Showing papers on "Parametric oscillator published in 1998"
TL;DR: In this article, the authors report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system, which can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.
Abstract: The Mathieu equation1 governs the forced motion of a swing2, the stability of ships3 and columns4, Faraday surface wave patterns on water5,6, the dynamics of electrons in Penning traps7, and the behaviour of parametric amplifiers based on electronic8 or superconducting devices9. Theory predicts that parametric resonances occur near drive frequencies of 2ω0/n, where ω0 is the system's natural frequency and n is an integer ⩾1. But in macroscopic systems, only the first instability region can typically be observed, because of damping and the exponential narrowing10 of the regions with increasing n. Here we report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system. Five instability regions can be measured, due to the low damping, stability and precise frequency control achievable in this system. The centre frequencies of the instability regions agree with theoretical predictions. We propose an application that uses parametric excitation to reduce the parasitic signal in capacitive sensing with microelectromechanical systems. Our results suggest that microelectromechanical systems can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.
449 citations
TL;DR: In this article, the authors studied parametric resonances when an elastic system is rotated around an annular disc with friction having a negative slope with velocity, and demonstrated that the effect of the in-plane system including the negative friction-velocity relationship is to introduce additional parametric resonance which are destabilised by the transverse damper, and to reduce the regions of instability of the other resonances.
141 citations
TL;DR: In this article, the authors investigated the possibility of preheating in hybrid inflation and found that the behavior of these fields after inflation depends crucially on the ratio of the coupling constant of the inflaton field to the symmetry breaking field.
Abstract: We investigate the possibility of preheating in hybrid inflation. This scenario involves at least two scalar fields: the inflaton field \ensuremath{\varphi}, and the symmetry breaking field \ensuremath{\sigma}. We found that the behavior of these fields after inflation, as well as the possibility of preheating (particle production due to parametric resonance), depends crucially on the ratio of the coupling constant \ensuremath{\lambda} (self-interaction of the field \ensuremath{\sigma}) to the coupling constant ${g}^{2}$ (interaction of \ensuremath{\varphi} and \ensuremath{\sigma}). For $\ensuremath{\lambda}\ensuremath{\gg}{g}^{2},$ the oscillations of the field \ensuremath{\sigma} soon after inflation become very small, and all the energy is concentrated in the oscillating field \ensuremath{\varphi}. For $\ensuremath{\lambda}\ensuremath{\sim}{g}^{2}$ both fields \ensuremath{\sigma} and \ensuremath{\varphi} oscillate in a rather chaotic way, but eventually their motion stabilizes, and parametric resonance with production of \ensuremath{\chi} particles becomes possible. For $\ensuremath{\lambda}\ensuremath{\ll}{g}^{2}$ the oscillations of the field \ensuremath{\varphi} soon after inflation become very small, and all the energy is concentrated in the oscillating field \ensuremath{\sigma}. Preheating can be very efficient if the effective masses of the fields \ensuremath{\varphi} and \ensuremath{\sigma} are much greater than the Hubble constant at the end of inflation, since those fields can then oscillate many times per $e$-fold, with a large amplitude. Preheating can also be efficient if these fields are coupled to other light scalar (or vector) fields \ensuremath{\chi}. In the recently proposed hybrid models with a second stage of inflation after the phase transition, both preheating and usual reheating are inefficient. Therefore for a very long time the universe remains in a state with vanishing pressure. As a result, density contrasts generated during the phase transition in these models can grow and collapse to form primordial black holes. Under certain conditions, most of the energy density after inflation will be stored in small black holes, which will later evaporate and reheat the universe.
116 citations
TL;DR: In this article, the authors used a widely tunable cw single-frequency optical parametric oscillator for trace gas detection in a photoacoustic trace-gas detection system for environmental monitoring and process control.
Abstract: H6) at 3.34 μm using a widely tunable cw single-frequency optical parametric oscillator. The high frequency and power stability and the continuous tunability of the parametric oscillator make it ideally suited for this application. Detection sensitivities of 0.5 ppb for ethane are obtained, which is comparable to the best results previously obtained with intracavity detection using line-tunable CO overtone lasers. The flexibility and compact size of cw single-frequency parametric oscillators can lead to portable photoacoustic trace-gas detection systems for environmental monitoring and process control.
