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 with the optical fiber in Minkowski space. We define two novel types of geometric phases associated with the evolution of the polarization vectors in the normal and binormal directions along with the optical fiber. We also identify the normal-Rytov parallel transportation law and binormal-Rytov parallel transportation law. Moreover, we derive their relationships with the Fermi-Walker transportation law in Minkowski space. Then we solve Maxwell's equations by using geometric quantities associated with the curved path, which characterizes the optical fiber. Finally, we investigate that electromagnetic wave propagation admits the Maxwellian evolution equation for the anholonomic coordinate system in Minkowski space.