Effects of coupling coefficient dispersion on the Fermi-Pasta-Ulam-Tsingou recurrence in two-core optical fibers

Abstract

<p>In a two-core optical fiber (TCF), the linear coupling coefficient between the two cores in general varies with the optical wavelength, a phenomenon known as coupling coefficient dispersion (CCD). Here we study the effects of CCD on the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena in a TCF. Modulation instability tends to be a precursor in the formation of breathers. The subsequent decay of breathers and re-emergence of modulation instability lead to FPUT type periodic patterns. For the symmetric or antisymmetric continuous-wave (CW) state of a TCF, CCD does not affect the modulation instability gain spectra. However, if asymmetric perturbations are applied to a symmetric CW state, CCD can drastically modify FPUT. In the anomalous dispersion regime, without CCD, only FPUT dynamics without energy transfer between the two cores occurs. With CCD effects, FPUT dynamics with strong energy transfer between the two cores can arise. As CCD increases, FPUT dynamics without energy transfer never vanishes, but the corresponding number of FPUT cycles can be drastically reduced to only one. In the normal dispersion regime, no FPUT dynamics with energy transfer between the two cores occurs. The major CCD effect is to significantly decrease the FPUT cycles, and only one FPUT cycle can be observed at relatively large magnitude of CCD values. As the magnitude of CCD increases further, more FPUT cycles arise again. Moreover, larger CCD will lead to higher (lower) propagation speed of the wave patterns in the anomalous (normal) dispersion regime respectively. To enhance theoretical insight, we perform a Floquet analysis for the linearized stability equations with periodic coefficients based on the FPUT dynamics in the normal dispersion regime. The monodromy matrix and eigenvalues can be computed explicitly. Larger eigenvalues correlate with stronger instability and more rapid disintegration of the periodic patterns, agreeing well with the trends of the numerical simulations.</p>