Solitons In Nonlinear Fibers Research Articles

Dark solitons and their bound states in a nonlinear fiber with second- and fourth-order dispersion

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit time-domain oscillating structures on a plane wave, and they have two types: the ones with or without the total phase step, while the multi-dark-soliton bound states exhibit different numbers of amplitude humps. By the modified linear stability analysis, we regard the SDSs as the results of the competition between periodicity and localization, and analytically give their existence condition, oscillation frequency, and propagation stability, which show good agreements with numerical results. We also provide a possible interpretation of the formation of the existing striped bright solitons (SBSs), and find that SBS will become the pure-quartic soliton when its periodicity and localization carry equal weight. Our results provide the theoretical support for the experimental observation of striped solitons in nonlinear fibers, and our method can also guide the discovery of striped solitons in other physical systems.

Periodic transmission theory of circularly symmetric multi-ring solitons in nonlinear Schrödinger equation

In this paper, the evolution characteristics of periodic transmission of circularly symmetric multi-ring solitons in optical nonlocal materials based on nonlinear Schrödinger equation are investigated in detail. The transmission expression of circularly symmetric multi-ring solitons has been derived. It was found that the number and size of rings in these solitons can be controlled by initial parameters. The transmission of circularly symmetric multi-ring solitons is similar to that of high-order temporal solitons in nonlinear fibers, exhibiting periodic variations. When the input energy is a specific value, the statistical width of circularly symmetric multi-ring solitons remains constant during transmission, otherwise it exhibits periodic changes, which can be considered as generalized breathing solitons. The influence of various parameters on the transmission characteristics has been analyzed in detail, and some important transmission characteristics have been intuitively demonstrated through numerical simulation.

Phase-controlled stable solitons in nonlinear fibers

Bright and grey coupled solitons with complex envelopes are obtained as exact solutions of the system describing doped optical nonlinear fibers. The solitons formed are found to be free of amplitude and phase instabilities during their evolution, leading to the realization of stable soliton propagation. The phase of the input solitons plays a crucial role in the formation of tanh–sech paired pulses. This soliton is not supported in a two-level atomic medium and is exclusive to the Λ system.

Second-quantized models for optical solitons in nonlinear fibers: Equal-time versus equal-space commutation relations

The dynamics of a quantum soliton propagating in nonlinear optical fibers is analyzed in the second-quantized picture in a fully canonical way. The quantum nonlinear Schr\"odinger equation with equal-time commutation relations for the field operators is solved using the formalism developed by Haus and Lai [J. Opt. Soc. Am. B $7,$ 386 (1990)]. The canonical approach is compared with the treatment of Haus and Lai based on phenomenological equal-space commutation relations. The two theories are shown to provide similar outcomes of a homodyne measurement. This result justifies the use of equal-space commutation relations in quantum studies of soliton propagation.