Showing papers on "Parametric oscillator published in 1997"
TL;DR: In this paper, the authors investigated a simple model of a massive inflaton field coupled to another scalar field with the interaction term, and developed the theory of preheating taking into account the expansion of the universe and back reaction of produced particles, including the effects of rescattering.
Abstract: Reheating after inflation occurs due to particle production by the oscillating inflaton field. In this paper we briefly describe the perturbative approach to reheating, and then concentrate on effects beyond the perturbation theory. They are related to the stage of parametric resonance, which we call preheating. It may occur in an expanding universe if the initial amplitude of oscillations of the inflaton field is large enough. We investigate a simple model of a massive inflaton field $\ensuremath{\varphi}$ coupled to another scalar field $\ensuremath{\chi}$ with the interaction term ${g}^{2}{\ensuremath{\varphi}}^{2}{\ensuremath{\chi}}^{2}$. Parametric resonance in this model is very broad. It occurs in a very unusual stochastic manner, which is quite different from parametric resonance in the case when the expansion of the universe is neglected. Quantum fields interacting with the oscillating inflaton field experience a series of kicks which, because of the rapid expansion of the universe, occur with phases uncorrelated to each other. Despite the stochastic nature of the process, it leads to exponential growth of fluctuations of the field $\ensuremath{\chi}$. We call this process stochastic resonance. We develop the theory of preheating taking into account the expansion of the universe and back reaction of produced particles, including the effects of rescattering. This investigation extends our previous study of reheating after inflation. We show that the contribution of the produced particles to the effective potential $V(\ensuremath{\varphi})$ is proportional not to ${\ensuremath{\varphi}}^{2}$, as is usually the case, but to $|\ensuremath{\varphi}|$. The process of preheating can be divided into several distinct stages. In the first stage the back reaction of created particles is not important. In the second stage back reaction increases the frequency of oscillations of the inflaton field, which makes the process even more efficient than before. Then the effects related to scattering of $\ensuremath{\chi}$ particles on the oscillating inflaton field terminate the resonance. We calculate the number density of particles ${n}_{\ensuremath{\chi}}$ produced during preheating and their quantum fluctuations $〈{\ensuremath{\chi}}^{2}〉$ with all back reaction effects taken into account. This allows us to find the range of masses and coupling constants for which one can have efficient preheating. In particular, under certain conditions this process may produce particles with a mass much greater than the mass of the inflaton field.
1,827 citations
TL;DR: In this paper, the Lame equation is used to describe the parametric resonance which leads to particle production in a conformally invariant theory of preheating, where the classical oscillating inflaton field decays into particles.
Abstract: We consider preheating in the theory $1/4 \lambda \phi^4 + 1/2 g^2\phi^2\chi^2 $, where the classical oscillating inflaton field $\phi$ decays into $\chi$-particles and $\phi$-particles. The parametric resonance which leads to particle production in this conformally invariant theory is described by the Lame equation. It significantly differs from the resonance in the theory with a quadratic potential. The structure of the resonance depends in a rather nontrivial way on the parameter $g^2/\lambda$. We construct the stability/instability chart in this theory for arbitrary $g^2/\lambda$. We give simple analytic solutions describing the resonance in the limiting cases $g^2/\lambda\ll 1$ and $g^2/\lambda \gg 1$, and in the theory with $g^2=3\lambda$, and with $g^2 =\lambda$. From the point of view of parametric resonance for $\chi$, the theories with $g^2=3\lambda$ and with $g^2 =\lambda$ have the same structure, respectively, as the theory $1/4 \lambda \phi^4$, and the theory $\lambda /(4 N) (\phi^2_i)^2$ of an N-component scalar field $\phi_i$ in the limit $N \to \infty$. We show that in some of the conformally invariant theories such as the simplest model $1/4 \lambda\phi^4$, the resonance can be terminated by the backreaction of produced particles long before $ $ or $ $ become of the order $\phi^2$. We analyze the changes in the theory of reheating in this model which appear if the inflaton field has a small mass.
387 citations
TL;DR: In this paper, the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency were obtained using the Lewis and Riesenfeld invariant method.
Abstract: We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] to obtain the exact Schr\"odinger wave functions for a harmonic oscillator with time-dependent mass and frequency. Exact coherent states for such system are also constructed.
