Search results for "Stability"
showing 10 items of 3085 documents
Bistable phase locking in a low fresnel number nondegenerate optical oscillator with injected signal
2011
Degenerate four-wave mixing oscillators are phase-bistable cavities. In such systems, above the oscillation threshold, two equivalent states, of equal intensities but opposite phases are generated. This phase bistability extends over the whole range of stable emission, unlike the intensity bistability (in, e.g. a saturable absorber cavity) that exits in a limited range of injection. When the cavity Fresnel number is large different patches of the beam transverse section can have different phases and a pattern forms. Basic patterns here are phase fronts (or domain walls), which are 1D structures separating regions with opposite phase that manifest as dark lines (as the phase jumps by p acros…
Bistable phase locking in rocked lasers
2006
Abstract We investigate analytically and numerically the dynamics of single mode lasers with periodic ac injection (rocked lasers). Such lasers show phase bistability as the phase of the light emitted by such lasers can lock to either of two values shifted by π. Locking regimes for different lasers are studied showing that the system response is strongly modified in class B lasers due to the influence of relaxation oscillations.
Cavity solitons in lasers with spatially modulated injected signal
2009
The injection of a monochromatic signal into a laser is a well-known technique for locking the laser phase to that of the injection. Some years ago another type of injection, called rocking [1,2], was introduced to render the laser phase-locking bistable. Rocking consists of the modulation of the amplitude injection so that its sign changes periodically, or even randomly [3], in time. Here we present an alternative to rocking that leads to the same type of behaviour, namely the appearance of bistable phase locking and, in the case of large Fresnel number lasers, to stable (phase bistable) cavity solitons and extended patterns. The new type of injection we present here is monochromatic, unli…
STRUCTURAL INSTABILITY IN FERROELECTRICS: SUPERIMPOSING HAMILTONIAN AND STOCHASTIC DYNAMICS
2008
ABSTRACT Structural instability of ferroelectrics distinguished by appearance of coexisting phases and spatial inhomogeneity is at variance with the predictions of statistics in the canonical ensemble. A more refined description includes ergodicity breaking which become apparent at critical temperature when the system resides in metastable state and its development lead to one of possible minimum energy states. In this study the domain growth and switching is reproduced within the framework of Fokker-Planck approach. The mathematical technique is developed for empiric Landau Hamiltonians and improved for application to first principles effective Hamiltonians with supercells and elementary l…
Intra--Galactic thin shell wormhole and its stability
2013
In this paper, we construct an intra-galactic thin shell wormhole joining two copies of identical galactic space times described by the Mannheim-Kazanas de Sitter solution in conformal gravity and study its stability under spherical perturbations. We assume the thin shell material as a Chaplygin gas and discuss in detail the values of the relevant parameters under which the wormhole is stable. We study the stability following the method by Eiroa and we also qualitatively analyze the dynamics through the method of Weierstrass. We find that the wormhole is generally unstable but there is a small interval in radius for which the wormhole is stable.
Ising and Bloch walls of phase domains in two-dimensional parametric wave mixing
2004
Oscillators driven by a degenerate wave mixing process are bistable in the phase of the generated radiation. In systems with a large Fresnel number, domains of opposite phase form therefore spontaneously. A simple model predicts a real field in which phase domains are separated by Ising-type walls. In this paper we show experimentally (using complex field reconstruction from measurements) and theoretically (by an extended model) that the optical field can be real as well as complex valued and that complex field fronts are related to the front curvature.
Universal description of pattern formation in optical oscillators under bichromatic injection
2018
We study pattern formation in a complex Swift–Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a bichromatic injection when the instability is toward long (transverse) wavelengths. Applications include two-level lasers and photorefractive oscillators. Under such an injection, the original continuous phase symmetry of the system is replaced by a discrete one and phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures, such as phase domains and dark-ring (phase) cavity solitons. The stability o…
Spin-up instability of electromagnetically levitated spherical bodies
2000
Stability of a solid sphere in both uniform and linear alternating magnetic fields is considered with respect to virtual rotations. When the frequency of the alternating magnetic field exceeds a certain critical threshold depending on the configuration of the field, the sphere is found to spin up around a horizontal axis. The physical mechanism of this instability is the same as that of operation of a single-phase induction motor. Sufficiently small rotational disturbances can be completely suppressed by imposing an axial steady magnetic field of strength comparable to that of the alternating field. Nonlinear stability analysis shows that for sufficiently high frequencies, spin-up can be ca…
Pattern formation through phase bistability in oscillatory systems with space-modulated forcing.
2010
We propose a novel forcing technique of spatially extended self-oscillatory systems able to excite phase bistability and the dissipative structures associated with it. The forcing is time periodic at a frequency close to the oscillators' frequency and is spatially modulated. The effects of this type of forcing are demonstrated analytically and numerically in a directly driven complex Ginzburg-Landau equation. Both spatially periodic and spatially random drives prove to be effective.
Instabilities in a staircase stratified shear flow
2017
We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can r...