Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

Abstract

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP11 mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γb=±δβ21z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV+ and IV− modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP11 mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber.