PROPAGATION OF POLARIZED LIGHT AND ELECTROMAGNETIC CURVES IN THE OPTICAL FIBER IN WALKER 3-MANIFOLDS

Abstract

In the present paper, we define the three cases of the geometric phase equations associated with a monochromatic linearly polarized light wave traveling along an optical fiber in three dimensional Walker manifold (M, g^ε_f). Walker manifolds have many applications in mathematics and theoretical physics. We are working in the context of a pseudo-Riemannian manifold (i.e. a manifold equipped with a non-degenerate arbitrary signature metric tensor). That is, we generalize the motion of the light wave in the optical fiber and the associated electromagnetic curves that describe the motion of a charged particle under the influence of an electromagnetic field over a Walker space defined as a pseudo-Riemannian manifold with a light-like distribution, parallel to the Levi-Civita junction. These manifolds (especially Lorentzian) are important in physics because of their applications in general relativity. Then, we obtain the Rytov curves related to the cases of geometric phase models. Moreover, we give some examples and visualize the evolution of the electric field along the optical fiber in (M, g^ε_f ) via MAPLE program.