Showing papers on "Parametric oscillator published in 2002"

Fiber-based optical parametric amplifiers and their applications

Abstract: An applications-oriented review of optical parametric amplifiers in fiber communications is presented. The emphasis is on parametric amplifiers in general and single pumped parametric amplifiers in particular. While a theoretical framework based on highly efficient four-photon mixing is provided, the focus is on the intriguing applications enabled by the parametric gain, such as all-optical signal sampling, time-demultiplexing, pulse generation, and wavelength conversion. As these amplifiers offer high gain and low noise at arbitrary wavelengths with proper fiber design and pump wavelength allocation, they are also candidate enablers to increase overall wavelength-division-multiplexing system capacities similar to the more well-known Raman amplifiers. Similarities and distinctions between Raman and parametric amplifiers are also addressed. Since the first fiber-based parametric amplifier experiments providing net continuous-wave gain in the for the optical fiber communication applications interesting 1.5-/spl mu/m region were only conducted about two years ago, there is reason to believe that substantial progress may be made in the future, perhaps involving "holey fibers" to further enhance the nonlinearity and thus the gain. This together with the emergence of practical and inexpensive high-power pump lasers may in many cases prove fiber-based parametric amplifiers to be a desired implementation in optical communication systems.

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Abstract: Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.

Faraday patterns in bose-Einstein condensates.

Abstract: Temporal periodic modulation of the interatomic s-wave scattering length in Bose-Einstein condensates is shown to excite subharmonic patterns in the atom density through a parametric resonance. The dominant wavelength of the spatial structures is primarily selected by the excitation frequency but also affected by the depth of the spatial modulation via a nonlinear resonance. These phenomena represent analogues of the Faraday patterns excited in vertically vibrated liquids.

Narrow-band frequency tunable light source of continuous quadrature entanglement

Abstract: We report the observation of nonclassical quantum correlations of continuous light variables from an altogether different type of source. It is a frequency nondegenerate optical parametric oscillator below threshold, where signal and idler fields are separated by 740 MHz corresponding to two free spectrum ranges of the parametric oscillator cavity. The degree of entanglement observed, $\ensuremath{-}3.8\mathrm{dB},$ is the highest to date for a narrow-band tunable source suitable for atomic quantum memory and other applications in atomic physics. Finally we use the latter to visualize the Einstein-Podolsky-Rosen paradox.

Electron entanglement via a quantum dot.

Abstract: This Letter presents a method of electron entanglement generation. The system under consideration is a single-level quantum dot with one input and two output leads. The leads are arranged such that the dot is empty, single-electron tunneling is suppressed by energy conservation, and two-electron virtual cotunneling is allowed. Such a configuration effectively filters the singlet-state portion of a two-electron input, yielding a nonlocal spin-singlet state at the output leads. Coulomb interaction mediates the entanglement generation, and, in its absence, the singlet state vanishes. This approach is a four-wave mixing process analogous to the photon entanglement generated by a ${\ensuremath{\chi}}^{(3)}$ parametric amplifier.

Single-frequency continuous-wave optical parametric oscillator system with an ultrawide tuning range of 550 to 2830 nm

Abstract: We present a cw single-frequency laser source with what is to our knowledge the largest emission range ever demonstrated, from the green to the mid-IR range. It employs a cw optical parametric oscillator with subsequent resonant frequency doubling. Typical output powers are 30–500 mW, with 160 mW at 580 nm. Mode-hop-free oscillation, high absolute frequency stability, 20-kHz-signal linewidth, and up to 38-GHz continuous tuning are demonstrated. Both PPLN and PPKTP are used as nonlinear materials, and their performance is compared.

Self-referencing of the carrier-envelope slip in a 6-fs visible parametric amplifier

Abstract: We demonstrate a scheme for parametric amplification that allows us to measure the drift of the carrier-envelope phase of the output signal pulses. The method is based on the unique double phase-matching properties of a noncollinearly pumped BBO crystal, making possible the detection of the interference between the signal and the frequency-doubled idler. Additionally, the suggested device greatly simplifies the single-shot measurement of the phase evolution in Ti:sapphire laser amplifiers by dispensing with harmonic synthesis from the spectral edges of an octave-wide supercontinuum.

