Fermi–Pasta–Ulam–Tsingou recurrence in two-core optical fibers

Abstract

The Fermi–Pasta–Ulam–Tsingou recurrence (FPUT) refers to the property of a multi-mode nonlinear system to return to the initial states after complex stages of evolution. FPUT in two-core optical fibers (TCFs) is studied by taking symmetric continuous waves as initial conditions. Analytically the dynamics is governed by linearly coupled nonlinear Schrödinger equations. A ‘cascading mechanism’ is investigated theoretically to elucidate the FPUT dynamics. Higher-order modes grow in ‘locked step’ with the fundamental one until a breather emerges, which results in a triangular spectrum, in consistency with observations in many experiments. In terms of optical physics, FPUT with in-phase perturbations is identical to that in single-core fibers (SCFs). For quadrature-phase perturbations (those with π/2 phase shifts between the two cores), symmetry is broken and the FPUT dynamics is rich. For normal dispersion, FPUT otherwise absent in SCFs arises for TCFs. The optical fields change from a phase-shifted FPUT pattern to an ‘in-phase’ pattern. The number of FPUT cycles eventually saturates. For anomalous dispersion, in-phase FPUT and ‘repulsion’ between wave trains in the two cores are observed. Preservation of the phase difference between waves in the two cores depends on the dispersion regime. An estimate based on modulation instability provides a formula for predicting the first occurrence of FPUT. These results enhance the understanding of the physics of TCFs, and help the evaluation of the performance of long-distance communication based on multi-core fibers.