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 galaxy buildup. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems, which is based on a periodic antiphase modulation of spectrally dependent losses arranged in a zigzag way: an effective filtering is imposed at symmetrically located wave numbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of both key classical concepts of modulation instabilities, i.e., the Benjamin-Feir instability and the Faraday instabiltyity. We demonstrate how the 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.

Observation of Geometric Parametric Instability Induced by the Periodic Spatial Self-Imaging of Multimode Waves

“…In the case of externally forced systems, PI is commonly referred to as the Faraday instability, following its initial observation in hydrodynamics under the external modulation of the vertical position of an open fluid tank [2]. Besides fluid mechanics, Faraday-like patterns were subsequently reported in a variety of physical contexts such as crystallization dynamics, chemical systems, or laser physics [3][4][5][6][7]. In addition to parametrically forced systems, many physical systems naturally exhibit collective oscillations that may lead to a so-called geometric-type of parametric instability (GPI).…”

Dissipative parametric modulation instability and pattern formation in nonlinear optical systems

“…Such a dynamics is different with respect to the growth process of sidebands modes in both well-known Benjamin-Feir and classical dispersive Faraday instability: in particular, in the former the growth is monotonic, while in the latter it is oscillatory, but the most unstable modes ±k m oscillate in phase. 13 We are hence in presence of a new growth dynamics which makes the dissipative parametric instability through zig-zag modulation of the dissipation for different spectral components a unique example in the landscape of nonlinear instabilities.…”

“…In this paper we describe in detail a recently proposed scheme of dissipative parametric modulation, achieved through spectrally dependent zig-zag filtering, which can be implemented both in nonlinear fiber lasers leading to the generation of stable pulse trains, and in spatially extended optical systems too, giving rise in that case to pattern formation in one and in two spatial dimensions. 13 The generated coherent structures undergo a self-similar periodic evolution that will be characterized in the following sections and are the new self-organized stable state achieved in the nonlinear stage of the instability.…”

High repetition rate multi-similariton laser

“…Institució We present the numerical demonstration of an harmonically mode-locked multi-similariton laser supporting a low jitter, stable train of self similar high repetition rate pulses exploiting, as mode-locking mechanism, the principle of dissipative Faraday instability (DFI) induced by zigzag modulation of spectral losses [1,2]. At variance with the theoretical and experimental studies on the DFI [1,2], where the amplification was distributed along the fiber, we propose here a lumped amplification scheme suitable for a more flexible design of mode-locked lasers pumped by rare-earth gain medium (Erbium, Ytterbium).…”