Suppression and Control of Modulation Instability

Author: Shubham Kumar
Title: Suppression and Control of  Modulation Instability
Director: Prof. Muriel Botey i Cumella, Prof. Ramon Herrero Simon and Prof. Kestutis Staliunas
Presentation date: June 21, 2017
Link to text: http:/www.tdx.cat/handle/10803/456080

Abstract: 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 spontaneously loses stability with respect to exponentially growing modulation modes. Therefore, the control and suppression of MI is vital for the stabilization of various such pattern- forming nonlinear systems. The stabilization of discrete systems, with a finite number of unstable modes, remain a difficult challenge in spite of the extensive attempts of the last few decades. The challenge is vastly greater in spatially- extended systems that present a continuum (infinite number) of unstable spatial modes, and their stabilization is a significantly more ambitious goal In this thesis, 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 point.

A second, much-more-powerful, mechanism is then developed, based on this initial understanding, in which the stabilization procedure is generalized, to form a ‘stabilization on demand’ scheme, which successfully suppresses the MI for highly complex nonlinear systems. This method relies on a Genetically Optimized multiple resonant modulations of the system’s potential, to suit arbitrarily complex stabilization requirements. These 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.

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 External Cavity Surface Emitting semiconductor lasers (VECSELs). In BAS amplifiers the stabilization relies on a two-dimensional spatial modulation of the pump current, provided, for instance, through fishnet-like electrodes. While in VECSELs, 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.