Dynamical Casimir Effect in a Leaky Cavity at Finite Temperature

Abstract: The phenomenon of particle creation within an almost resonantly vibrating cavity with losses is investigated for the example of a massless scalar field at finite temperature. A leaky cavity is designed via the insertion of a dispersive mirror into a larger ideal cavity (the reservoir). In the case of parametric resonance the rotating wave approximation allows for the construction of an effective Hamiltonian. The number of produced particles is then calculated using response theory as well as a nonperturbative approach. In addition, we study the associated master equation and briefly discuss the effects of detuning. The exponential growth of the particle numbers and the strong enhancement at finite temperatures found earlier for ideal cavities turn out to be essentially preserved. The relevance of the results for experimental tests of quantum radiation via the dynamical Casimir effect is addressed. Furthermore, the generalization to the electromagnetic field is outlined.

Improving short and long term frequency stability of the opto-electronic oscillator

Abstract: For the first time, the high Q components of the optoelectronic oscillator, i.e. the optical fiber, and the narrow pass band microwave filter in the oscillator loop were thermally stabilized to improve the oscillator short- and long-term frequency stability. In our design, the temperature of these elements is kept above ambient and stabilized with the help of resistive heaters and temperature controllers. With this scheme the free running oscillator demonstrates a short-term frequency stability of 0.02 ppm and frequency vs. temperature slope of -0.1 ppm//spl deg/C (at 20-30/spl deg/C) with an exceptional spectral purity (-143 dBc/Hz at 10 kHz offset frequency). Locking the opto-electronic oscillator to a standard reference oscillator, oscillating at 100 MHz further stabilized the 10 GHz microwave carrier frequency.

Piezoelectric adjusting element

Abstract: The invention relates to a piezoelectric adjusting element, in particular a piezoelectric motor in the form of a monolithic plate-shaped or cylindrical piezoelectric oscillator comprised of a first and of a second kind of main surfaces and of groups of electrodes that are allocated to them, comprised of a housing, a driven element, at least one friction layer arranged on the housing or on the driven element, a driving element that is connected to an electric excitation source and that is in friction contact with the friction layer, and the piezoelectric oscillator is excited by way of the groups of electrodes [to form] standing longitudinal acoustic waves in the direction of an oscillator resonant length and in the direction of an oscillator resonant height of this piezoelectric oscillator, and the oscillator resonant length is equal to an integral multiple of the wave length of the standing longitudinal wave that vibrates in its direction, and the oscillator resonant height is equal to one half of the wave length of the standing longitudinal wave that vibrates in its direction, and the oscillator resonant length as well as the oscillator resonant height are chosen in such a way that the frequencies of the standing longitudinal acoustic waves expanding through the piezoelectric oscillator are equal both in the direction of the oscillator resonant length as well as in the direction of the oscillator resonant height.

Is an oscillator-based measurement adequate in a liquid environment?

Abstract: Oscillator-based measurements with quartz crystal resonators are analyzed. The investigations have shown that classical thickness monitors as well as many chemical vapor sensors based on a quartz crystal microbalance (QCM) work properly, even with simple oscillators. It was demonstrated that, for applications in a liquid environment, more sophisticated electronics are necessary. Also a comparison between the experimental results in liquids and the theoretical predictions is hardly possible without the knowledge of the oscillator behavior. As our solution, we present an automatic gain-controlled oscillator with two output signals, the oscillator frequency, and a signal that represents the damping of the quartz resonator. A calibration method is introduced, which allows one to calculate the series resonance frequency f/sub s/ and the series resistance R/sub s/ from these oscillator signals.

Periodic quantum tunnelling and parametric resonance with cigar-shaped Bose-Einstein condensates

Abstract: We study the tunnelling properties of a cigar-shaped Bose-Einstein condensate by using an effective 1D nonpolynomial nonlinear Schrodinger equation (NPSE). First we investigate a mechanism to generate periodic pulses of coherent matter by means of a Bose condensate confined in a potential well with an oscillating height of the energy barrier. We show that it is possible to control the periodic emission of matter waves and the tunnelling fraction of the Bose condensate. We find that the number of emitted particles strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the centre of mass of the condensate inside the potential well. Then we use NPSE to analyse the periodic tunnelling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency of the oscillating energy barrier. The macroscopic quantum self-trapping (MQST) of the condensate can be suppressed under the condition of parametric resonance between the frequency of the energy barrier and the frequency of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.

