Waves Called Solitons

Remoissenet, M.

doi:10.1007/978-3-662-03321-0

Cited by 274 publications

(297 citation statements)

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“…As indicated up to now, the nonlinear metamaterial work that is emerging globally builds, credibly, upon the fact that solitons [8,9] already have well-known roots in hydrodynamics dating back to John Scott Russell in 1834. It is interesting that this early work was not appreciated for some considerable time, yet, like the metamaterial world, it was also a global revolution.…”

Section: Introductionmentioning

confidence: 93%

“…It is set up to lead to computer simulation of the behaviour of the double negative member of the metamaterial family. Since the type of NLSE produced here is dispersion-based it is capable of generating nonlinear waves called temporal solitons [8,9] in such metamaterials. As discussed, in detail, later on, soliton means a nonlinear wave, in the form of a pulse, or a beam, in which broadening due to dispersion, or diffraction, is balanced by the presence of nonlinear amplitudes.…”

Section: Introductionmentioning

confidence: 99%

“…As discussed, in detail, later on, soliton means a nonlinear wave, in the form of a pulse, or a beam, in which broadening due to dispersion, or diffraction, is balanced by the presence of nonlinear amplitudes. Hence, the temporal soliton [8,9] family member is a pulse in which broadening due to linear dispersion is balanced by the nonlinearity. It is selected here, without loss of generality, because it can form the basis of a delightful discussion of what have become known as rogue waves [10].…”

Section: Introductionmentioning

confidence: 99%

“…The pulse-based basic physics of stable nonlinear excitations is that they rely upon balancing phase changes across their width that arise from the material dispersion and nonlinearity. They are stable if they are described by what is known as the one-dimensional cubic nonlinear [8,9] Schrödinger equation (NLSE) briefly introduced earlier on. This fundamental one-dimensional NLSE is a completely satisfactory model to describe how electromagnetic pulses behave in a bounded dielectric, but any important additions to this basic equation have to be investigated as well and leads us towards the appreciation of the self-steepenng of pulses, for example.…”

Section: Introductionmentioning

confidence: 99%

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Waves in hyperbolic and double negative metamaterials including rogues and solitons

et al. 2017

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The topics here deal with some current progress in electromagnetic wave propagation in a family of substances known as metamaterials. To begin with, it is discussed how a pulse can develop a leading edge that steepens and it is emphasised that such self-steepening is an important inclusion within a metamaterial environment together with Raman scattering and third-order dispersion whenever very short pulses are being investigated. It is emphasised that the self-steepening parameter is highly metamaterial-driven compared to Raman scattering, which is associated with a coefficient of the same form whether a normal positive phase, or a metamaterial waveguide is the vehicle for any soliton propagation. It is also shown that the influence of magnetooptics provides a beautiful and important control mechanism for metamaterial devices and that, in the future, this feature will have a significant impact upon the design of data control systems for optical computing. A major objective is fulfiled by the investigations of the fascinating properties of hyperbolic media that exhibit asymmetry of supported modes due to the tilt of optical axes. This is a topic that really merits elaboration because structural and optical asymmetry in optical components that end up manipulating electromagnetic waves is now the foundation of how to operate some of the most successful devices in photonics and electronics. It is pointed out, in this context, that graphene is one of the most famous plasmonic media with very low losses. It is a two-dimensional material that makes the implementation of an effectivemedium approximation more feasible. Nonlinear non-stationary diffraction in active planar anisotropic hyperbolic metamaterials is discussed in detail and two approaches are compared. One of them is based on the averaging over a unit cell, while the other one does not include sort of averaging. The formation and propagation of optical spatial solitons in hyperbolic metamaterials is also considered with a model of the response of hyperbolic metamaterials in terms of the homogenisation ('effective medium') approach. The model has a macroscopic dielectric tensor encompassing at least one negative eigenvalue. It is shown that light propagating in the presence of hyperbolic dispersion undergoes negative (anomalous) diffraction. The theory is ten broadened out to include the influence of the orientation of the optical axis with respect to the propagation wave vector. Optical rogue waves Nanotechnology Nanotechnology 28 (2017) 444001 (41pp) https://doi.org/10.1088/1361-6528/aa679211 Author to whom any correspondence should be addressed.0957-4484/17/444001+41$33.00 © 2017 IOP Publishing Ltd Printed in the UK 1 are discussed in terms of how they are influenced, but not suppressed, by a metamaterial background. It is strongly discussed that metamaterials and optical rogue waves have both been making headlines in recent years and that they are, separately, large areas of research to study. A brief background of the inevitable linkage of them i...

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Waves in hyperbolic and double negative metamaterials including rogues and solitons

et al. 2017

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“…It should be remarked at this point, that discretization may affect through ͗␥ l ͘ most simulations of thermal pair nucleation too. 2,13 The question of an independent determination of M l could be tackled for instance in the underdamped diffusion regime, ␣Ӷ 0 , at the cost of large radiation effects. 12,18 Alternately, one could study the oscillations of a trapped, frictionless soliton around a minimum of the PN potential, 30 or rely on a collective variable scheme.…”

Section: B the Kink Effective Massmentioning

confidence: 99%

Elastic strings in solids: Discrete kink diffusion

et al. 2001

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The diffusive dynamics of a single discrete 4 soliton coupled to an overdamped heat bath is analyzed in detail. The Langevin equation for the soliton center of mass is derived in general form and compared with the outcome of extensive numerical simulation. The effective mass of the moving soliton must be renormalized dynamically for lattice constants of the order of its size or smaller. The corresponding mobility curve and diffusion coefficient are determined numerically: At variance with the earlier literature, discreteness effects persist even at high temperature and in the presence of strong drives.

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A thermodynamic theory on the nonlinear viscoelasticity of glassy polymers, 1. Constitutive equation

Cho¹,

Kim

2000

Macromol. Theory Simul.

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Waves Called Solitons

Cited by 274 publications

References 0 publications

Waves in hyperbolic and double negative metamaterials including rogues and solitons

Waves in hyperbolic and double negative metamaterials including rogues and solitons

Elastic strings in solids: Discrete kink diffusion

A thermodynamic theory on the nonlinear viscoelasticity of glassy polymers, 1. Constitutive equation

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