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Showing papers on "Parametric oscillator published in 2004"


Journal ArticleDOI
TL;DR: In this paper, a fully non-linear finite difference model was developed based on inviscid flow equations for liquid sloshing induced by harmonic base excitations, which is valid for any water depth except for small depth when viscous effects would become important.

218 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan and found that the linear harmonic oscillator appears as the λ → 0 limit of this oscillator whose energy spectrum and eigenfunctions are compared to the linear ones.

106 citations


Journal ArticleDOI
TL;DR: Noise of a sufficiently large strength leads to an instability in the presence of an external periodic force, the output signal shows a nonmonotonic dependence on the strength and the rate of a color noise (stochastic resonance).
Abstract: The multiplicative noise in the equation of motion of an underdamped harmonic oscillator produced by a fluctuating damping parameter has a dramatic effect on the average coordinate of an oscillator. Noise of a sufficiently large strength leads to an instability. In the presence of an external periodic force, the output signal shows a nonmonotonic dependence on the strength and the rate of a color noise (stochastic resonance). Contrary to the case of a random frequency, this effect exists for white noise as well.

91 citations


Journal ArticleDOI
TL;DR: In this paper, an explicit asymptotic formula for the norms of the spectral projections of the non-self-adjoint harmonic oscillator H is given. But the spectral expansion of e−Ht is norm convergent if and only if t is greater than a certain explicit positive constant.
Abstract: We obtain an explicit asymptotic formula for the norms of the spectral projections of the non-self-adjoint harmonic oscillator H. We deduce that the spectral expansion of e−Ht is norm convergent if and only if t is greater than a certain explicit positive constant.

83 citations


Journal ArticleDOI
TL;DR: In this article, a study of sinusoidally forced oscillations of a fractional oscillator was conducted, and it was shown that the system exhibits a rich variety of damping characteristics, which do not find any parallel in the damped harmonic oscillator system.
Abstract: A study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics. While some aspects of the damping mimic the characteristic features of a damped harmonic oscillator, there are others, which do not find any parallel in the damped harmonic oscillator system. It is clearly demonstrated that the “free” and “forced” oscillations of a fractional oscillator are characterized by different damping parameters. While both depend on the fractional index α , the “free” oscillation damping depends on the “natural frequency”, ω 0 , of the oscillator, the “forced” oscillation damping depends in addition, on the “driving frequency”, ω . Furthermore, there is a different power-law tail associated with each of these cases.

73 citations


Journal ArticleDOI
TL;DR: Phase-stabilized 12-fs, 1-nJ pulses from a commercial Ti:sapphire oscillator are directly amplified in a chirped-pulse optical parametric amplifier and recompressed to yield near-transform-limited 17.3-fs pulses.
Abstract: Phase-stabilized 12-fs, 1-nJ pulses from a commercial Ti:sapphire oscillator are directly amplified in a chirped-pulse optical parametric amplifier and recompressed to yield near-transform-limited 17.3-fs pulses. The amplification process is demonstrated to be phase preserving and leads to 85‐µJ, carrier-envelope-offset phase-locked pulses at 1 kHz for 0.9 mJ of pump, corresponding to a single-pass gain of 8.5×104.

71 citations


Journal ArticleDOI
TL;DR: In this paper, a fully quantum treatment of the non-degenerate optical parametric oscillator is presented, and the results are compared with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function with a view to locating regions of agreement and disagreement between the two.
Abstract: We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

64 citations


01 May 2004
TL;DR: In this paper, a fully quantum treatment of the non-degenerate optical parametric oscillator is presented, and the results are compared with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function with a view to locating regions of agreement and disagreement between the two.
Abstract: We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

63 citations


Journal ArticleDOI
TL;DR: A waveguide array is presented that behaves as an oscillator, showing periodic image reconstruction, focusing, and transverse wave-packet oscillation, which is fundamentally different from previously demonstrated oscillations in Wannier-Stark waveguide arrays.
Abstract: A waveguide array is presented that behaves as an oscillator, showing periodic image reconstruction, focusing, and transverse wave-packet oscillation. The oscillator has a finite width, which removes the need for premature truncation. The array waveguide oscillator shows properties analogous to those of a pedagogically important one-dimensional quantum harmonic oscillator, which are fundamentally different from previously demonstrated oscillations in Wannier–Stark waveguide arrays. Calculations of the entire array waveguide oscillator are presented that quantify higher-order corrections to the coupled-mode approach. These results can be extended to waveguide oscillators in other systems, such as electrons in superlattices.

