The Rytov–Vladimirskii Phase and Interferometric Measurements

Abstract

A systematic approach to the description of the topological Rytov–Vladimirskii phase was developed and a new formalism for calculating the phase in specific optical systems was constructed. This formalism uses special matrix operators that describe the variations in both the direction and polarization of optical beam as a result of its reflection and refraction at the interface between two media. The structure of the Rytov–Vladimirskii phase in optical systems with focusing lens is studied. Due to the presence of a focusing lenses, the beam trajectories are nonplanar and the Rytov–Vladimirskii phase has a singular point. At this point, the Rytov–Vladimirskii phase is not defined. It is shown that, at the singular point, the phase of a solution to the Maxwell equations is strictly defined, but its polarization is not defined. As an example, the Linnik and Mach–Zehnder interferometers are considered.