Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

Isoard, Mathieu; Камчатнов, А. М.; Pavloff, Nicolas

doi:10.1103/physreva.99.053819

Cited by 28 publications

(39 citation statements)

References 53 publications

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“…Consequently, small oscillating fluctuations of the beam intensity field on top of a fixed background are described by the standard Bogoliubov theory [18][19][20][21], as was recently confirmed experimentally [14,17]. Large perturbations on top of a small background on the other hand lead to the creation of dispersive shock waves [22][23][24][25]. Recently, this platform was also exploited to explore the generation of topological defects and the associated turbulence [26,27], as well as analogue cosmological Sakharov oscillations in the density-density correlations of a quantum fluid of light [28,29].…”

Section: Introductionmentioning

confidence: 83%

“…The = case is instead used to define the norm N r (q ⊥ ) of the -th Bogoliubov mode. These conditions summarize as i X † 0, (q ⊥ )Π * 0, (q ⊥ ) − Π T 0, (q ⊥ )X 0, (q ⊥ ) = N r (q ⊥ )δ (24) (in this section we do not sum over repeated indices). Notice that the norm is real and can be either positive or negative.…”

Section: Properties Of Bogoliubov Modes and Orthonormalization Relationsmentioning

confidence: 99%

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Spin-orbit-coupled fluids of light in bulk nonlinear media

Martone,

Bienaimé,

Cherroret

2021

Preprint

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We show that nonparaxial polarized light beams propagating in a bulk nonlinear Kerr medium naturally exhibit a coupling between the motional and the polarization degrees of freedom, realizing a spin-orbit-coupled mixture of fluids of light. We investigate the impact of this mechanism on the Bogoliubov modes of the fluid, using a suitable density-phase formalism built upon a linearization of the exact Helmholtz equation. The Bogoliubov spectrum is found to be anisotropic, and features both low-frequency gapless branches and high-frequency gapped ones. We compute the amplitudes of these modes and propose a couple of experimental protocols to study their excitation mechanisms. This allows us to highlight a phenomenon of hybridization between density and spin modes, which is absent in the paraxial description and represents a typical fingerprint of spin-orbit coupling.

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Section: Introductionmentioning

confidence: 83%

Section: Properties Of Bogoliubov Modes and Orthonormalization Relationsmentioning

confidence: 99%

Spin-orbit-coupled fluids of light in bulk nonlinear media

Martone,

Bienaimé,

Cherroret

2021

Preprint

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“…Near this edge, solutions of Whitham's equations are selfsimilar and depend on the variable z = x/t 1/3 . Although this solution can be obtained in analytic form [43,44], the self-similarity domain is relatively small, and we do not discuss this theory here. The solution of Whitham's equations in the entire DSW domain was obtained in [29,44].…”

Section: Motion Of Edges Of Dispersive Shock Wavesmentioning

confidence: 99%

“…Although this solution can be obtained in analytic form [43,44], the self-similarity domain is relatively small, and we do not discuss this theory here. The solution of Whitham's equations in the entire DSW domain was obtained in [29,44]. In approaching the small-amplitude edge, the DSW evolution again becomes self-similar, with the modulation parameters depending on z = x/t.…”

Section: Motion Of Edges Of Dispersive Shock Wavesmentioning

confidence: 99%

Gurevich–Pitaevskii problem and its development

Камчатнов¹

2021

Phys.-Usp.

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We present an introduction to the theory of dispersive shock waves in the framework of the approach proposed by Gurevich and Pitaevskii (Zh. Eksp. Teor. Fiz., 65, 590 (1973) [Sov. Phys. JETP, 38, 291 (1974)]) based on the Whitham theory of modulation of nonlinear waves. We explain how Whitham equations for a periodic solution can be derived for the Korteweg-de Vries equation and outline some elementary methods to solve them. We illustrate this approach with solutions to the main problems discussed by Gurevich and Pitaevskii. We consider a generalization of the theory to systems with weak dissipation and discuss the theory of dispersive shock waves for the Gross-Pitaevskii equation.Dedicated to the 90th birthday of A. V. Gurevich Content 1. Introduction 2. Korteweg-de Vries equation 3. Modulation of linear waves 4. Whitham theory 5. Generalized hodograph method 6. Formulation of the Gurevich-Pitaevskii problem 7. Evolution of the initial discontinuity in the Korteweg-de Vries theory 8. Breaking of the wave with a parabolic profile 9. Breaking of a cubic profile 10. Motion of edges of dispersive shock waves 11. Theorem on the number of oscillations in dispersive shock waves 12. Theory of dispersive shock waves for the Korteweg-de Vries equation with dissipation 13. Gross-Pitaevskii equation 14. Evolution of the initial discontinuity in the Gross-Pitaevskii theory 15. Piston problem 16. Uniformly accelerated piston problem 17. Motion of edges of 'quasi-simple' dispersive shock waves 18. Breaking of a cubic profile in the Gross-Pitaevskii theory 19. Conclusions References

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“…In optics, the hydrodynamics interpretation relies on the Madelung transforms which identify the light intensity to the fluid density and the phase gradient to the fluid velocity [18]. Recently several works have studied analytically shock wave formation in one and two dimensions [19,20]. Optical systems allow for repeatable experiments and precise control of the experimental parameters.…”

Section: Introductionmentioning

confidence: 99%

Blast waves in a paraxial fluid of light

Abuzarli,

Bienaimé,

Giacobino

et al. 2021

Preprint

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We study experimentally blast wave dynamics on a weakly interacting fluid of light. The fluid density and velocity are measured in 1D and 2D geometries. Using a state equation arising from the analogy between optical propagation in the paraxial approximation and the hydrodynamic Euler's equation, we access the fluid hydrostatic and dynamic pressure. In the 2D configuration, we observe a negative differential hydrostatic pressure after the fast expansion of a localized over-density, which is a typical signature of a blast wave for compressible gases. Our experimental results are compared to the Friedlander waveform hydrodynamical model [1]. Velocity measurements are presented in 1D and 2D configurations and compared to the local speed of sound, to identify supersonic region of the fluid. Our findings show an unprecedented control over hydrodynamic quantities in a paraxial fluid of light.

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Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

Cited by 28 publications

References 53 publications

Spin-orbit-coupled fluids of light in bulk nonlinear media

Spin-orbit-coupled fluids of light in bulk nonlinear media

Gurevich–Pitaevskii problem and its development

Blast waves in a paraxial fluid of light

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