59 citations


Journal ArticleDOI
TL;DR: A system for parametric conversion of high-energy,Q-switched laser pulses from 1.064 microm to 2.1 microm in KTiOPO, using a two-stage system, achieves high beam quality and efficiency.
Abstract: Arisholm, Gunnar; Nordseth, Ornulf; Rustad, Gunnar. Optical parametric master oscillator and power amplifier for efficient conversion of high-energy pulses with high beam quality. Optics Express 2004 ;Volum 12.(18) s. 4189-4197

56 citations


Journal ArticleDOI
TL;DR: In this article, the phenomenon of parametric resonance is explained and investigated both analytically and with the help of a computer simulation, for the example of the rotary oscillations of a simple linear system.
Abstract: The phenomenon of parametric resonance is explained and investigated both analytically and with the help of a computer simulation. Parametric excitation is studied for the example of the rotary oscillations of a simple linear system— mechanical torsion spring pendulum excited by periodic variations of its moment of inertia. Conditions and characteristics of parametric resonance and regeneration are found and discussed in detail. Ranges of frequencies within which parametric excitation is possible are determined. Stationary oscillations at the boundaries of these ranges are investigated. The simulation experiments aid greatly an understanding of basic principles and peculiarities of parametric excitation and complement the analytical study of the subject in a manner that is mutually reinforcing.

Journal ArticleDOI
TL;DR: A system for the active real-time hyperspectral imaging of gases using a combination of a compact, pump-enhanced, continuous-wave optical parametric oscillator as an all-solid-state mid-infrared source of coherent radiation and an electro-mechanical polygonal imager.
Abstract: We demonstrate a system for the active real-time hyperspectral imaging of gases using a combination of a compact, pump-enhanced, continuous-wave optical parametric oscillator as an all-solid-state mid-infrared source of coherent radiation and an electro-mechanical polygonal imager. The wide spectral coverage and high spectral resolution characteristics of this source means that the system is capable of being selectively tuned into the absorption features of a wide variety of gaseous species. As an example we show how the largest absorption coefficient exhibited by methane at 3057.7cm(-1) can be accessed (amongst others) and gas plumes imaged in concentrations as low as 30ppm.m using a parametric oscillator based on periodically-poled RbTiOAsO(4) (PP-RTA).

Journal ArticleDOI
TL;DR: It is demonstrated a synchronously pumped high-gain optical parametric oscillator with feedback through a fiber, using a passively mode-locked Yb:YAG thin-disk laser as a pump source, and the transverse beam quality of the generated signal is M2 < 1.6.
Abstract: We demonstrate a synchronously pumped high-gain optical parametric oscillator with feedback through a fiber, using a passively mode-locked Yb:YAG thin-disk laser as a pump source. We obtain as much as 19-W average signal power at a wavelength of 1.45 µm in 840-fs pulses and 7.8 W of idler power at 3.57 µm. The repetition rate of the pulses is 56 MHz, and the transverse beam quality of the generated signal is M^2 < 1.6.

Journal ArticleDOI
TL;DR: In this article, it is shown that it is nonlinearity rather than damping that limits the growth of a resonantly excited mode, although damping is needed for steady-state oscillations to occur.
Abstract: Periodic changes in the tension of a taut string parametrically excite transverse motion in the string when the driving frequency is close to twice the natural frequency of any transverse normal mode of the string. The literature on this phenomenon is synthesized and extended to include the effects of damping as well as nonlinearity. It is shown that it is nonlinearity rather than damping that limits the growth of a resonantly excited mode, although damping is needed for steady-state oscillations to occur. The validity of the usual approximation that the string tension depends only on time and not on space is checked by modeling a string as point masses joined by massless linear springs. It is found that although this approximation is likely to be violated in practice, the violation does not have a significant effect on the results. The source of the disagreement in the literature for the speed of longitudinal waves in a stretched string is identified.

Journal ArticleDOI
TL;DR: In this paper, the authors present an experimental study on four-wave mixing between two signals within a two-pump fiber-optical parametric amplifier (2P-FOPA) and demonstrate that the intensity of FWM spurious tones depend strongly on the signal power and length of the nonlinear medium.
Abstract: We present an experimental study on four-wave mixing (FWM) between two signals within a two-pump fiber-optical parametric amplifier (2P-FOPA). We demonstrate that the intensity of FWM spurious tones depend strongly on the signal power and length of the nonlinear medium and present two regimes as a function of the pumps' power. We also compare the amounts of FWM as a function of channel spacing in the 2P-FOPA with or without pumps and show that the presence of parametric gain enhances FWM over a broad spectral range.

Journal ArticleDOI
TL;DR: In this article, the collective oscillations of one-dimensional repulsive Bose gas with external harmonic confinement in two different regimes are studied, the mean-field regime and the Tonks-Girardeau regime, where the resonance has the character of a linear parametric resonance, and analytical expressions for the nonlinearity managed soliton width and the frequency of slow secondary oscillations near the fixed point.
Abstract: The collective oscillations of one-dimensional (1D) repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean-field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean-field regime we predict bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point. We confirm the analytical predictions by direct numerical simulations of the 1D GrossPitaevskii equation and the effective nonlinear Schrodinger equation with quintic nonlinearity and trap potential.