177 citations
TL;DR: In this paper, the authors investigated the dynamic response of an axially accelerating string, where the time dependent velocity is assumed to vary harmonically about a constant mean velocity, and they found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequencies are close to the sum of any two natural frequencies, but no instabilities are detected up to the first order of perturbation.
171 citations
TL;DR: In this article, the decay of the inflaton was studied numerically by solving the full nonlinear equations of motion on the lattice and it was shown that parametric resonance is effective in transferring energy from the infaton to a scalar field as long as the self-interactions of the second field are very small.
Abstract: We study numerically the decay of the inflaton by solving the full nonlinear equations of motion on the lattice. We confirm that parametric resonance is effective in transferring energy from the inflaton to a scalar field as long as the self-interactions of the second field are very small. However, in the very broad resonance case $(q\ensuremath{\gg}1)$ the decay rate is limited by scatterings, which significantly slows down the decay. We also find that the inflaton cannot decay via parametric resonance into a scalar field with moderate self-interactions. This means that the preheating stage may be completely absent in many natural inflationary models.
139 citations
TL;DR: In this paper, the authors measured and modeled parametric gain and oscillation for two-crystal ring oscillators arranged for walkoff compensation, and showed how the orientation of the crystals determined the relative sign of the nonlinear mixing coefficient in the two crystals.
Abstract: We measure and model parametric gain and oscillation for two crystals arranged for walkoff compensation. We show how the orientation of the crystals determines the relative sign of the nonlinear mixing coefficient in the two crystals. This sign dramatically influences small signal gain and oscillator performance, and we show how to determine the correct crystal orientation from parametric-gain measurements. The performance of two-crystal oscillators is examined with particular attention to beam tilts, conversion efficiency, and beam quality. We find reduced efficiency and increased oscillation threshold when the coefficients have opposite signs in a two-crystal ring oscillator. Sign reversal seems to have little influence on spectral purity or far-field beam profiles when the oscillator is seeded.
109 citations
TL;DR: In this paper, the exact Schrodinger wave functions for a time-dependent harmonic oscillator with and without an inverse quadratic potential were obtained using the Lewis and Riesenfeld invariant method.
Abstract: We use the Lewis and Riesenfeld invariant method to obtain the exact Schr\"odinger wave functions for a time-dependent harmonic oscillator with and without an inverse quadratic potential. As a particular case we also obtain the wave functions for the Caldirola-Kanai oscillator.
103 citations
TL;DR: Using a single-frequency miniature Nd:YAG ring laser as a pump source results in SRO output with high spectral purity and frequency stability(<10 MHz/min), which can be continuously tuned over 2 GHz without mode hops.
Abstract: We demonstrate single-frequency operation of a cw quasi-phase-matched singly resonant optical parametric oscillator (SRO). We obtained widely tunable output from 1.66 to 1.99 µm (signal) and from 2.29 to 2.96 µm (idler) by employing a periodically poled lithium niobate multigrating chip. Using a single-frequency miniature Nd:YAG ring laser as a pump source results in SRO output with high spectral purity and frequency stability (<10 MHz/min), which can be continuously tuned over 2 GHz without mode hops. We obtain a minimum SRO threshold of 260 mW by resonating the pump wave in the SRO cavity.
102 citations
TL;DR: This work describes what is to their knowledge the first high-sensitivity spectroscopy experiment using twin beams emitted by a cw optical parametric oscillator, and records a very weak two-photon absorption signal.
Abstract: Nondegenerate optical parametric oscillators generate above-threshold signal and idler beams that have intensity fluctuations correlated at the quantum level (twin beams). We describe what is to our knowledge the first high-sensitivity spectroscopy experiment using twin beams emitted by a cw optical parametric oscillator: a very weak two-photon absorption signal, in the 10-7 range, is recorded on the 4S1/2–5S1/2 transition of atomic potassium with a noise background that is reduced by 1.9 dB with respect to the shot-noise limit of the light used in the experiment.
101 citations
TL;DR: In this paper, the number of photons produced by parametric resonance in a cavity with vibrating walls was calculated for the case that the frequency of vibrating wall is $n{\ensuremath{\omega}}_{1}$ $(n=1,2,3,\dots{}), where n is the fundamental mode frequency of the electromagnetic field in the cavity.
