approximation respectively. We know that the effects induced by thespin-spin interaction are independent of the polarization of light.Due to thespin-spin interaction, there is a novel and smallpolarization-independentdeflection of the ray trajectory of the polarized lightwhose directionis along the inhomogeneity gradient of medium n.Thespin-spin interaction doesn’t change the Berry phase of photon and leads to a correction phase to the dynamical phase.(2) By means of the eikonal-based complex geometrical optics,which describesthe phase front and cross section of a light beam using the quadraticexpansion of a complex-valued eikonal,we investigatethe polarizationevolution of a polarized Gaussian beam in a smoothly inhomogeneousisotropicmedium.The linear complex-valued eikonal terms areintroducedfirstly to describe the polarization-dependent transverse shifts of the beam intheinhomogeneous medium.We find that the polarization-dependenttransverse shifts of the beamsinclude two parts: one originates from thecoupling between the spin angular momentum and theextrinsic orbitalangular momentum due to the curve trajectory of the center of gravity of thepolarized Gaussian beam, and the other from the coupling between the spinangular momentum and the intrinsic orbitalangular momentum due to therotation of the beam with respect to the central ray.