Gap solitons in Bragg gratings with dispersive reflectivity

Atai, Javid; Malomed, Boris A.

doi:10.1016/j.physleta.2005.05.081

Cited by 72 publications

(29 citation statements)

References 36 publications

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“…This agrees very well with the numerical results [34,36]. For m = 0.3, (6) predicts that sidelobes exist in the range −0.75 ω 0.75.…”

Section: Analysis Of Soliton Tailssupporting

confidence: 90%

“…[34][35][36] it was reported that there exists a critical value of the dispersive reflectivity parameter above which sidelobes appear in the solitons' profiles. Formation of sidelobes may be characterized by means of an asymptotic analysis of soliton's tail.…”

Section: Analysis Of Soliton Tailsmentioning

confidence: 99%

“…In Refs. [34,35] a model was proposed that takes into regard the spatial dispersion of reflectivity. A key result in these works is that, for both quiescent and moving GSs, dispersive reflectivity results in the expansion of the stability region.…”

Section: Introductionmentioning

confidence: 99%

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Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Dasanayaka

Atai

2011

Phys. Rev. E

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Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

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“…This agrees very well with the numerical results [34,36]. For m = 0.3, (6) predicts that sidelobes exist in the range −0.75 ω 0.75.…”

Section: Analysis Of Soliton Tailssupporting

confidence: 90%

Section: Analysis Of Soliton Tailsmentioning

confidence: 99%

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Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Dasanayaka

Atai

2011

Phys. Rev. E

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“…One possible modification that was proposed in Ref. (36) is to incorporate the contribution of spatial dispersion of Bragg reflectivity into the standard model. Such a model may be applicable to systems where reflection spectra have broad and inhomogeneous bandgaps, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Bragg superstructures (37,38) and gratings written on photonic wires (39). It was also shown that the presence of dispersive reflectivity does significantly alter the stability of solitons and the outcomes of their collisions (36,40).…”

Section: Introductionmentioning

confidence: 99%

Interaction dynamics of Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

Chowdhury

Atai

2016

Journal of Modern Optics

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The interactions of quiescent Bragg grating (BG) solitons in a semilinear dual-core system, where one core is nonlinear and is equipped with a BG with dispersive reflectivity and the other core is linear are investigated. It has been previously shown that the model supports stable quiescent solitons which may or may not have sidelobes in their profiles. The interaction of in-phase solitons can lead to various outcomes such as generation of two moving solitons with equal or unequal velocities, merger of solitons into a quiescent one, generation of three solitons (one quiescent and two moving ones) and destruction of solitons. The presence of sidelobes can radically change the interaction dynamics, e.g. in-phase solitons can repel or form a temporary bound state which subsequently splits into two separating solitons. We have identified the outcome regions for in-phase interactions through systematic numerical simulations in the plane of dispersive reflectivity vs. frequency. We have also analysed the effect of initial separation on the outcomes of interactions. It is found that when sidelobes are present in solitons' profiles, the outcomes of the interactions are strongly dependent on the initial separation. ARTICLE HISTORY

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Solitary waves described by a high‐order system in optical fiber Bragg gratings with arbitrary refractive index

Кан

Kudryashov

2021

Math Methods in App Sciences

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A system of the fourth-order nonlinear differential equations for description of wave propagation in optical fiber Bragg gratings is considered. This system of equations also takes into account arbitrary refractive index. The model includes non-local nonlinearity too. The studied system of equations is transformed into a system of ordinary differential equations using traveling wave variables. Compatibility conditions for the obtained system are defined and analyzed. Exact solutions of the model in the form of solitary waves are found.

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Gap solitons in Bragg gratings with dispersive reflectivity

Cited by 72 publications

References 36 publications

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Interaction dynamics of Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

Solitary waves described by a high‐order system in optical fiber Bragg gratings with arbitrary refractive index

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