Optical skyrmions in nonlinear birefringence media: semiclassical approach incorporating effective gauge field

Abstract A theoretical study is presented for the optical skyrmion (or optical spin vortex) which is expected to occur in nonlinear birefringence media. This is investigated from the aspect of the quantum spinor condensate, whose order parameter is given by the photon field (vector potential). The procedure is based on an extended paraxial approximation; namely, the low-energy oscillation amplitude of the vector potential is decoupled from the high-frequency part. The result is the (2+1) field theory, which is described by a two-component spinor and is expressed in terms of the Stokes parameters. First, we consider the skyrmion for the case of a pure photon field. There are two specific topics: one concerns the polarization singularity, which is a trajectory of the center line of the skyrmion, called the ‘C-line’, which means the trajectory of circular polarization . The other is semiclassical quantization, which is derived for the equation of motion of the vortex (or skyrmion) center. Here, a brief comment is given for an analogy with the Hall effect occurring in the superconductivity vortex. The theory is extended such that the photon field allows a coupling with an effective gauge field. We examine the skyrmion–gauge field coupling from two aspects: one is strong coupling, in which the gauge field acts so as to stabilize the skyrmion. The other is weak coupling, for which the interaction between the gauge phonon and skyrmion motion is treated by a perturbation scheme, which provides the basis for the possible detection of gauge phonons.