Abstract: We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n{\ensuremath{\omega}}_{1}$ $(n=1,2,3,\dots{}),$ which is a generalization of other works considering only $2{\ensuremath{\omega}}_{1}$, where ${\ensuremath{\omega}}_{1}$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time evolution of quantum fields, we introduce a method that is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.
70 citations
TL;DR: By properly tuning the resonator/oscillator pair, the dynamic range of the response can be extended and made more linear, closely tracking the response of the resonators alone.
Abstract: The resonant frequency of a thickness-shear mode resonator operated in contact with a fluid was measured with a network analyzer and with an oscillator circuit. The network analyzer measures changes in the device's intrinsic resonant frequency, which varies linearly with (ρη)1/2, where ρ and η are liquid density and viscosity, respectively. The resonator/oscillator combination, however, responds differently to liquid loading than the resonator alone. By applying the operating constraints of the oscillator to an equivalent-circuit model for the liquid-loaded resonator, the response of the resonator/oscillator pair can be determined. By properly tuning the resonator/oscillator pair, the dynamic range of the response can be extended and made more linear, closely tracking the response of the resonator alone. This allows the system to measure higher viscosity and higher density liquids with greater accuracy.
TL;DR: In this article, the authors derived the theory of subharmonic emission by parametrically excited distortion modes, which can explain the low level of the threshold, accounts for the observed oscillating ripples on bubble surface and demonstrates the coincidence between the frequency band where the emission of ω i ± ω p 2 signals were registered, and the one where parametric excitation of distortion modes are possible.
TL;DR: In this article, the process of modulational instability of nonlinear plane waves is investigated in media with periodically and randomly varying nonlinearity, and the wave behavior is analyzed in the parametric instability region under the joint action of periodic modulation and the self-steepening effect.
Abstract: The process of modulational instability of nonlinear plane waves is investigated in media with periodically and randomly varying nonlinearity. The wave behavior is analyzed in the parametric instability region under the joint action of periodic modulation and the self-steepening effect, and a recurrence phenomena is observed for the nonlinear wave in the parametric resonance region. Stochastic parametric resonance is predicted in the case of a random media. The increment value of stochastic parametric resonance obtained numerically is in good agreement with the theoretical estimate.
TL;DR: In this paper, the non-linear modal interaction between liquid hydrodynamic impact and an elastic support structure is examined using a special saw-tooth time transformation (STTT) technique to describe the in-phase and out-of-phase strongly nonlinear periodic regimes.
TL;DR: In this paper, the performance characteristics of a continuous-wave intracavity optical parametric oscillator are described by using an experimental arrangement comprising a KTP singly resonant oscillator located within a Ti:sapphire laser cavity and analyzed by use of a steady-state model.
Abstract: Performance characteristics of a continuous-wave intracavity optical parametric oscillator are described by use of an experimental arrangement comprising a KTP singly resonant oscillator located within a Ti:sapphire laser cavity and analyzed by use of a steady-state model. Internal and external powers, circulating fields, tuning ranges, spectral bandwidths, and amplitude-stability levels are measured and discussed. The nonresonant idler tunes from 2.53 to 2.87 microm, delivers a maximum output power of approximately 0.4W and displays long-term amplitude-stable operation. The total downconverted power approaches the optimum power coupled out of the Ti:sapphire laser in the absence of frequency conversion.
TL;DR: In this paper, the gain response of a frequency-degenerate but polarization-nondegenerate traveling-wave optical parametric amplifier that consists of a type II phase-matched potassium titanyl phosphate crystal pumped by a frequencydoubled Q-switched mode-locked Nd:YAG laser was investigated.
Abstract: We experimentally investigate the gain response of a frequency-degenerate but polarization-nondegenerate traveling-wave optical parametric amplifier that consists of a type II phase-matched potassium titanyl phosphate crystal pumped by a frequency-doubled Q-switched mode-locked Nd:YAG laser. Both the optical phase-sensitive and phase-insensitive configurations of the parametric amplifier are studied. Experimental results are in excellent agreement with the theory of an optical parametric amplifier when the Gaussian-beam nature of the various fields is taken into account. In the phase-sensitive configuration a gain of >100 (20 dB) could be easily obtained in the amplified quadrature, which is limited only by the available pump power. Because of gain-induced diffraction and phase fluctuations, however, maximum deamplification in the orthogonal quadrature is limited to <0.5(-3 dB).
