Spatially Dispersive Shock Waves in Nonlinear Optics

Barsi, Christopher; Wan, Wenjie; Jia, Shu; Fleischer, Jason W.

doi:10.1007/978-1-4614-3538-9_9

Cited by 3 publications

(5 citation statements)

References 114 publications

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“…Intense laser beam propagation through defocusing (normal dispersion) optical media can lead to the generation of DSWs. Observations in optical fibers [8,200,16] and in spatial optics [10,11,13,14,15,201] support the interpretation of light as a dispersive hydrodynamic medium.…”

Section: Dsws In Nonlinear Opticsmentioning

confidence: 71%

Dispersive shock waves and modulation theory

Hoefer

2016

Physica D: Nonlinear Phenomena

294

590

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There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.~B.~Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schr\"{o}dinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.Comment: review article, 68 pages, 52 figure

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Section: Dsws In Nonlinear Opticsmentioning

confidence: 71%

Dispersive shock waves and modulation theory

Hoefer

2016

Physica D: Nonlinear Phenomena

294

590

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“…is of particular interest due to recent experiments exhibiting DSWs [6,8,7,45,46]. For 0 < γ ≪ 1, the leading order behavior of (3.3) and (3.4) correspond to the cubic NLS.…”

Section: Gnls Equationmentioning

confidence: 98%

“…Slowly varying initial data ensures the applicability of the dispersionless system (4.4) up to breaking when t = O(1/ε). This choice of initial data has been used in photonic DSW experiments [45]. Figure 4 shows the results for the gNLS equation (3.1) with power law nonlinearity f (ρ) = ρ p .…”

Section: Dispersive Breaking Timementioning

confidence: 99%

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Shock Waves in Dispersive Eulerian Fluids

Hoefer

2014

J Nonlinear Sci

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The long time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convex or concave) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrödinger equation. These include superfluids (Bose-Einstein condensates and ultracold Fermions) and "optical fluids". Estimates of breaking times for smooth initial data and the long time behavior of the shock tube problem are presented. Numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory.

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“…In particular, it is well-known that light behaves as an ideal inviscid perfect fluid in an optical medium that exhibits a weakly self-defocusing Kerr nonlinearity 11,[18][19][20][21] . Accordingly, the propagation of light through such a medium can be modeled using shallow water wave Euler equations, which predict that any initial modulations experience a strong steepening that leads to the formation of a gradient catastrophe and subsequently DSWs 6,7,[19][20][21]29 . This analogy has attracted significant attention, as it highlights the elegant prospect of using nonlinear optical systems as convenient laboratory testbeds for the exploration of universal DSW physics.…”

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confidence: 99%

Vectorial dispersive shock waves in optical fibers

Nuño

Finot

et al. 2019

Commun Phys

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Dispersive shock waves are a universal phenomenon encountered in many fields of science, ranging from fluid dynamics, Bose-Einstein condensates and geophysics. It has been established that light behaves as a perfect fluid when propagating in an optical medium exhibiting a weakly self-defocusing nonlinearity. Consequently, this analogy has become attractive for the exploration of dispersive shock wave phenomena. Here, we observe of a novel class of vectorial dispersive shock waves in nonlinear fiber optics. Analogous to blast-waves, identified in inviscid perfect fluids, vectorial dispersive shock waves are triggered by a nonuniform double piston imprinted on a continuous-wave probe via nonlinear cross-phase modulation, produced by an orthogonally-polarized pump pulse. The nonlinear phase potential imparted on the probe results in the formation of an expanding zone of zero intensity surrounded by two repulsive oscillating fronts, which move away from each other with opposite velocities.

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Spatially Dispersive Shock Waves in Nonlinear Optics

Cited by 3 publications

References 114 publications

Dispersive shock waves and modulation theory

Dispersive shock waves and modulation theory

Shock Waves in Dispersive Eulerian Fluids

Vectorial dispersive shock waves in optical fibers

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