Journal ArticleDOI
TL;DR: In this article, the static and dynamic behavior of a compressed circular cylindrical shell having geometric imperfections is analyzed, mainly performed by means of the Donnell's nonlinear shallow-shell theory.

Proceedings ArticleDOI
TL;DR: In this paper, a numerical and an analytical model for the dynamic analysis of comb-driven microscanners under different excitation schemes are presented, where the numerical model is based on a second order nonlinear differential equation.
Abstract: Accurate prediction of the dynamic behavior of comb-driven MEMS microscanners is important to optimize the actuator and structure design. In this paper, a numerical and an analytical model for the dynamic analysis of comb-driven microscanners under different excitation schemes are presented. The numerical model is based on a second order nonlinear differential equation. Due to the nature of the torque function, this governing equation of motion is a parametric nonlinear ODE, which exhibits hysteretic frequency domain behavior and subharmonic oscillations. . Experimental results and approximate analytical expressions for this nonlinear torque function of the comb-drive are presented. Amplitude and phase relationship between the excitation signal and the resultant oscillations at different excitation frequencies are measured and we show that they are in close agreement with the numerical simulations. Analytical model uses perturbation methods to reach approximate close-form expressions for the dynamic behavior of the device in the first parametric resonance region. It is also utilized to predict the stability regions on the frequency-excitation voltage plane, where the device exhibit hysterical characteristics. Analytical and numerical modeling approaches proposed in this paper provides a simple yet powerful way to analyze the nonlinear frequency response of comb-driven actuators and simplify the design process for a microscanner based system.

Journal ArticleDOI
01 Jan 2004-Pramana
TL;DR: In this paper, the authors obtained exact wave functions for a general time-dependent quadratic harmonic oscillator and the coherent states, both inx andp-spaces, were calculated.
Abstract: By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant frequency oscillates with a large amplitude, even after a sufficient time elapse.

Journal ArticleDOI
TL;DR: In this paper, the authors present a mathematical model for the dynamics of an electrostatically actuated microcantilever for the common case of cantilevers excited by a periodic voltage, and show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation.
Abstract: We present a mathematical model for the dynamics of an electrostatically actuated microcantilever For the common case of cantilevers excited by a periodic voltage, we show that the underlying linearized dynamics are those of a periodic system described by a Mathieu equation. We present experimental results that confirm the validity of the model, and in particular, illustrate that parametric resonance phenomena occur in capacitively actuated micro-cantilevers. We propose a system where the current measured is used as the sensing signal of the cantilever state and position through a dynamical observer. By investigating how the best achievable performance of an optimal observer depends on the excitation frequency, we show that the best such frequency is not necessarily the resonant frequency of the cantilever.

Journal ArticleDOI
TL;DR: In this paper, the authors extend the Lewis and Riesenfeld method of solving the time-dependent Schrodinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized timedependent inverted harmonic oscillator.
Abstract: We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrodinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exponentially increasing mass.

Journal ArticleDOI
TL;DR: This paper investigates the stability of a fluid-structure interaction problem in which a flexible elastic membrane immersed in a fluid is excited via periodic variations in the elastic stiffness parameter, and formulates the equations of motion in two dimensions using the immersed boundary formulation.
Abstract: In this paper, we investigate the stability of a fluid-structure interaction problem in which a flexible elastic membrane immersed in a fluid is excited via periodic variations in the elastic stiffness parameter. This model can be viewed as a prototype for active biological tissues such as the basilar membrane in the inner ear, or heart muscle fibers immersed in blood. Problems such as this, in which the system is subjected to internal forcing through a parameter, can give rise to "parametric resonance." We formulate the equations of motion in two dimensions using the immersed boundary formulation. Assuming small amplitude motions, we can apply Floquet theory to the linearized equations and derive an eigenvalue problem whose solution defines the marginal stability boundaries in parameter space. The eigenvalue equation is solved numerically to determine values of fiber stiffness and fluid viscosity for which the problem is linearly unstable. We present direct numerical simulations of the fluid-structure interaction problem (using the immersed boundary method) that verify the existence of the parametric resonances suggested by our analysis.