75 citations
TL;DR: In this article, the performance of a β-barium borate optical parametric oscillator pumped by the second harmonic of a femtosecond Ti:sapphire laser is analyzed and compared with experimental measurements.
Abstract: The current theoretical understanding, in terms of numerical simulations and simple models, of the various modes of operation of the visible-range β-barium borate optical parametric oscillator pumped by the second harmonic of a femtosecond Ti:sapphire laser is analyzed and compared with experimental measurements. These observations include operation of the optical parametric oscillator without prisms and the associated self-compression that is due to cascaded second-order effects. The performance of the oscillator with group-delay-dispersion compensation prisms is described in terms of a simulation-based soliton model that determines the variation of pulse duration with group-delay dispersion, third-order dispersion, and wavelength.
66 citations
TL;DR: In this article, the Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means, including path integration, path integration and path integration.
Abstract: The Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means.
58 citations
TL;DR: In this article, the degenerate and non-degenerate mechanical parametric amplification in GaAs piezoresistive atomic force microscopy cantilevers due to an inherent mechanical nonlinearity was investigated.
Abstract: Preamplification of mechanical signals in external force detection systems can improve overall sensitivity in a case where sensitivity is limited by secondary detection noise. We report experimental data on degenerate and nondegenerate mechanical parametric amplification in GaAs piezoresistive atomic force microscopy cantilevers due to an inherent mechanical nonlinearity. The mechanical nonlinearity is estimated to be a result of curvature at the cantilever base. Characteristics of parametric amplification such as phase sensitive gain, small signal gain, gain saturation, and self-oscillation have been studied. A small signal phase sensitive gain of 19.5 dB was observed for the degenerate parametric amplifier.
55 citations
01 Apr 1998
TL;DR: In this article, a nonlinear analysis of the basic state gives the critical value of the control parameter for the primary instability onset, the nature of the most unstable modes and their growth rate above criticality.
Abstract: Introduction Instabilities in nonlinear systems driven far from equilibrium often consist of a transition from a motionless state to one varying periodically in space or time. Various examples, widely studied in the past, are Rayleigh – Benard convection, Couette–Taylor flow, waves in shear flows, instabilities of liquid crystals, oscillatory chemical reactions,…. The appearance of periodic structures in these systems driven externally by a forcing homogeneous in space or constant in time, corresponds to a bifurcation, characterized by one or several modes that become unstable as a control parameter is varied. Linear stability analysis of the basic state gives the critical value of the control parameter for the primary instability onset, the nature of the most unstable modes and their growth rate above criticality. Many examples have been studied for a long time and can be found for instance in the books of Chandrasekhar (1961) or Drazin and Reid (1981). However, linear stability analysis does not describe the saturation mechanism of the primary instability, and thus a nonlinear analysis should be performed to determine the selected pattern, its dynamics and in particular the secondary instabilities that occur as the control parameter is increased above criticality. Before considering these problems, we present some examples of the characteristic phenomena that occur above a pattern-forming instability onset. Example: the Faraday instability As a first example, consider a cylindrical vessel containing a liquid and its vapor (or any other gas), vertically vibrated at frequency ω e (see Fig. 1.1).
54 citations
TL;DR: In this article, the existence of a nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields was demonstrated with nucleation of an expanding bubble.
Abstract: During preheating after inflation, parametric resonance rapidly generates very large fluctuations of scalar fields. In models where the inflaton field $\ensuremath{\varphi}$ oscillates in a double-well potential and interacts with another scalar field $X$, fluctuations of $X$ can keep the $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\varphi}$ symmetry temporarily restored. If the coupling of $\ensuremath{\varphi}$ to $X$ is much stronger than the inflaton self-coupling, the subsequent symmetry breaking is a first-order phase transition. We demonstrate the existence of this nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields. In particular, we observe nucleation of an expanding bubble.
50 citations
49 citations
TL;DR: In this paper, the authors studied the effect of thermal and quantum noise on the evolution of matter fields and demonstrated that noise can increase the rate of particle production, at least if it is temporally uncorrelated.
