Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions

In this paper, we obtain the N th-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique. Then, via an improved asymptotic analysis method relying on the balance between different algebraic terms, we derive the explicit expressions of all asymptotic solitons of the rational solutions with the order 1 ≤ N ≤ 4 . It turns out that the asymptotic solitons are localized in the straight lines or algebraic curves, and the exact solutions approach the curved asymptotic solitons with a slower rate than the straight ones. Moreover, we find that all the rational solutions exhibit just five different types of soliton interactions, and the interacting solitons are divided into two halves with each having the same amplitudes. Particularly for the curved asymptotic solitons, there may exist a slight difference for their velocities between at t and − t with certain parametric conditions. In addition, we reveal that the soliton interactions in the rational solutions with N ≥ 2 are stronger than those in the exponential and exponential-and-rational solutions.

Efficient harmonic generation in an adiabatic multimode submicron tapered optical fiber

Optical nanotapers fabricated by tapering optical fibers have attracted considerable interest as an ultimate platform for high-efficiency light-matter interactions. While previously demonstrated applications relied exclusively on the low-loss transmission of only the fundamental mode, the implementation of multimode tapers that adiabatically transmit several modes has remained very challenging, hindering their use in various emerging applications in multimode nonlinear optics and quantum optics. Here, we report the realization of multimode submicron tapers that permit the simultaneous adiabatic transmission of multiple higher-order modes including the LP02 mode, through introducing deep wet-etching of conventional fiber before fiber tapering. Furthermore, as a critical application, we demonstrate fundamental-to-fundamental all-fiber third-harmonic generation with high conversion efficiencies. Our work paves the way for ultrahigh-efficiency multimode nonlinear and quantum optics, facilitating nonclassical light generation in the multimode regime, multimode soliton interactions and photonic quantum gates, and manipulation of the evanescent-field-induced optical trapping potentials of atoms and nanoparticles.

Synthesis and dissociation of soliton molecules in parallel optical-soliton reactors

Mode-locked lasers have been widely used to explore interactions between optical solitons, including bound-soliton states that may be regarded as “photonic molecules”. Conventional mode-locked lasers normally, however, host at most only a few solitons, which means that stochastic behaviours involving large numbers of solitons cannot easily be studied under controlled experimental conditions. Here we report the use of an optoacoustically mode-locked fibre laser to create hundreds of temporal traps or “reactors” in parallel, within each of which multiple solitons can be isolated and controlled both globally and individually using all-optical methods. We achieve on-demand synthesis and dissociation of soliton molecules within these reactors, in this way unfolding a novel panorama of diverse dynamics in which the statistics of multi-soliton interactions can be studied. The results are of crucial importance in understanding dynamical soliton interactions and may motivate potential applications for all-optical control of ultrafast light fields in optical resonators.

Line Soliton Interactions for Shallow Ocean Waves and Novel Solutions with Peakon, Ring, Conical, Columnar, and Lump Structures Based on Fractional KP Equation

It is well known that the celebrated Kadomtsev-Petviashvili (KP) equation has many important applications. The aim of this article is to use fractional KP equation to not only simulate shallow ocean waves but also construct novel spatial structures. Firstly, the definitions of the conformable fractional partial derivatives and integrals together with a physical interpretation are introduced and then a fractional integrable KP equation consisting of fractional KPI and KPII equations is derived. Secondly, a formula for the fractional n -soliton solutions of the derived fractional KP equation is obtained and fractional line one-solitons with bend, wavelet peaks, and peakon are constructed. Thirdly, fractional X-, Y- and 3-in-2-out-type interactions in the fractional line two- and three-soliton solutions of the fractional KPII equation are simulated for shallow ocean waves. Besides, a falling and spreading process of a columnar structure in the fractional line two-soliton solution is also simulated. Finally, a fractional rational solution of the fractional KP equation is obtained including the lump solution as a special case. With the development of time, the nonlinear dynamic evolution of the fractional lump solution of the fractional KPI equation can change from ring and conical structures to lump structure.