Soluble saturable refractive-index nonlinearity model

Wood, Van E.; Evans, E.D.; Kenan, Richard P.

doi:10.1016/0030-4018(88)90302-1

Cited by 50 publications

(19 citation statements)

References 15 publications

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“…20,21 The core material is assumed to have a self-defocusing saturable refractive index of the form [22][23][24] n NL (I) = − n 2 I sat 2 1 − 1…”

Section: 2mentioning

confidence: 99%

“…For definiteness, we present illustrative results for the case of γ = 0.2-note that the drift instability uncovered by Kivshar 24 does not tend to appear for that parameter choice. Equation (4.13) predicts bistability for solutions with ν = 1.0 and that the planewave backgrounds must have lower-and upper-branch peak intensities of ρ 0 2.383 and ρ 0 6.167, respectively (see Fig.…”

Section: Black Solitonsmentioning

confidence: 99%

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Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

Christian

Lundie

2017

J. Nonlinear Optic. Phys. Mat.

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We present, to the best of our knowledge, the first exact dark spatial solitons of a nonlinear Helmholtz equation with a self-defocusing saturable refractive-index model. These solutions capture oblique (arbitrary-angle) propagation in both the forward and backward directions, and they can also exhibit a bistability characteristic. A detailed derivation is presented, obtained by combining coordinate transformations and directintegration methods, and the corresponding solutions of paraxial theory are recovered asymptotically as a subset. Simulations examine the robustness of the new Helmholtz solitons, with stationary states emerging from a range of perturbed input beams.

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“…20,21 The core material is assumed to have a self-defocusing saturable refractive index of the form [22][23][24] n NL (I) = − n 2 I sat 2 1 − 1…”

Section: 2mentioning

confidence: 99%

Section: Black Solitonsmentioning

confidence: 99%

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

Christian

Lundie

2017

J. Nonlinear Optic. Phys. Mat.

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“…While several trial functions are available for describing a saturable refractive index [25][26][27], all of which share similar qualitative features, our principal interest lies with that proposed by Wood, Evans, and Kenan [28]. Their model appears to be unique in that it allows the corresponding governing equations to be integrated exactly-for instance, families of transverse guided modes in dielectric planar waveguides were obtained by solving the Helmholtz equation and enforcing continuity conditions at the boundary between substrates.…”

Section: Introductionmentioning

confidence: 99%

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems

2018

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We consider an envelope equation with space-time symmetry for describing scalar waves in systems with spatiotemporal dispersion and a generic saturable nonlinearity. Exact bright and gray solitons are derived by direct integration methods and coordinate transformations, with the results for cubicquintic systems [see companion article-submitted to Phys. Rev. A] recovered in the limit of weak saturation. Classic predictions from a nonlinear-Schrödinger formulation of the propagation problem are shown to emerge asymptotically as subsets of the more general spatiotemporal solutions. The robustness of the new solitons against perturbations to the local pulse shape is then tested by deploying integral stability criteria, symmetry principles, and numerical analysis.

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“…The most familiar generalizations are classic cubic-quintic [9][10][11][12][13] and the power-law [14,15] models. More complicated refractive-index distributions involve polynomial- [16][17][18] and saturable-type [19,20] non-linearities.…”

Section: Paraxial Versus Non-paraxial Solitonsmentioning

confidence: 99%

Helmholtz bright and boundary solitons

Christian¹,

McDonald²,

Chamorro‐Posada³

2007

J. Phys. A: Math. Theor.

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Abstract. We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as "edge solitons"). Extensive numerical simulations compare the stability properties of recentlyreported Helmholtz bright solitons, for this type of polynomial non-linearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts. Helmholtz bright and boundary solitons 2 IntroductionSolitons are ubiquitous entities in nature. Whenever linear effects (such as dispersion, diffraction or diffusion) are balanced exactly by non-linearity (self-phase modulation, self-focusing or reactionkinetic properties, respectively), robust self-trapped structures -solitons -can emerge as dominant modes of the system dynamics. These localized self-stabilizing non-linear waves arise widely in nature since quite different physical systems are governed by a relatively small set of universal equations, at least to first approximation. Solitons are often sech ("bell")-or tanh ("S")-shaped structures. The latter class are sometimes referred to as kink solitons, and they generally possess topologically non-trivial phase distributions. Phase-topological kink solitons appear in a range of physically diverse systems, and play the role of "fronts" and "domain walls". In classical mechanics, for example, they describe collective long-wave excitations on a line of weakly-coupled pendula. In condensed matter, kink solitons arise in simple models of one-dimensional lattice-dynamics when studying the motion of dislocations and domain walls in ferromagnetic crystals, and they also play a key role in the phenomenological understanding of phase transitions. In chemical kinetics, kink solitons appear as solutions to reaction-diffusion equations. They also occur in hydrodynamics, plasma physics, quantum field theory and cosmology. Comprehensive reviews of these systems can be found in Refs. [1][2][3][4].Our principle concern in this paper is with spatial soliton beams found in non-linear optics [5,6]. These types of soliton can arise when the tendency of a collimated light beam to diffract is opposed by the non-linear properties of the optical medium. When these two effects (diffractive broadening, and narrowing due to self-focusing) become comparable, then a stationary beam can exist whose transverse intensity distribution is invariant along the propagation direction. Spatial solitons are of theoretical interest as particular solutions to generic non-linear evolution equations, but they are also the subject of considerable experimental investigation. The robu...

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Soluble saturable refractive-index nonlinearity model

Cited by 50 publications

References 15 publications

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systems

Helmholtz bright and boundary solitons

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