Journal ArticleDOI
TL;DR: This work demonstrates a PPLN based pump-enhanced, singly-resonant optical parametric oscillator configured in a traveling wave geometry and pumped by a Ti:sapphire laser with superiority of traveling wave over standing wave geometries.
Abstract: We demonstrate a PPLN based pump-enhanced, singly-resonant optical parametric oscillator configured in a traveling wave geometry and pumped by a Ti:sapphire laser. The inclusion of a low finesse etalon within the OPO cavity stabilizes the signal frequency, and rotation of the etalon allows this frequency to be systematically hopped from axial mode to nearest neighbor axial mode over the entire free spectral range of the etalon (83GHz). Tuning of the pump frequency allows the signal frequency to be smoothly tuned over a cavity free spectral range. More than 35mW of single frequency idler power was generated in the spectral range 2800–3000nm for 600mW pump power. The superiority of traveling wave over standing wave geometries in these regards is discussed.

Journal ArticleDOI
TL;DR: In this article, a two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated, where the transport speed is assumed to be a constant mean speed with small harmonic variations.
Abstract: Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton's second law. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. Closed-form solutions for the amplitude of the vibration and the existence conditions of nontrivial steady-state response in two-to-one parametric resonance are obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Lyapunov's linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions for two-to-one parametric resonance. Some numerical examples highlighting the effects of the related parameters on the stability conditions are presented.

Journal ArticleDOI
TL;DR: In this article, the intrinsic anharmonicity of each NEMS oscillator is measured using a term quadratic in the amplitude of oscillation for each oscillator, and the conditions for this measurement scheme to be quantum limited are derived and the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon number eigenstate.
Abstract: We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear fiber compression experiment with high-power femtosecond pulses from a passively mode-locked thin disk Yb:YAG laser is described.
Abstract: We report on nonlinear experiments pumped with high-power femtosecond pulses from a passively mode-locked thin disk Yb:YAG laser: a nonlinear fiber compression experiment, generating 33-fs pulses with 18 W average power and a fiber-feedback parametric oscillator generating 19 W of signal power in the 1.5-?m region and 7.8 W of idler power at a wavelength of 3.57 ?m.

Journal ArticleDOI
TL;DR: In this paper, the instability of oscillations of a weightless rod with a concentrated mass, sliding periodically along the rod axis is investigated, where the amplitude of the displacement of the mass and viscous friction, due to the air resistance, is assumed to small, while the periodic excitation function is arbitrary.

Journal ArticleDOI
TL;DR: In this article, the dynamic response of a parametrically excited cantilever beam with a pendulum is theoretically and experimentally presented, and the equation of motion and associated boundary conditions are derived considering the static friction of the rotating motion at the supporting point (pivot) of the pendulum.
Abstract: The dynamic response of a parametrically excited cantilever beam with a pendulum is theoretically and experimentally presented. The equation of motion and the associated boundary conditions are derived considering the static friction of the rotating motion at the supporting point (pivot) of the pendulum. It is theoretically shown that the static friction at the pivot of the pendulum plays a dominant role in the suppression of parametric resonance. The boundary conditions are different between two states in which the motion of the pendulum is either trapped by the static friction or it is not. Because of this variation of the boundary conditions depending on the pendulum motion, the natural frequencies of the system are automatically and passively changed and the bifurcation set for the parametric resonance is also shifted, so that parametric resonance does not occur. Experimental results also verify the effect of the pendulum on the suppression of parametric resonance in the cantilever beam.

Proceedings ArticleDOI
06 Jun 2004
TL;DR: In this paper, a parametric resonance-based mass sensor is presented, comprised of a single-crystal silicon micro-oscillator with sensitivity at the pico-gram (10 -12 g) level when operating in air.
Abstract: We present a parametric resonance-based mass sensor, comprised of a single-crystal silicon micro-oscillator with sensitivity at the pico-gram (10 -12 g) level when operating in air. This mass sensor detects mass change by measuring frequency shift at the boundary of the first order parametric resonance ‘tongue’. High sensitivity is achievable due to the sharp jump in amplitude caused by parametric resonance at predictable drive frequencies. Pt deposition using focused ion beam and water vapor are used to change the mass of the testing oscillator. The results show that the sensitivity can be > 1 order higher than the same oscillator working at simple harmonic resonance mode. The effect of noise on mass sensing ability in this nonlinear dynamic system is considered as well.

Journal ArticleDOI
TL;DR: In this article, a Hamiltonian model consisting of two fields injected simultaneously within a perfect cavity to interact with a single atom was introduced, and the interaction between the fields has been taken into account and considered to be in the parametric amplifier form.
Abstract: In the present work we introduce a Hamiltonian model consisting of two fields injected simultaneously within a perfect cavity to interact with a single atom. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. The model can be regarded as a generalization of the Jaynes–Cummings model as well as a generalization of the parametric amplifier model. Under a certain condition, which is carefully selected, the exact solution for the Heisenberg equations of motion is obtained. Employing this solution we managed to discuss some statistical properties such as the atomic inversion, the photon number distribution, the squeezing phenomenon, the Glauber second-order correlation function and Phase distribution. Also the Q-function is considered.