Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

Chen, Shihua; Baronio, Fabio; Soto-Crespo, J. M.; Grelu, Philippe; Mihalache, Dumitru

doi:10.1088/1751-8121/aa8f00

Cited by 186 publications

(113 citation statements)

References 223 publications

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“…For two polarization components, the corresponding set of two coupled NLSEs is completely integrable. In this framework [55], polarizationmodulation instability was found to be the origin of coupled bright or dark rogue waves [40,56].…”

Section: Modulation Instability and Dark Rogue Wavesmentioning

confidence: 98%

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

et al. 2020

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Material characteristics and input-field specifics limit controllability of nonlinear electromagneticfield interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves. Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.field [18]. In the past few decades, experimental and theoretical investigations(for an intuitive explanation of dealing with plasmonic loss for waveguide application, see [19]) report stable propagation of linear and nonlinear SPWs employing ultra-low loss metallic-type layers such as single-crystal [20] and mono-crystal [21] metallic film, structured Fano metamaterials [22], semiconductor metamaterials [23] and superconducting metamaterials [24]. These investigations reveal that plasmonic excitation and stable propagation need minimal metallic nanostructure roughness [25]. Therefore, polaritonic frequency combs, and generally space-time control of nonlinear SPWs, are unfortunately challenging due to material limitations and driving field characteristics [26-28].Propagation of an optical pulse in nonlinear media leads to the appearance of strongly localized bright and dark waves such as soliton [29], rogue waves and breathers in nearly conservative systems [30]. Bright rogue waves and breathers are highly localized nonlinear solitary waves with oscillatory amplitudes [31,32]. These waves are valuable for their applications to phase and intensity modulation schemes [33,34], as well as the formation of bound states and molecule-like behavior [35]. More generally, dissipative rogue waves and breathers [36] have potential applications to nonlinear systems such as mode-locked lasers [37] and frequencycomb generators [38]. By contrast, dark rogue waves were only observed during multimode polarized light propagation ...

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Section: Modulation Instability and Dark Rogue Wavesmentioning

confidence: 98%

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

et al. 2020

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“…2(g) and 2(i)]. Among mechanisms for rogue wave excitation [2], the MI analysis, which uncovers the growth of periodic perturbations on an unstable continuous-wave background, opens a convenient way for understanding and predicting the rogue waves [10,23,45]. For our coupled NLS-MB system (8), the plane-wave solutions (14) are perturbed according to…”

Section: Intriguing Rogue Wave Dynamicsmentioning

confidence: 99%

“…This great success is the result of the fundamental interest on one side, and the multidisciplinary diffusion of soliton concept a few decades ago on the other side, as both solitons and rogue waves are associated to the integrability of a class of nonlinear wave equations and generally share the same Darboux transformation [10]. Compared to the stationary solitons, rogue waves are modeled as transient wave-packets localized in both space and time, to mimic the episodic giants that seemingly appear from nowhere and disappear without a trace [11].…”

Section: Introductionmentioning

confidence: 99%

“…Rogue wave research flourishes now in both theoretical and experimental aspects [10,12,14], providing novel perspectives for the manifestation of extreme waves in a variety of nonlinear media. To reflect the diversity and complexity of media, it requires the study of the propagation models that go beyond the scalar nonlinear Schrödinger (NLS) equation, such as the extended scalar models [15][16][17][18] and the coupled multicomponent models [19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

Chen

Baronio

et al. 2017

Opt. Express

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Abstract:The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

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“…What is more, a hierarchy of other soliton equations have also been verified possessing different types of RW solutions [59][60][61][62][63]; for a recent review on rogue waves in scalar, vector, and multidimensional nonlinear systems, see Ref. [64].…”

Section: Introductionmentioning

confidence: 99%

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

Cao

Mihalache

2018

Nonlinear Dyn

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A new variant of the (2 + 1)-dimensional [(2 + 1)d] Boussinesq equation was recently introduced by J. Y. Zhu, arXiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended (2 + 1)d Boussinesq equation by using the traveling wave method. Second, N -soliton, breather, and rational solutions are obtained by using the Hirota bilinear method and the long wave limit. Nonsingular rational solutions of two types were obtained analytically, namely: (i) rogue-wave solutions having the form of W-shaped lines waves and (ii) lump-type solutions. Two generic types of semi-rational solutions were also put forward. The obtained semi-rational solutions are as follows: (iii) a hybrid of a first-order lump and a bright one-soliton solution and (iv) a hybrid of a first-order lump and a first-order breather.

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Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

Cited by 186 publications

References 223 publications

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

Surface-polaritonic phase singularities and multimode polaritonic frequency combs via dark rogue-wave excitation in hybrid plasmonic waveguide

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

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