Pattern generation by dissipative parametric instability

Abstract

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic antiphase modulation of spectrally-dependent losses arranged in a zig-zag way: an effective filtering is imposed at symmetrically located wavenumbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of the both key classical concepts of modulation instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate how dissipative parametric instability can lead to the formation of stable patterns in one and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems.

References in corpus (5)

• Quantum fluids of light
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Transverse Patterns in Nonlinear Optical Resonators
• Modulational instability in dispersion oscillating fiber ring cavities
• Modulational instability in a layered Kerr medium: Theory and Experiment

Cited by in corpus (10)

• Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves
• Observation of mode-locked spatial laser solitons
• Stabilization of Broad Area Semiconductor Laser sources by simultaneous index and pump modulations
• Threshold of complexity and Arnold tongues in Kerr ring microresonators
• Universal threshold and Arnold tongues in Kerr ring microresonators
• Theory of filter-induced modulation instability in driven passive optical resonators
• Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide
• Self-induced Faraday instability laser
• Dissipative Dicke time crystals: an atoms' point of view
• Noise-induced standing waves in oscillatory systems with time-delayed feedback