Parametric oscillator

About: Parametric oscillator is a research topic. Over the lifetime, 5836 publications have been published within this topic receiving 95631 citations. The topic is also known as: Parametric excitation.

Surface waves in closed basins under principal and autoparametric resonances

Abstract: The method of multiple scales is used to analyze the nonlinear response of the surface of a liquid in a cylindrical container to a principal parametric resonant excitation in the presence of a two‐to‐one internal (autoparametric) resonance. Four autonomous first‐order ordinary‐differential equations are derived for the modulation of the amplitudes and phases of the two modes involved in the internal resonance when the higher mode is being excited by a principal parametric resonance. The modulation equations are used to determine the periodic oscillations and their stability. The force‐response curves exhibit the jump and saturation phenomena as well as a Hopf bifurcation, whereas the frequency‐response curves exhibit the jump phenomenon and supercritical and subcritical Hopf bifurcations. Limit‐cycle solutions of the modulation equations are found between the Hopf frequencies; they correspond to aperiodic motions of the liquid surface. All limit cycles deform and lose stability by either pitchfork or cyclic‐fold bifurcations as the excitation frequency or amplitude is varied. The pitchfork bifurcation breaks the symmetry of the limit cycles whereas the cyclic‐fold bifurcation causes cyclic jumps, which may result in a transition to chaos. Period‐three motions are found in a very narrow range of the excitation frequency.

High-intensity localized structures in the degenerate optical parametric oscillator: Comparison between the propagation and the mean-field models

Abstract: The degenerate optical parametric oscillator may generate very high-intensity two-dimensional localized structures. A quantitative comparison of the propagation and the mean-field models is presented for different mistunings, corresponding to monostable and bistable homogeneous solutions. In both models, we study the circular domain walls as an example of localized structures. The peak intensities are comparable; the difference lies mainly in their domain of existence as a function of the pump amplitude parameter.

Parametric resonance of a repulsive force MEMS electrostatic mirror

Abstract: We investigate the nonlinear dynamic behavior of an electrostatic MEMS mirror. The MEMS mirror is driven by repulsive force actuators, which avoid pull-in instability and enable large travel ranges. In parallel-plate actuators, the force on the structure is toward the substrate limiting the range of motion to the capacitor gap. Unlike parallel-plate, repulsive force actuators push the mirror away from the substrate not limiting the motion. The highly nonlinear nature of the repulsive force and the large motions create unique characteristics that differ from parallel-plate actuators. Repulsive force actuators show linear natural frequency hardening with increased DC voltages unlike parallel-plate ones that have frequency softening. A large parametric resonance is another attribute of repulsive force actuators as the limitations of a small gap and pull-in instability are eliminated. To simulate the system response, we use a lumped parameter model with linear and cubic stiffness modulated by the excitation voltage that causes parametric resonances. Using the shooting technique, we obtained simulations that agree well with the nonlinear responses observed in our experiments. As the limitation of a small gap is overcome, the electrostatic force triggers large principal parametric resonances with amplitudes as large as the primary resonance. The parametric resonance is more pronounced at low DC excitation levels when geometric nonlinearities are not significant (axial stress is low). While the initial gap is only 2 μm, under parametric resonance, our one-millimeter diameter mirror reaches ±43 μm at 1.2 kHz when the excitation level is as low as VDC = 40 V, VAC =1 V in a vacuum. The ability to achieve parametric resonances with repulsive force actuation can serve and improve the signal-to-noise ratio and speed in various applications such as confocal microscopy.

Operation of the SUPARAMP at 33 GHz

Abstract: A 9‐mm degenerate parametric amplifier has been constructed using a linear series array of unbiased Josephson junctions as the active nonlinear element. We used a balanced diode mixer as a synchronous detector, with a single source serving both as the pump and as the mixer local oscillator. A stable net gain of 15 dB in an instantaneous bandwidth (FWHM) of 3.4 GHz has been achieved. We measured a system noise temperature of 220±5 K (DSB) with a SUPARAMP contribution of only 20±10 K. Output saturation, however, has been observed. This complicates the interpretation of our noise‐temperature measurements and may render them upper limits. Comparison is made with the results of an earlier 3‐cm SUPARAMP. The data are in substantial agreement with theoretical predictions.

Causal gravitational waves as a probe of free streaming particles and the expansion of the Universe

Abstract: The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition or parametric resonance, is largely fixed by causality, offering a clean window into the early Universe. In this work, this low frequency end of the spectrum is analyzed with an emphasis on a physical understanding, such as the suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement due to being frozen out while outside the horizon. Due to the difference between sub-horizon and super-horizon physics, it is inevitable that there will be a distinct spectral feature that could allow for the direct measurement of the conformal Hubble rate at which the phase transition occurred. As an example, free-streaming particles (such as the gravity waves themselves) present during the phase transition affect the production of super-horizon modes. This leads to a steeper decrease in the spectrum at low frequencies as compared to the well-known causal k3 super-horizon scaling of stochastic gravity waves. If a sizable fraction of the energy density is in free-streaming particles, they even lead to the appearance of oscillatory features in the spectrum. If the universe was not radiation dominated when the waves were generated, a similar feature also occurs at the transition between sub-horizon to super-horizon causality. These features are used to show surprising consequences, such as the fact that a period of matter domination following the production of gravity waves actually increases their power spectrum at low frequencies.