Observation of the snake instability of a spatially extended temporal bright soliton

Abstract

The transverse snake instability of the bright soliton solution of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation is experimentally studied. We observed this instability in the spatial distribution of the temporal spectrum of spatially extended femtosecond pulses propagating in normally dispersive self-defocusing planar semiconductor waveguide.

On transverse stability of discrete line solitons

“…It is well known that in homogeneous media, line solitons in the nonlinear Schrödinger (NLS) equation and other related wave equations are always transversely unstable [32] (see also [2,8,9] for applications in optics and [17,29] for reviews). This instability has been observed in recent optical experiments [11,12,19]. In the presence of a one-dimensional periodic potential, many line solitons are still transversely unstable [1,22].…”

Elimination of transverse instability in stripe solitons by one-dimensional lattices

“…It is well known that in homogeneous nonlinear optical media, a bright soliton stripe, uniform along the transverse stripe (say y) direction but localized along the orthogonal transverse (say x) direction, is unstable upon propagation along the longitudinal z direction when transverse perturbations are present [1][2][3][4][5][6][7][8][9]. When a onedimensional (1D) optical lattice is introduced along the x or y direction, the soliton stripe is still transversely unstable under self-focusing nonlinearity [10,11].…”

Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion

“…This process is usually called modulational instability (MI). Spatio-temporal dynamics induced by solitonic MI in continuous systems has not only been studied theoretically [10,11,12], but more recently observed experimentally [13,14,15]. Similar instabilities can be expected to occur for the discrete solitons in waveguide arrays.…”