Article

Intrinsic localized modes in parametrically driven arrays of nonlinear resonators

Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel.
Physical Review E (Impact Factor: 2.33). 10/2009; 80(4 Pt 2):046202. DOI: 10.1103/PhysRevE.80.046202
Source: PubMed

ABSTRACT We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.

Full-text

Available from: Boris A. Malomed, Nov 05, 2014
1 Follower
 · 
112 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: The creation of stable 1D and 2D localized modes in lossy nonlinear media is a fundamental problem in optics and plasmonics. This article gives a mini review of theoretical methods elaborated on for this purpose, using localized gain applied at one or several hot spots (HS). The introduction surveys a broad class of models for which this approach was developed. Other sections focus in some detail on basic 1D continuous and discrete systems, where the results can be obtained, partly or fully, in an analytical form (and verified by comparison with numerical results), which provides deeper insight into the nonlinear dynamics of optical beams in dissipative nonlinear media. Considered, in particular, are the single and double HS in the usual waveguide with the self-focusing (SF) or self-defocusing (SDF) Kerr nonlinearity, which gives rise to rather sophisticated results in spite of apparent simplicity of the model, solitons attached to a PT-symmetric dipole embedded into the SF or SDF medium, gap solitons pinned to an HS in a Bragg grating, and discrete solitons in a 1D lattice with a hot site.
    Journal of the Optical Society of America B 10/2014; 31(10). DOI:10.1364/JOSAB.31.002460 · 1.81 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Both low frequency and high frequency impurity modes have been produced in a SiN micromechanical cantilever array by illumination with either an infrared or visible laser. When such laser-induced impurities are placed near a driven intrinsic localized mode (ILM) it is either repelled or attracted. By measuring the linear response spectrum for these two cases it was found that vibrational hopping of the ILM takes place when the natural frequency of the ILM and an even symmetry linear local mode are symmetrically located about the driven ILM frequency so that parametric excitation of these two linear modes is enhanced, amplifying the lateral motion of the ILM. Numerical simulations are consistent with these signature findings. It is also demonstrated that the correct sign of the observed interaction can be found with a harmonic lattice-impurity model but the magnitude of the effect is enhanced in a nonlinear lattice.
    Chaos An Interdisciplinary Journal of Nonlinear Science 12/2014; 25(1). DOI:10.1063/1.4905254 · 1.76 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: We report on an experimental observation of synchronization and abrupt transitions between standing wave patterns in arrays of micromechanical oscillators. The architecture of flexible cantilever arrays parametrically excited by and interacting through time-dependent fringing electrostatic fields allows tuning of an interaction potential and supports traveling waves. The arrays consisting of 500 mu m long and 5 mu m thick single crystal Si cantilevers were fabricated from silicon on insulator substrates. The out-of-plane resonant responses were visualized by time-averaged temporally aliased video imaging and measured by laser Doppler vibrometry. Our experimental and reduced order model results collectively demonstrate that under a slowly varying drive frequency the standing wave patterns remain unchanged in certain frequencies intervals, followed by an abrupt change in the pattern. (C) 2014 AIP Publishing LLC.
    Applied Physics Letters 08/2014; 105(7):071909. DOI:10.1063/1.4893593 · 3.52 Impact Factor