We demonstrate that the \(1+1\) dimensional, normal-dispersion, nonlinear Schrödinger equation with an “internal viscosity” has a stable “dark” shock wave (SW) solution, which is the invasion of the empty (dark) domain into the energy-carrying one. It may be interpreted as an optical SW in a loss-compensated nonlinear optical fiber. We predict that it can be created experimentally with a temporal width of a few picoseconds at a carrier-wave background power about 10 W. We develop a theoretical analysis that captures the physics of the SW propagation. The prediction that the SW velocity has a constant value in the limit of small viscosity, and scales as the square root of the viscosity in the large viscosity limit, are confirmed by the full dynamics simulations.
ASJC Scopus subject areas
- Physics and Astronomy(all)