TL;DR: Periodically poled lithium niobate has been used in a singly resonant optical parametric oscillator pumped by a cw mode-locked Ti:sapphire laser.
Abstract: Periodically poled lithium niobate has been used in a singly resonant optical parametric oscillator pumped cw mode-locked Ti:sapphire laser. A tuning range of 1.15 to 2.4µm was achieved when the pump was tuned, and this range was limited only by the mirror reflection bandwidth. Thresholds as low as 18 mW and an overall slope efficiency of 44% were observed, with average output powers of 130 mW (70 mW) for the signal (idler).
TL;DR: In this article, a two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position, where the normal and tangential motion are coupled through a velocity-dependent friction law.
Abstract: A two-degree-of-freedom translational system has been developed to study the influence of normal force oscillations on the stability of the steady sliding position. Excited by a small, periodic surface roughness, the normal and tangential motion are coupled through a velocity-dependent friction law. The linearized system has been examined using the first-order averaging technique of Krylov and Boguliubov. In addition to the primary forced resonance, a 2:1 parametric resonance and a 1/2 sub-harmonic resonance have been encountered. Arising from velocity-dependent coupling of the normal and tangential modes and the periodic normal force variations, the parametric resonance has been found to produce locally unstable responses in some cases. Conditions for the stability of the local response based upon local friction curve slope, static normal force, system damping, and surface velocity have been derived for a broad range of frequency.
Patent•
29 Jan 1997TL;DR: In this paper, an optical parametric amplifier was used as an amplifying gate for received light from the media to detect objects in a turbid media, and an optical gating pulse from a second parametric amplifier was used to respond to and amplify only ballistic photons from the object in the media.
Abstract: A system for detecting objects in a turbid media utilizes an optical parametric amplifier as an amplifying gate for received light from the media. An optical gating pulse from a second parametric amplifier permits the system to respond to and amplify only ballistic photons from the object in the media.
TL;DR: An optical parametric oscillator that is pumped by population-trapped atoms that are prepared with maximum coherence that is based on the use of an effective nonlinear susceptibility that is of the same order as the linear susceptibility is described.
Abstract: We describe an optical parametric oscillator that is pumped by population-trapped atoms that are prepared with maximum coherence. The oscillator is based on the use of an effective nonlinear susceptibility that is of the same order as the linear susceptibility. Because the parametric gain is obtained in a single coherence length, the gain bandwidth can exceed the degenerate frequency. In Pb vapor the calculated gain is maximized at 1.88 µm and has a bandwidth of ∼7500 cm-1.
TL;DR: The spectral and temporal characteristics of a 1.064-mm pumped, continuously tunable optical parametric oscillator using a periodically poled lithium niobate nonlinear crystal are observed.
Abstract: We have observed the spectral and temporal characteristics of a 1.064-mm pumped, continuously tunable optical parametric oscillator (OPO) using a periodically poled lithium niobate nonlinear crystal. An efficient secondary OPO pumped by the resonant signal of the primary OPO was observed. Predictions obtained from theory agree with observed results and provide insight into the dynamics of pulsed parametric oscillation. 1997 Optical Society of America.
TL;DR: In this paper, an exact quantum treatment of the generalized model of a degenerate parametric oscillator, in which self-phase modulation of the signal mode using the steady-state solution of the Fokker-Planck equation in the complex P-representation was presented.
TL;DR: Efficient generation of new spectral components owing to second-order cascading in a seeded broadband beta -barium borate typeI phase-matching parametric amplifier is demonstrated.
Abstract: Efficient generation of new spectral components owing to second-order cascading in a seeded broadband β-barium borate type I phase-matching parametric amplifier is demonstrated. One can vary the number and magnitude of these components by changing amplification bandwidth (wavelength) and phase-matching conditions. The phenomenon is treated theoretically by use of a formalism developed previously for the case of cascaded self-diffraction.
