Maxwellian evolution equations along the uniform optical fiber in Minkowski space

Abstract

We firstly discuss the geometric phase rotation for an electromagnetic wave traveling along the optical fiber in Minkowski space. We define two types of novel geometric phases associated with the evolution of the polarization vectors in the normal and binormal directions along the optical fiber by identifying the normal-Rytov parallel transportation law and binormal-Rytov parallel transportation law and derive their relationships with the new types of Fermi-Walker transportation law in Minkowski space. Then we describe a novel approach of solving Maxwell's equations in terms of electromagnetic field vectors and geometric quantities associated with the curved path characterizing the path uniform optical fiber by using the traveling wave transformation method. Finally, we investigate that electromagnetic wave propagation along the uniform optical fiber admits an interesting family of Maxwellian evolution equation having numerous physical and geometric applications for anholonomic coordinate system in Minkowski space