Abstract: Explosive particle production due to parametric resonance is a crucial feature of reheating in inflationary cosmology. Coherent oscillations of the inflaton field act as a periodically varying mass in the evolution equation for matter fields which couple to the inflaton. This in turn results in the parametric resonance instability. Thermal and quantum noise will lead to a nonperiodic perturbation in the mass. We study the resulting equation for the evolution of matter fields and demonstrate that noise (at least if it is temporally uncorrelated) will increase the rate of particle production. We also estimate the limits on the magnitude of the noise for which the resonant behavior is qualitatively unchanged.
TL;DR: A femtosecond optical parametric oscillator based on a periodically poled KTiOPO(4) crystal for which quasi-phase matching is achieved with a 24microm poling period was reported in this article.
Abstract: We report a femtosecond optical parametric oscillator based on a periodically poled KTiOPO(4) crystal for which quasi-phase matching is achieved with a 24-microm poling period. The singly resonant parametric oscillator, synchronously pumped by a Ti:sapphire laser at a wavelength of 758 nm, generates a signal at 1200 nm and an idler at 2060 nm. The maximum signal power conversion efficiency of the device is 22% with a pump depletion of 69%. We tune the signal wavelength over a 200-nm band by changing the cavity length. In addition, pump wavelength tuning provides output tunability in the 1000-1235-nm range.
TL;DR: The possibility of frequency conversion by operation of a similar pulsed parametric oscillator away from degeneracy is suggested and the output signal pulses exhibit improved spectral symmetry and a reduced time-bandwidth product compared with the pump pulses.
Abstract: We report operation of an all-fiber degenerate optical parametric oscillator that employs a nonlinear-fiber Sagnac interferometer as a parametric amplifier. Synchronous pumping with 3.9-ps pulses at 1544 nm yields 0.83-ps output pulses. The wide bandwidth of the fiber parametric amplifier causes the oscillator to act as a pulse compressor. The output signal pulses exhibit improved spectral symmetry and a reduced time-bandwidth product compared with the pump pulses. Currently, the net group-velocity dispersion in the passive section of the fiber cavity limits the signal-pulse bandwidth and hence the minimum-obtainable pulse width. This experiment suggests the possibility of frequency conversion by operation of a similar pulsed parametric oscillator away from degeneracy.
Patent•
03 Feb 1998TL;DR: In this article, an optical parametric oscillator system was proposed for a continuous wave pump laser system having a single-frequency pump source, which includes means for controlling the cavity length of the resonator, the pump frequency of the pump source and the temperature of the nonlinear medium.
Abstract: An optical parameter oscillator system is proposed for use in a continuous wave pump laser system having a single-frequency pump source. The system comprises a single-resonance resonator having a nonlinear medium to produce a first and second parametrically generated wave in response to the pump wave from the single-frequency pump source. The system includes means for controlling the cavity length of the resonator, means for controlling the pump frequency of the pump source and means for controlling the temperature of the nonlinear medium. The system provides for a reliable singly-resonant optical parametric oscillator capable of emitting laser light with high spectral purity and frequency stability over a wide spectral range and is resistant to mode hopping.
TL;DR: In this paper, a doubly resonant optical para-metric oscillator was demonstrated to operate on a single mode pair for 18 h without mode hops, and whose output frequencies can be tuned by almost 10 GHz without mode hop by the tuning of the pump laser frequency.
Abstract: We demonstrate a doubly resonant optical para- metric oscillator that operated on a single mode pair for 18 h without mode hops, and whose output frequencies can be tuned by almost 10 GHz without mode hops by the tuning of the pump laser frequency. The tuning range is limited by the available pump tuning range. Active stabilization is used that minimizes the detuning of the parametrically generated waves with respect to the DRO cavity resonances. Absolute fre- quency stabilization of the idler wave is achieved by locking its frequency to an ultra-stable cryogenic reference resonator, using the pump laser frequency as control parameter. The fre- quency instability reached is below the 1-kHz level.
TL;DR: It is observed that two distinct phase states that differ in their oscillator thresholds and their signal-idler phase differences, in good agreement with theory, are observed.
