Theoretical Investigation Of State Transition And Interaction Of Optical Localized Waves

Dynamics of nonlinear localized waves becomes a subject of intense research in nonlinear physics these days. In general, the nonlinear localized waves can be classified into three types: soliton, rogue wave (RW) and breather. In this paper, based on the pre-existing experimental results and theoretical models, we intend to study the optical RWs and breathers in a variety of nonlinear optical systems via the analytical method (Darboux transformation and similar trans-formation) in combination with the perturbation theory (modulation instability analysis). The theoretical scheme of the optical RWs generated on Gaussian background beam is presented, and the corresponding effect of modulated physical parameters on the optical RW excitation is analyzed. A variety of state transitions induced by the higher-order effects, including the transition between RWs and solitons, the transition between breathers and solitons, and the transition between breathers and periodic waves are explored. The corresponding characteris-tics and physical mechanism of the state transitions are revealed. The coexistence and inelastic interaction between vector localized waves in a multi-mode fiber system are presented. The details are as follows:1. Optical RWs generation on the Gaussian background beamBased on the fact that the infinite-width plane-wave background cannot exist in the real physical systems, we analytically study optical RWs generation on a finite-width Gaussian background beam, for the first time. An exact first- and second-order RW solution on the Gaussian background beam is given. The theoretical scheme of the density modulation and phase modulation of the experimental initial excitation is presented. These results may provide theoretical foundation for the experimental realization.2. State transitions of localized waves and the mechanism induced by higher-order effects in a single-mode fiberHow to establish the exact relation between different types of nonlinear localized waves is an open question. We systematically study this question in a single-mode nonlinear optical fiber with higher-order effects, for the first time. The exact explicit solutions that describe a va-riety of state transitions and the corresponding existence conditions are presented. We find that the state transition between the Peregrine RW and W-shaped traveling wave is consistent with the modulation instability (MI) analysis that involves MI region and stability region in low per-turbation frequency region. The link between the MI growth rate and transition characteristic is strictly established. The nonlinear superposition characteristic of the transition is revealed. Fi-nally, we investigate the state transitions between the Akhmediev breathers and periodic waves, the Kuznetsov-Ma breathers and the single-peak solitons on a nonzero background, the general breathers and the multi-peak solitons on a nonzero background. These analytical results will enrich our understanding of the relations of state transitions between the different-type nonlin-ear localized waves and provide theoretical foundation for the experimental realization of the state transitions.3. State transitions and interaction of vector localized waves induced by higher-order effects in a multi-mode fiberBased on the fact that several amplitudes rather than a single one need to be considered in a variety of complex systems, we study the transition and interaction of vector localized waves in a two-mode optical fiber. The state transitions between vector (one and two) RWs and (one and two) solitons are revealed. It is demonstrated strictly that these transitions occur as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region. In particular, our results show that the W-shaped-anti-W-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes an inelastic fusion process. Our results show that these properties have no analogues in the case without higher-order effects.4. Vector breathers and the inelastic interaction in a multi-mode fiberBased on the fact that elastic collision between scalar RWs is observed in a single-mode optical fiber, we study the breathers, their collision, and the interaction between breathers and other types of nonlinear localized waves (solitons and RWs) in three-mode optical fiber. We find that there exist three types of breathers with different structures, i.e., the bright, dark and four-petaled ones. The "Y-shaped" collisions between different-type breathers are revealed. We present the explicit conditions of the coexistence between breathers and other types of nonlinear localized waves. The corresponding inelastic interaction structures are also revealed. In particular, we demonstrate for the first time that one breather and two RWs with different structures can coexist and interact with each other.