Trapping Bragg solitons by a pair of defects

Abstract

We study collisions of moving solitons in a fiber Bragg grating with a structure composed of two local defects of the grating, attractive or repulsive. Results are summarized in the form of diagrams showing the share of the trapped energy as a function of the soliton's velocity and defects' strength. The moving soliton can be trapped by a cavity bounded by repulsive defects; a well-defined region of the most efficient trapping is identified. The trapped soliton performs persistent oscillations in the cavity, with the frequency in the GHz range. For attractive defects, essential differences are found from the earlier studied case of the collision of a soliton with a single defect: in this case, too, there appears a well-defined region of the most efficient trapping, and the largest velocity, up to which the soliton can be captured, increases. The findings may be significant for experiments aimed at the creation of "standing-light" pulses in the fiber gratings and for related applications. Collisions between identical solitons moving across the two-defect structure are also studied. On the attractive set, soliton-soliton collisions may give rise to symmetric capture of the solitons by both defects or merger into a single pulse trapped at one defect.

Periodic nanostructures for photonics

“…[310], the interaction of gap solitons with localized defects, that support linear defect modes, has been investigated and parameter regimes for the capture at, reflection from, and transmission through defect sites have been identified. In addition, it has been realized that the aforementioned three regimes of soliton-defect interaction may even occur when the gap solitons interact with delta-like defects, which themselves do not exhibit linear defect modes [311] and pairs of such defects are capable of trapping gap solitons [312]. In addition, an analysis of solitary wave interacting with a defect that exhibits gain in an overall lossy Bragg grating has been presented in Ref.…”

Light Pulse Interaction with Narrow Defects in Fiber Bragg Gratings

“…The effect of a narrow defect is a jump of the envelopes along the characteristic lines of the hyperbolic NLCME. This has been previously modeled by adding Dirac-delta functions to the NLCME [16,17,18]. This formulation covers only the particular case of x-symmetric defects and, even in this case, it does not provide information about the relation between the deffect shape and the resulting jump.…”

“…The analysis that can be found in the literature use the NLCME with some Dirac delta terms added to somehow take into account the localized effect of a narrow defect (see, e.g., [16,17,18]). These terms are added in a completely heuristic way, just to try to qualitatively reproduce the dynamics of the process, and they have no connection with the actual shape of the grating distortion.…”

“…(41)) is also better suited for numerical computations than the previous Dirac-delta formulation used in [16,17,18]. The Dirac-deltas have to be approximated by introducing very high values of the functions at a very narrow region of the spatial grid, and this procedure is obviously problematic from the point of view of ensuring the order of accuracy of the numerical method.…”

Breaking bonds in the atomic force microscope: Extracting information

“…The most widely cited approach to model this type of experiment was put forward by Evans and Ritchie, 5 who used a simplified form of the bond potential in order to calculate the loading-rate dependent breaking probability. Various authors have since extended this model taking into account rebinding, 6 multiple strands, 7 specific force profiles, 8 and to describe experiments with a constant force loading rate. 9,10 A lot of data have been analyzed recently with the help of Monte Carlo simulations.…”