Waves, Solitons and Turbulence in Optical Systems - Abstract

Staliunas, Kestutis

A novel zig-zag-like modulation instability, and its realization in nonlinear optics

Pattern formation in nonlinear spatially extended systems (including nonlinear optical systems) universally occur through modulation instabilities: a homogeneous state loses its stability with respect to growing modulation modes. Well known modulation instabilities are so called Benjamin Feir instability, also parametric (Faraday) instabilities. We report a novel type of instabilty, principally different from the above mentioned known instabilities. The instability we report relies on the specially modulated (in spectral domain) losses: the losses are applied alternatively on the "left" and on the "right" wing of spectra (here comes the zig-zag-like character). We note that losses (e.g. diffusion) generally stabilize the system, by damping potentially unstable modes. In the case proposed by us, when the losses applied in a zig-zag way, the process counterintuitively excites the modulation modes, and the patterns. We will present the theory of such zig-zag instability in general (on modulated Ginzburg-Landau equation), and provide numerical calculations justifying predictions in several specific cases: laser with manipulated losses, and the fiber laser. In the latter case we also present the experimental demonstration of instability, and the recordings of emerging patterns.