Abstract: We demonstrate self-phase locking in a type II phase-matched optical parametric oscillator by mutual injection locking. An intracavity quarter-wave plate provides polarization mixing between the orthogonally polarized signal and idler that induces signal–idler self-phase locking when their frequency difference is within the capture range. We observed two distinct phase states that differ in their oscillator thresholds and their signal–idler phase differences, in good agreement with theory.
TL;DR: In this article, a simple and intuitive calculational method for estimating the efficiency of parametric amplification as a function of parameters is presented, which is important for determining whether resonant amplification plays an important role in the reheating process.
Abstract: Parametric resonance has been discussed as a mechanism for copious particle production following inflation. Here we present a simple and intuitive calculational method for estimating the efficiency of parametric amplification as a function of parameters. This is important for determining whether resonant amplification plays an important role in the reheating process. We find that significant amplification occurs only for a limited range of couplings and interactions.
TL;DR: Photon-number distributions for parametric fluorescence from a nondegenerate optical parametric amplifier are measured with a novel self-homodyne technique and a difference between the fluorescence gain and the signal gain of the parametric amplifiers is observed.
Abstract: Photon-number distributions for parametric fluorescence from a nondegenerate optical parametric amplifier are measured with a novel self-homodyne technique. These distributions exhibit the thermal-state character predicted by theory. However, a difference between the fluorescence gain and the signal gain of the parametric amplifier is observed. We attribute this difference to a change in the signal-beam profile during the traveling-wave pulsed amplification process.
TL;DR: A smoothly tunable, single-frequency continuous-wave optical parametric oscillator for high-resolution spectroscopy based on potassium titanyl phosphate that is resonant for both signal and idler fields, resulting in a device with a very low pump power threshold.
Abstract: We report the use of a smoothly tunable, single-frequency continuous-wave optical parametric oscillator (OPO) for high-resolution spectroscopy. The OPO is based on potassium titanyl phosphate and is resonant for both signal and idler fields, resulting in a device with a very low pump power threshold of 30??mW.?The frequency-selective nature of the doubly resonant oscillator ensures that the signal and idler modes can be tuned across the entire phase-match bandwidth without the need for additional intracavity frequency-selective components. Smooth frequency tuning of the output of the OPO is obtained by tuning of the pump laser. To demonstrate the practicality of our OPO we recorded the absorption spectrum of cesium vapor in the 1-µm spectral region.
TL;DR: A diode-laser pumped cw optical parametric oscillator based on quasi-phase-matched periodically poled lithium tantalate that generates a single-frequency idler wave with an output of as much as 244 mW is reported on.
Abstract: We report on a diode-laser pumped cw optical parametric oscillator (OPO) based on quasi-phase-matched periodically poled lithium tantalate. Pumped by the 2.3-W single-frequency, nearly diffraction-limited 925-nm output of an InGaAs diode master-oscillator power amplifier, the pump and signal resonant OPO generates a single-frequency idler wave with an output of as much as 244??mW. The wavelengths of the signal and idler waves are widely tunable in the range 1.55–2.3 µm by use of different poling periods (27.3 to 27.9 µm) and by variation of the crystal temperature in the range 70–190?°C.
TL;DR: In this article, the authors derived general expressions for a two-time correlation function and the photon number distribution in terms of the Q-function for the signal mode produced by a degenerate parametric oscillator operating below threshold.
TL;DR: In this article, a high-power continuous-wave optical parametric oscillator based on the nonlinear material KTiOAsO4 and pumped internal to a tunable Ti:sapphire laser is described.
Abstract: A high-power continuous-wave optical parametric oscillator based on the nonlinear material KTiOAsO4 and pumped internal to a tunable Ti:sapphire laser is described. The use of the intracavity pumping approach has enabled operation of a singly resonant oscillator (SRO), resulting in the generation of as much as 1.46 W of infrared power in a 11.5-mm-long crystal. Amplitude-stable signal and idler outputs, each in excess of 500 mW, over the respective wavelength ranges of 1.11–1.20 and 2.44–2.86 μm have been extracted from the SRO. We demonstrate up to 90% down-conversion of the optimum Ti:sapphire output power to the SRO, confirming our recent theoretical predictions. The performance characteristics of the device demonstrate that practical, stable, and efficient operation of continuous-wave SROs at watt-level output power can be readily achieved in conventional birefringent materials by exploiting the intracavity pumping approach.