Measuring irreversible dynamics of a quantum harmonic oscillator

Abstract: We show that the unitary evolution of a harmonic oscillator coupled to a two-level system can be undone by a suitable manipulation of the two-level system---more specifically, by a quasi-instantaneous phase change. This enables us to isolate the dissipative evolution to which the oscillator may be exposed in addition. With this method we study the decoherence time of a photon mode in cavity QED, and that of the quantized harmonic motion of trapped ions. We comment on the relation to spin echoes and multipath interferometry.

Critical quantum fluctuations in the degenerate parametric oscillator

Abstract: We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Asymptotic solutions for a damped non-linear quasi-periodic Mathieu equation

Abstract: Quasi-periodic (QP) solutions of a weakly damped non-linear QP Mathieu equation are investigated near a double primary parametric resonance. A double multiple scales method is applied to reduce the original QP oscillator to an autonomous system performing two successive reduction. The problem for approximating QP solutions of the original system is then transformed to the study of stationary regimes of the induced autonomous system. Explicit analytical approximations to QP oscillations are obtained and comparisons to numerical integration of the original QP oscillator are provided.

Form and width of the spectral line of a Josephson flux-flow oscillator.

Abstract: The behavior of a Josephson flux-flow oscillator in the presence of both bias current and magnetic field fluctuations has been studied. To derive the equation for slow phase dynamics in the limit of small noise intensity the Poincare method has been used. Both the form of spectral line and the linewidth of the flux-flow oscillator have been derived analytically on the basis of known frequency modulation theory technique, known limiting cases are considered, limits of their applicability are discussed and appearance of excess noise is explained. Good coincidence of theoretical description with experimental results has been demonstrated.

Demonstration of improved beam quality in an image-rotating optical parametric oscillator

Abstract: We performed laboratory and numerical modeling studies of an optical parametric oscillator with 90° intracavity image rotation. We found that the signal beam was more symmetric than that from comparable cavities without image rotation, and it had low values of the beam quality factor, M2. Oscillator performance agreed well with our numerical model.

Entangled-cavity optical parametric oscillator for mid-infrared pulsed single-longitudinal-mode operation.

Abstract: We report a pulsed doubly resonant optical parametric oscillator that uses an original entangled-cavity geometry. This compact source (total volume of 1 L, including the pump laser) displays single-frequency operation (linewidth, 10 kHz, low threshold <10 µJ, and wide tuning in the mid-infrared. These properties qualify pulsed doubly resonant optical parametric oscillators as powerful tools for applications in such fields as nonlinear spectroscopy, lidar, and pollutant detection.

Frequency-Agile Terahertz-Wave Parametric Oscillator

Abstract: We demonstrated a pulse-to-pulse frequency-tunable LiNbO3 terahertz-wave parametric oscillator, pumped with a Q-switched Nd:YAG laser. Rapid tuning from 1 to 2 THz, with random frequency accessibility, was achieved by rotating the pump beam angle using an optical beam scanner and a telescope.

Optical parametric oscillator with a 10-GHz repetition rate and 100-mW average output power in the spectral region near 1.5 μm

Abstract: We demonstrate a synchronously pumped optical parametric oscillator that emits picosecond pulses at an ∼1.55‐µm wavelength with a repetition rate as a high as 10 GHz and as much as 100 mW of average power. It is pumped with a diode-pumped passively mode-locked 10-GHz Nd:YVO4 laser. Because of its high repetition rate and its potential for ultrabroad tunability, this kind of system is useful for telecom applications. It should be scalable to 40 GHz and higher as required for future telecom networks.

Periodic Quantum Tunneling and Parametric Resonance with Cigar-Shaped Bose-Einstein Condensates

Abstract: We study the tunneling properties of a cigar-shaped Bose-Einstein condensate by using an effective 1D nonpolynomial nonlinear Schr\"odinger equation (NPSE). First we investigate a mechanism to generate periodic pulses of coherent matter by means of a Bose condensate confined in a potential well with an oscillating height of the energy barrier. We show that is possible to control the periodic emission of matter waves and the tunneling fraction of the Bose condensate. We find that the number of emitted particles strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Then we use NPSE to analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency of the oscillating energy barrier. The macroscopic quantum self-trapping (MQST) of the condensate can be suppressed under the condition of parametric resonance between the frequency of the energy barrier and the frequency of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.

