Snake instability of the 2+1D spatio-temporal bright soliton stripe

This paper presents an experimental study of the stability of the bright soliton stripe ruled by the 2+1D hyperbolic nonlinear Schrodinger (NLS) equation. From a mathematical viewpoint, the originality of this demonstration is to provide evidence for the existence of an antisymmetric unstable mode in the bright soliton stripe of the hyperbolic NLS equation. This experiment has been performed with femtosecond laser pulses so that the sech-shaped soliton envelope is generated in the temporal domain while the spatial transverse coordinate constitutes the homogeneous coordinate of the stripe. These pulses propagating in a planar AlGaAs waveguide exhibits a self-defocusing Kerr nonlinearity at photon energies just below the energy bandgap. Since the chromatic dispersion of AlGaAs is positive (normal dispersion) close to the bandgap energy, the spatio-temporal propagation equation must include a second-order derivative with a sign opposite to that of diffraction. Therefore this system is ruled by the 2+1D hyperbolic NLS equation.