Coupled-Mode Theory for Cross-Polarization Coupling in Optical Fibers

Both the coupled-wave equations (CWEs) and coupled-power equations (CPEs) derived from coupled-mode theory (CMT) are presented, along with their analytical solutions, to describe the cross-polarization coupling (CPC) in single-mode fibers (SMFs) and polarization-maintaining fibers (PMFs). In the CWEs, various perturbations are captured by a single complex coupling parameter. The real part of this parameter represents conventional CPC induced by refractive index fluctuations, while the imaginary part accounts for other perturbations that manifest as measurement errors in CPC. As a simpler alternative, the CPEs are also introduced to verify the theory by measuring CPC in terms of polarization cross talk (PCT) or polarization extinction ratio (PER). Both the CWEs and CPEs are solved under general initial conditions that allow for imperfect linear polarization at the input, contrasting with the common assumption of ideally linear polarization. This imperfect input is shown to introduce an additional source of measurement error, which - together with the perturbations captured by the imaginary part of the coupling parameter - can be systematically explained via the proposed CMT framework and supporting numerical calculations. Finally, experimental observations of errors in PCT or PER measurements during routine PMF production are also accounted for by this theory, offering valuable insights for more accurate characterization of CPC in SMF including PMFs.