Showing papers on "Parametric oscillator published in 2000"

Electromagnetic Noise and Quantum Optical Measurements

Abstract: 1. Maxwell's Equations, Power, and Energy.- 1.1 Maxwell's Field Equations.- 1.2 Poynting's Theorem.- 1.3 Energy and Power Relations and Symmetry of the Tensor.- 1.4 Uniqueness Theorem.- 1.5 The Complex Maxwell's Equations.- 1.6 Operations with Complex Vectors.- 1.7 The Complex Poynting Theorem.- 1.8 The Reciprocity Theorem.- 1.9 Summary.- Problems.- Solutions.- 2. Waveguides and Resonators.- 2.1 The Fundamental Equations of Homogeneous Isotropic Waveguides.- 2.2 Transverse Electromagnetic Waves.- 2.3 Transverse Magnetic Waves.- 2.4 Transverse Electric Waves.- 2.4.1 Mode Expansions.- 2.5 Energy, Power, and Energy Velocity.- 2.5.1 The Energy Theorem.- 2.5.2 Energy Velocity and Group Velocity.- 2.5.3 Energy Relations for Waveguide Modes.- 2.5.4 A Perturbation Example.- 2.6 The Modes of a Closed Cavity.- 2.7 Real Character of Eigenvalues and Orthogonality of Modes.- 2.8 Electromagnetic Field Inside a Closed Cavity with Sources.- 2.9 Analysis of Open Cavity.- 2.10 Open Cavity with Single Input.- 2.10.1 The Resonator and the Energy Theorem.- 2.10.2 Perturbation Theory and the Generic Form of the Impedance Expression.- 2.11 Reciprocal Multiports.- 2.12 Simple Model of Resonator.- 2.13 Coupling Between Two Resonators.- 2.14 Summary.- Problems.- Solutions.- 3. Diffraction, Dielectric Waveguides, Optical Fibers, and the Kerr Effect.- 3.1 Free-Space Propagation and Diffraction.- 3.2 Modes in a Cylindrical Piecewise Uniform Dielectric.- 3.3 Approximate Approach.- 3.4 Perturbation Theory.- 3.5 Propagation Along a Dispersive Fiber.- 3.6 Solution of the Dispersion Equation for a Gaussian Pulse.- 3.7 Propagation of a Polarized Wave in an Isotropic Kerr Medium.- 3.7.1 Circular Polarization.- 3.8 Summary.- Problems.- Solutions.- 4. Shot Noise and Thermal Noise.- 4.1 The Spectrum of Shot Noise.- 4.2 The Probability Distribution of Shot Noise Events.- 4.3 Thermal Noise in Waveguides and Transmission Lines.- 4.4 The Noise of a Lossless Resonator.- 4.5 The Noise of a Lossy Resonator.- 4.6 Langevin Sources in a Waveguide with Loss.- 4.7 Lossy Linear Multiports at Thermal Equilibrium.- 4.8 The Probability Distribution of Photons at Thermal Equilibrium.- 4.9 Gaussian Amplitude Distribution of Thermal Excitations.- 4.10 Summary.- Problems.- Solutions.- 5. Linear Noisy Multiports.- 5.1 Available and Exchangeable Power from a Source.- 5.2 The Stationary Values of the Power Delivered by a Noisy Multiport and the Characteristic Noise Matrix.- 5.3 The Characteristic Noise Matrix in the Admittance Representation Applied to a Field Effect Transistor.- 5.4 Transformations of the Characteristic Noise Matrix.- 5.5 Simplified Generic Forms of the Characteristic Noise Matrix.- 5.6 Noise Measure of an Amplifier.- 5.6.1 Exchangeable Power.- 5.6.2 Noise Figure.- 5.6.3 Exchangeable Power Gain.- 5.6.4 The Noise Measure and Its Optimum Value.- 5.7 The Noise Measure in Terms of Incident and Reflected Waves.- 5.7.1 The Exchangeable Power Gain.- 5.7.2 Excess Noise Figure.- 5.8 Realization of Optimum Noise Performance.- 5.9 Cascading of Amplifiers.- 5.10 Summary.- Problems.- Solutions.- 6. Quantum Theory of Waveguides and Resonators.- 6.1 Quantum Theory of the Harmonic Oscillator.- 6.2 Annihilation and Creation Operators.- 6.3 Coherent States of the Electric Field.- 6.4 Commutator Brackets, Heisenberg's Uncertainty Principle and Noise.- 6.5 Quantum Theory of an Open Resonator.- 6.6 Quantization of Excitations on a Single-Mode Waveguide.- 6.7 Quantum Theory of Waveguides with Loss.- 6.8 The Quantum Noise of an Amplifier with a Perfectly Inverted Medium.- 6.9 The Quantum Noise of an Imperfectly Inverted Amplifier Medium.