TL;DR: The performance characteristics of a doubly (signal and idler) resonant continuous-wave optical parametric oscillator based on periodically poled lithium niobate and pumped by a 100-mW single-mode laser diode at 810 nm are reported.
Abstract: The performance characteristics of a doubly (signal and idler) resonant continuous-wave optical parametric oscillator based on periodically poled lithium niobate and pumped by a 100-mW single-mode laser diode at 810 nm are reported. Pump power thresholds as low as 16 mW and wavelength tuning over the range 1.15–1.25 µm at the signal and 2.31–2.66 µm at the idler were achieved through variation of crystal temperature, pump wavelength, and grating period. Up to 5 mW of signal output was obtained with the single-mode diode pump, and signal powers of up to 39 mW were obtained when pumping with a 400-mW injection-locked broad-area diode laser.
TL;DR: A low-threshold twin-beam generator using a cw triply resonant optical parametric oscillator consisting of two coupled cavities: one that resonates the signal and idler waves and the other the pump field is demonstrated.
Abstract: We demonstrate a low-threshold twin-beam generator using a cw triply resonant optical parametric oscillator consisting of two coupled cavities: one that resonates the signal and idler waves and the other the pump field. An intensity correlation of 5.5 dB was observed at 3 MHz for a type-II phase-matched KTP optical parametric oscillator.
TL;DR: In this paper, a CCII-based double-resistance controlled sinusoidal oscillator employing grounded resistors and capacitors is presented, which exhibits low active and passive sensitivities; voltage and current tracking error effects on the current conveyors can easily be eliminated with careful design.
TL;DR: In this paper, a high-repetition-rate intracavity opti- cal parametric oscillator (IOPO) based on a non-critically phase-matched KTP crystal placed inside the resonator of a Q-switched Nd:YAG laser was reported.
Abstract: We report a high-repetition-rate intracavity opti- cal parametric oscillator (IOPO) based on a non-critically phase-matched KTP crystal placed inside the resonator of a Q-switched Nd:YAG laser. The IOPO, operating at 1k Hz , produces average powers up to 0:35 W at 1:57 mm and 0:15 W at 3:29 mm. The dynamics of the IOPO is in good qualitative agreement with numerical simulations.
TL;DR: In this paper, the authors apply the solutions of the quantum Langevin equations to calculate the variances of the quadrature operators for the signal mode produced by a degenerate parametric oscillator coupled to a single-mode squeezed vacuum reservoir.
TL;DR: Analytically the existence of nondegenerate symbiotic solitary waves in quadratic media with absorption losses is shown and this configuration leads to the spontaneous formation of new solitary waves when used inside a singly resonant optical parametric oscillator.
Abstract: We show analytically the existence of nondegenerate symbiotic solitary waves in quadratic media with absorption losses. We study these new solitary waves in the particular case of a backward quasi-phase-matching configuration. Our numerical simulations reveal that, when it is used inside a singly resonant optical parametric oscillator, this configuration leads to the spontaneous formation of new solitary waves.
TL;DR: In this paper, the maximum signal wave power is 23 mW at a wavelength of 1243 nm and the spectral bandwidth of the signal wave is less than 750 kHz, which provides a threshold pump power of 16 mW.
Abstract: (RTA), which provides a threshold pump power of 16 mW. The maximum signal wave power is 23 mW at a wavelength of 1243 nm. The spectral bandwidth of the signal wave is less than 750 kHz.
TL;DR: A singly resonant pulsed intracavity KTiOPO>(4) optical parametric oscillator that uses a semi-monolithic microchip laser design and a novel quadrupole deflector Q switch to give 4-microJ signal pulses.
Abstract: We report a singly resonant pulsed intracavity KTiOPO>(4) optical parametric oscillator that uses a semi-monolithic microchip laser design. The compact (50-mm-long), low-threshold (1.3-W) cavity uses a novel quadrupole deflector Q switch to give 4-microJ pulses at 1.064 microm and 0.4-microJ signal pulses of 5.6-ns duration at 1.53 microm with a repetition frequency of 5 kHz when it is pumped with a 2-W laser diode. The signal pulses are diffraction limited and single frequency.