Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes

AbstractCarbon nanotube (CNT) can work as excellent saturable absorber (SA) due to its advantages of fast recovery, low saturation intensity, polarization insensitivity, deep modulation depth, broad operation bandwidth, outstanding environmental stability, and affordable fabrication. Its successful application as SA has promoted the development of scientific research and practical application of mode-locked fiber lasers. Besides, mode-locked fiber laser constitutes an ideal platform for investigating soliton dynamics which exhibit profound nonlinear optical dynamics and excitation ubiquitous in many fields. Up to now, a variety of soliton dynamics have been observed. Among these researches, CNT-SA is a key component that suppresses the environmental perturbation and optimizes the laser system to reveal the true highly stochastic and non-repetitive unstable phenomena of the initial self-starting lasing process. This review is intended to provide an up-to-date introduction to the development of CNT-SA based ultrafast fiber lasers, with emphasis on recent progress in real-time buildup dynamics of solitons in CNT-SA mode-locked fiber lasers. It is anticipated that study of dynamics of solitons can not only further reveal the physical nature of solitons, but also optimize the performance of ultrafast fiber lasers and eventually expand their applications in different fields.

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Theory of the deformation of aligned polyethylene

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0171 ◽

2015 ◽

Vol 471 (2180) ◽

pp. 20150171 ◽

Cited By ~ 7

Author(s):

A. Hammad ◽

T. D. Swinburne ◽

H. Hasan ◽

S. Del Rosso ◽

L. Iannucci ◽

...

Keyword(s):

Load Transfer ◽

Tensile Load ◽

Equation Of Motion ◽

Dislocation Dynamics ◽

Viscoelastic Deformation ◽

Transfer Length ◽

Soliton Dynamics ◽

Fluctuation Dissipation ◽

Pull Out ◽

Definition Of

Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel–Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies between solitons and an equation of motion for solitons are derived. The equation of motion is based on Langevin dynamics and the fluctuation–dissipation theorem and it leads to the rigorous definition of an effective mass for solitons. It forms the basis of a soliton dynamics in direct analogy to dislocation dynamics. Close parallels are drawn between solitons in aligned polymers and dislocations in crystals, including the configurational force on a soliton. The origins of the strain rate and temperature dependencies of the viscoelastic behaviour are discussed in terms of the formation energy of solitons. A failure mechanism is proposed involving soliton condensation under a tensile load.

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