Suppression and control of modulation instability

Resumen

Dynamical instabilities which lead to spontaneous pattern formation are present in a wide variety of nonlinear dynamical systems, both in nature as well as in technological areas. The instabilities may be saturating, leading to stationary and regular patterns, or not, leading to complex periodic structures or spatiotemporal chaos. Such pattern formation occurs universally, ranging diversely from fields such as biology and ecology to optics, hydrodynamics, condensed matter systems etc. Modulation Instability (MI), initially studied on systems such as deep-water waves, plasmas, nonlinear optics, and electromagnetics, is crucial to many current key technologies and research fields such as lasers, chemical systems, Bose-Einstein condensates of attracting atoms, high energy physics, ecology and vegetation, hydrodynamics, astrophysics etc. Despite the enormous variety of patterns in various different systems, the onset of such unstable spatiotemporal dynamics always originates through a modulation instability, when the initial, maximally-symmetric homogeneous state of the system spontaneous loses stability with respect to exponentially growing modulation modes. Therefore, the control and suppression of the MI, especially in spatially-extended systems that present a continuum (an infinite number) of unstable spatial modes, is vital for the stabilization of various such pattern-forming nonlinear systems and achieving this remains an ambitious goal. In this study, a fundamental new understanding of the MI in spatially-extended systems is developed, and a mechanism for the complete suppression of MI in such unstable systems is presented. The mechanism relies on an appropriate manipulation of the dispersion of the system, through a properly designed spatiotemporal modulation of its potential. This mechanism of MI suppression relies on a `resonant¿ interaction between the spatial and temporal frequencies of the modulation, which only occurs when the modulation geometry is close to the resonance. A second, much-more powerful, mechanism is also developed based on this initial understanding, in which the stabilization procedure is generalized, to form a `stabilization on demand¿ scheme, which achieves successful stabilization even for highly complex nonlinear systems. This method, based on the introduction of multiple `resonant¿ modulations of the system¿s potential relies on a Genetic Algorithm based optimization procedure, to suit arbitrarily complex stabilization requirements in various systems. The results bear general character, as they have been developed on the Complex Ginzburg-Landau model, which provides a universal description of MI across various systems from lasers to chemical systems, Bose-Einstein condensates, biological systems etc. Lastly, both methods are successfully applied to real-world systems, by providing a robust stabilization of MI in Broad Area Semiconductor (BAS) amplifiers and Vertical Cavity Surface Emitting semiconductor lasers. In BAS amplifiers the stabilization relays on a two-dimensional spatial modulation of the pump current, as may be provided through fishnet-like electrodes. While in the case of Vertical Cavity lasers the same may be achieved via a spatiotemporal modulation. These results have been demonstrated for realistic parameters, including large nonlinear coefficients and at high operating powers, representing a significant breakthrough in the stabilization of these widely prevalent and indispensable photonic devices.