TL;DR: In this article, the normal and time ordered spatial intensity correlation function of the signal field in a degenerate parametric oscillator below threshold, with spherical mirrors, was calculated, and the correlation is maximal between points opposite each other with respect to the axis of the system.
Abstract: We calculate the normal and time ordered spatial intensity correlation function of the signal field in a degenerate parametric oscillator below threshold, with spherical mirrors. In the far field, it exhibits a two peak structure, and the correlation is maximal between points opposite each other with respect to the axis of the system. This feature provides direct spatial evidence of the twin photon emission, and identifies states of the radiated field with local nonclassical squeezing properties.
TL;DR: In this article, the authors describe configurations of a novel synchronously pumped femtosecond optical parametric oscillator based on the crystal RbTiOAsO4 and operating with a signal-pulse-repetition frequency as high as 344 MHz.
Abstract: We describe configurations of a novel synchronously pumped femtosecond optical parametric oscillator based on the crystal RbTiOAsO4 and operating with a signal-pulse-repetition frequency as high as 344 MHz. Average signal powers as high as 600 mW and pulse durations of 78 fs are demonstrated at a wavelength of 1.25 µm, and a characterization of the signal output using frequency-resolved optical gating implies asymmetric near-sech2t intensity-profile pulses with significant amounts of spectral cubic phase.
01 Jan 1997
TL;DR: In this article, an exact quantum treatment of the generalized model of a degenerate parametric oscillator, in which they allow for self-phase modulation of the signal mode, is presented.
Abstract: We present an exact quantum treatment of the generalized model of a degenerate parametric oscillator, in which we allow for self-phase modulation of the signal mode. Using the steady-state solution of the Fokker-Planck equation in the complex P-representation we obtain an exact analytical result for the Wigner quasiprobability distribution function. The obtained Wigner function allows us to give an explicit phase-space description of the nonlinear system under consideration, including the critical transition behavior in the monostable and bistable (with respect to the signal mode intensity versus the pump field intensity) operation regimes and in the threshold region. The competitive effects influenced by the self-phase modulation and the phase-space tristability are analyzed. Nonclassical effects of quadrature squeezing and quantum superposition are discussed as well.
TL;DR: In this article, a non-linear parametrically self-excited system with two degrees of freedom under harmonic external excitation was analyzed and the amplitude and the width of synchronization areas were determined.
Abstract: Vibration analysis of a non-linear parametrically self-excited system with two degrees of freedom under harmonic external excitation was carried out in the present paper. External excitation in the main parametric resonance area was assumed in the form of standard force excitation or inertial excitation. Close to the first and second free vibrations frequency, the amplitudes of the system vibrations and the width of synchronization areas were determined. Stability of obtained periodic solutions was investigated. The analytical results were verified and supplemented with the effects of digital and analog simulations.
Patent•
31 Jan 1997TL;DR: The frequency agile OPO device as mentioned in this paper converts a fixed wavelength pump laser beam to arbitrary wavelengths within a specified range with pulse to pulse agility, at a rate limited only by the repetition rate of the pump laser.
Abstract: The frequency agile OPO device converts a fixed wavelength pump laser beam to arbitrary wavelengths within a specified range with pulse to pulse agility, at a rate limited only by the repetition rate of the pump laser. Uses of this invention include Laser radar, LIDAR, active remote sensing of effluents/pollutants, environmental monitoring, antisensor lasers, and spectroscopy.
TL;DR: In this paper, a synchronously pumped intracavity frequency-doubled optical parametric oscillator that employs a single KTiOPO4 crystal for both parametric generation and frequency doubling is presented.
Abstract: We report a synchronously pumped intracavity frequency-doubled optical parametric oscillator that employs a single KTiOPO4 crystal for both parametric generation and frequency doubling. Both nonlinear processes are phase matched for the same direction of propagation in the crystal. The parametric oscillator, pumped by a femtosecond Ti:sapphire laser at a wavelength of 745 nm, generates a green output beam at 540 nm with a 29% power conversion efficiency. Angle tuning in conjunction with pump wavelength tuning provides output tunability in the 530–585-nm range.
TL;DR: In this paper, it was shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator with frequency changes from being real to imaginary and vice versa repeatedly.
Abstract: A time-dependent unitary (canonical) transformation is found that maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.