Thibault Congy



Contact Information

Institution:
Department of Mathematical Sciences Loughborough University
Loughborough, Leicestershire
LE11 3TU

Group: Linear and nonlinear waves
Mail: t.congy at lboro.ac.uk

Short CV: PDF


Ma tronche

Research activity

keywords: quantum fluids, nonlinear optics, shock wave, instability

Caustic For my PhD project, I studied self-accelerating Airy beams with the experimental group of S. Barad (Tel Aviv University). These nondiffracting auto - accelerating waves have received considerable attention in recent years. We showed that they can form spontaneously as a laser beam propagates in a defocusing nonlinear medium, inside a cylindrical channel with a reflective boundary. The beam forms a ring-shaped optical caustic, which, following reflection from the boundary, converges to a focal point. By means of a semi-classical treatment, we have demonstrated that the radially symmetric wave has an Airy-function profile.
Modulational instability I have also been interested in nonlinear effects in two-component Bose-Einstein condensates in one dimension. Using a muliple scale expansion, we have shown that these condensates experience phenomena similar to those encoutered in fluid mechanics or nonlinear optics. Nonlinear density excitations are well described by a KdV-type equation. In the presence of spin-orbit coupling, excitations of the polarization experience modulational instabilities also known as the Benjamin-Feir instability.
Shock wave In the limit where intra-species and inter-species interaction constants are very close, the dynamics of the density and the polarization waves decouple. The polarization wave-dynamics is governed by the dissipationless Landau-Lifshitz equation. Dispersive shock waves (DSW) can be observed in this system. Thanks to the Whitham theory of waves modulation, we have described the DSW within the Gurevitch-Pitaevskii scheme. The DSW can be seen as a nonlinear periodic wave for which its parameters (amplitude, velocity, ...) vary slightly over one period of space and time.
Snaking!
In 2013 I did a 3 months internship at Trento. Under the supervision of F. Dalfovo, I studied the stability of solitons in two-dimensional Bose-Einstein condensate. Grey solitons in condensate with repulsive interractions undergo a dynamical instability for long wavelength transverse excitations. This phenomenon is called « snake oscillations ».
Numerical simulation of the 2D Gross-Pitaevkii equation for an initial 1D dark-soliton profile (k represents the wavenumber of the transverse excitation)
k=30 (WEBM GIF)   k=60 (WEBM GIF)