We study the interactions of a Bragg-grating soliton with a localized attractive defect which is a combined perturbation of the grating and refractive index. A family of exact analytical solutions for solitons trapped by the delta-like defect is found. Direct simulations demonstrate that, up to the numerical accuracy available, the trapped soliton is stable at a single value of its intrinsic parameter ("mass"). Trapped solitons with larger mass relax to the stable one through the emission of radiation, while the solitons with smaller mass decay. Depending on values of parameters, simulations of collisions between moving solitons and the defect show that the soliton can get captured, pass through, or even bounce from the defect. If the defect is strong and the soliton is heavy enough, it may split, as a result of the collision, into three fragments: trapped, transmitted, and reflected ones.Comment: a latex text file and 11 jpg files with figures; an extended version of the paper will appear in Journal of the Optical Society of America
A model of a lossy nonlinear fiber grating with a "hot spot", which combines a local gain and an attractive perturbation of the refractive index, is introduced. A family of exact solutions for pinned solitons is found in the absence of loss and gain. In the presence of the loss and localized gain, an instability threshold of the zero solution is found. If the loss and gain are small, it is predicted what soliton is selected by the energy-balance condition. Direct simulations demonstrate that only one pinned soliton is stable in the conservative model, and it is a semi − attractor : solitons with a larger energy relax to it via emission of radiation, while those with a smaller energy decay. The same is found for solitons trapped by a pair of repulsive inhomogeneities. In the model with the loss and gain, stable pinned pulses demonstrate persistent internal vibrations and emission of radiation. If these solitons are nearly stationary, the prediction based on the energy balance underestimates the necessary gain by 10 − 15% (due to radiation loss). If the loss and gain are larger, the intrinsic vibrations of the pinned soliton become chaotic. The local gain alone, without the attractive perturbation of the local refractive index, cannot maintain a stable pinned soliton.For collisions of moving solitons with the "hot spot", passage and capture regimes are identified, the capture actually implying splitting of the soliton.
A model of the second-harmonic-generating ( (2) ) optical medium with a Bragg grating is considered. Two components of the fundamental harmonic ͑FH͒ are assumed to be resonantly coupled through the Bragg reflection, while the second harmonic ͑SH͒ propagates parallel to the grating, hence its dispersion ͑diffraction͒ must be explicitly taken into consideration. It is demonstrated that the system can easily generate stable three-wave gap solitons of two different types ͑free-tail and tail-locked ones͒ that are identified analytically according to the structure of their tails. The stationary fundamental solitons are sought for analytically, by means of the variational approximation, and numerically. The results produced by the two approaches are in fairly reasonable agreement. The existence boundaries of the soliton are found in an exact form. The stability of the solitons is determined by direct partial differential equation simulations. A threshold value of an effective FH-SH mismatch parameter is found, the soliton being stable above the threshold and unstable below it. The stability threshold strongly depends on the soliton's wave-number shift k and very weakly on the SH diffraction coefficient. Stationary two-soliton bound states are found, too, and it is demonstrated numerically that they are stable if the mismatch exceeds another threshold, which is close to that for the fundamental soliton. At kϽ0, the stability thresholds do not exist, as all the fundamental and two-solitons are stable. With the increase of the mismatch, the two-solitons disappear, developing a singularity at another, very high, threshold. The existence of the stable two-solitons is a drastic difference of the present model from the earlier investigated (2) systems. It is argued that both the fundamental solitons and two-solitons can be experimentally observed in currently available optical materials with the quadratic nonlinearity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.