Spin-orbit interaction in the field of an optical vortex of a few-mode fiber

Abstract

A quantum-mechanical analog of the spin-orbit interaction operator $\hat V$ is constructed for the fields of optical CV vortices and TE and TM modes in an optical fiber. It is shown that the polarization correction δβ to the propagation constant, which is the mean value of this operator, is a measure of the “level splitting” of the propagation constant $\tilde \beta$ in the scalar case. The difference in the operation of the individual parts of the operator $\hat V$ on the fields of CV vortices and on the fields of TM and TE modes is indicative of the presence of two different physical processes — circular and linear birefringence in the locally isotropic optical fiber. The conversion of the “scalar” field $\tilde e$ to a vector field e ₁ as a consequence of the spin-orbit interaction operator can be regarded as resulting from a re-radiation of the additional field e ₁ by the vortex field $\tilde e$, which rotates around the optical axis of the fiber. In this picture the additional field e ₁ can be regarded as being a “relativistic” correction to the vortex field for the distortions of the main field $\tilde e$ and arising as a result of the rotation of the field of the optical vortex in the medium of the few-mode fiber.