Abstract
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin–Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system—spectrally dependent losses—achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin–Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.
Highlights
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems
Understanding the mechanisms underlying generation of coherent structures from noise or uniform field distribution is a fundamental problem of nonlinear science and its numerous practical applications ranging from biology to astrophysics
Modulation instability is responsible for the symmetry breaking of homogeneous spatiotemporal states or wave envelopes and the formation of stable patterns in a variety of physical media
Summary
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. We experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system—spectrally dependent losses—achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. Faraday instability, which results from the periodic in time modulation of a dispersive parameter of the system[12] and was studied in different systems, ranging from vertically shaken granular media[13] to periodically driven spatially extended chemical systems[14], repulsive (defocusing-type) Bose–Einstein condensates[15,16] and nonlinear optics[17,18]. A new dissipative type of Faraday instability was demonstrated theoretically[19], in the framework of the complex Ginzburg– Landau equation, where a suitable parametric modulation of spectral losses can lead to pattern formation. The experimental results are in a good agreement with theoretical predictions and numerical simulations
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