Theory for mode coupling in perturbed fibers

Based on a systematic approach to expand non-ideal eigenmodes as superposition of ideal eigenmodes, we develop a theoretical formalism to study mode coupling in perturbed fibers. The formalism explicitly yields the maximum energy-conversion ratios among ideal eigenmodes and the corresponding propagation lengths to reach the maximum conversion, and errors inherent to the underlying perturbative assumption can be estimated straightforwardly. Moreover, the formalism provides a simple way to divide the modes into smaller approximately-decoupled subsets, thus substantially simplifying the theoretical analysis and more directly catching the physical essence. By employing the formalism to analyze a ring fiber under perturbations of ellipticity and misalignment, we find that stability of the ideal eigenmodes is sensitive to the specific perturbation form, i.e., with some modes strongly affected by the ellipticity but not the misalignment, or vice versa. Furthermore, it is revealed that the EH11 and HE31 modes are strongly coupled under perturbation of ellipticity despite the relatively large effective-refractive-index difference, which suggests possible inadequacy of a widely adopted criterion against the coupling of EH nu-1,p and HE nu+1,p modes.