Wave function of the time-dependent inverted harmonic oscillator

Abstract: Time-dependent mass and frequency inverted harmonic oscillator is discussed in light of the Lewis and Reisenfeld invariant method. The wave function is found in terms of the Weber function. As an example, we derive the wave function of the inverted Caldirola-Kanai oscillator.

1-Ghz-repetition-rate femtosecond optical parametric oscillator

Abstract: We report a 1-GHz-repetition-rate, low-pump-threshold, all-solid-state femtosecond optical parametric oscillator (OPO) based on periodically poled LiNbO3 and pumped by a GHz repetition rate Ti:sapphire laser. The OPO provides nearly transform-limited 65-fs-signal pulses tunable from 1160 to 1320 nm. The pump threshold is about 580 mW, and 43 mW signal power is obtained with 950-mW-pump power. Higher-order quasi-phase-matched sum frequency generation and second harmonic generation processes produce 10 mW blue light at 486 nm and 15 mW red light at 620 nm.

Efficient conversion from 1 to 2 microm by a KTP-based ring optical parametric oscillator.

Abstract: Conversion of Q-switched 1.064‐µm Nd:YAG laser pulses to the 2–2.2‐µm region with 46% efficiency is demonstrated with a KTP-based type 2 phase-matched optical parametric oscillator (OPO) with two pairs of walk-off compensating crystals in a ring resonator. With 10 mJ of pump energy, we obtain 2.5 mJ at the 2.06‐µm signal and 2.1 mJ at the 2.2‐µm idler, with a beam quality of M2≈1.4. With a ZnGeP2-based OPO pumped by the signal from the KTP OPO we achieved 14% conversion efficiency from 1.064 µm to the 3–5‐µm range.

Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach

Abstract: An open-loop nonlinear control strategy applied to a hinged-hinged shallow arch, subjected to a longitudinal end-displacement with frequency twice the frequency of the second mode (principal parametric resonance), is developed. The control action?a transverse point force at the midspan?is typical of many single-input control systems; the control authority onto part of the system dynamics is high whereas the control authority onto some other part of the system dynamics is zero within the linear regime. However, although the action of the controller is orthogonal, in a linear sense, to the externally excited first antisymmetric mode, beneficial effects are exerted through nonlinear actuator action due to the system structural nonlinearities. The employed mechanism generating the effective nonlinear controller action is a one-half subharmonic resonance (control frequency being twice the frequency of the excited mode). The appropriate form of the control signal and associated phase is suggested by the dynamics at reduced orders, determined by a multiple-scales perturbation analysis directly applied to the integral-partial-differential equations of motion and boundary conditions. For optimal control phase and gain?the latter obtained via a combined analytical and numerical approach with minimization of a suitable cost functional?the parametric resonance is cancelled and the response of the system is reduced by orders of magnitude near resonance. The robustness of the proposed control methodology with respect to phase and frequency variations is also demonstrated. ©2002 ASME

Swing excitation and magnetic activity in close binary systems

Abstract: Parametric resonance between the perturbation of a stellar convective zone affected by a companion of a close binary system and non-axisymmetric dynamo modes can play an important role in close binary systems This process in combination with the previously suggested α 2 mechanism is probably responsible for strongly non-axisymmetric magnetic activity observed in several close binaries The conditions required for swing excitation to occur in such systems are directly related to the status of rotational synchronization between the orbital motion and rotation of the star, which can be used as a tool to discover such objects One potential candidate ‐ an active RS CVn-type star ER Vulpeculae ‐ shows indications of the swing excitation

Quantum parametric resonance

Abstract: The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are shown to correspond to Floquet operators with qualitatively different properties. Their eigenfunctions, which are calculated exactly, exhibit a transition: for parameter values with classically stable solutions the eigenstates are normalizable while they cannot be normalized for parameter values with classically unstable solutions. Similarly, the spectrum of quasi energies undergoes a specific transition. These observations remain valid qualitatively for arbitrary linear systems exhibiting classically parametric resonance such as the paradigm example of a frequency modulated pendulum described by Mathieu's equation.