- 6.10 Noise in a Fiber with Loss Compensated by Gain.- 6.11 The Lossy Resonator and the Laser Below Threshold.- 6.12 Summary.- Problems.- Solutions.- 7. Classical and Quantum Analysis of Phase-Insensitive Systems.- 7.1 Renormalization of the Creation and Annihilation Operators.- 7.2 Linear Lossless Multiports in the Classical and Quantum Domains.- 7.3 Comparison of the Schrodinger and Heisenberg Formulations of Lossless Linear Multiports.- 7.4 The Schrodinger Formulation and Entangled States.- 7.5 Transformation of Coherent States.- 7.6 Characteristic Functions and Probability Distributions.- 7.6.1 Coherent State.- 7.6.2 Bose-Einstein Distribution.- 7.7 Two-Dimensional Characteristic Functions and the Wigner Distribution.- 7.8 The Schrodinger Cat State and Its Wigner Distribution.- 7.9 Passive and Active Multiports.- 7.10 Optimum Noise Measure of a Quantum Network.- 7.11 Summary.- Problems.- Solutions.- 8. Detection.- 8.1 Classical Description of Shot Noise and Heterodyne Detection.- 8.2 Balanced Detection.- 8.3 Quantum Description of Direct Detection.- 8.4 Quantum Theory of Balanced Heterodyne Detection.- 8.5 Linearized Analysis of Heterodyne Detection.- 8.6 Heterodyne Detection of a Multimodal Signal.- 8.7 Heterodyne Detection with Finite Response Time of Detector.- 8.8 The Noise Penalty of a Simultaneous Measurement of Two Noncommuting Observables.- 8.9 Summary.- Problems.- Solutions.- 9. Photon Probability Distributions and Bit-Error Rate of a Channel with Optical Preamplification.- 9.1 Moment Generating Functions.- 9.1.1 Poisson Distribution.- 9.1.2 Bose-Einstein Distribution.- 9.1.3 Composite Processes.- 9.2 Statistics of Attenuation.- 9.3 Statistics of Optical Preamplification with Perfect Inversion.- 9.4 Statistics of Optical Preamplification with Incomplete Inversion.- 9.5 Bit-Error Rate with Optical Preamplification.- 9.5.1 Narrow-Band Filter, Polarized Signal, and Noise.- 9.5.2 Broadband Filter, Unpolarized Signal.- 9.6 Negentropy and Information.- 9.7 The Noise Figure of Optical Amplifiers.- 9.8 Summary.- Problems.- Solutions.- 10. Solitons and Long-Distance Fiber Communications.- 10.1 The Nonlinear Schrodinger Equation.- 10.2 The First-Order Soliton.- 10.3 Properties of Solitons.- 10.4 Perturbation Theory of Solitons.- 10.5 Amplifier Noise and the Gordon-Haus Effect.- 10.6 Control Filters.- 10.7 Erbium-Doped Fiber Amplifiers and the Effect of Lumped Gain.- 10.8 Polarization.- 10.9 Continuum Generation by Soliton Perturbation.- 10.10 Summary.- Problems.- Solutions.- 11. Phase-Sensitive Amplification and Squeezing.- 11.1 Classical Analysis of Parametric Amplification.- 11.2 Quantum Analysis of Parametric Amplification.- 11.3 The Nondegenerate Parametric Amplifier as a Model of a Linear Phase-Insensitive Amplifier.- 11.4 Classical Analysis of Degenerate Parametric Amplifier.- 11.5 Quantum Analysis of Degenerate Parametric Amplifier.- 11.6 Squeezed Vacuum and Its Homodyne Detection.- 11.7 Phase Measurement with Squeezed Vacuum.- 11.8 The Laser Resonator Above Threshold.- 11.9 The Fluctuations of the Photon Number.- 11.10 The Schawlow-Townes Linewidth.- 11.11 Squeezed Radiation from an Ideal Laser.- 11.12 Summary.- Problems.- Solutions.- 12. Squeezing in Fibers.- 12.1 Quantization of Nonlinear Waveguide.- 12.2 The x Representation of Operators.- 12.3 The Quantized Equation of Motion of the Kerr Effect in the x Representation.- 12.4 Squeezing.- 12.5 Generation of Squeezed Vacuum with a Nonlinear Interferometer.- 12.6 Squeezing Experiment.- 12.7 Guided-Acoustic-Wave Brillouin Scattering.- 12.8 Phase Measurement Below the Shot Noise Level.- 12.9 Generation of Schrodinger Cat State via Kerr Effect.- 12.10 Summary.- Problems.- Solutions.- 13. Quantum Theory of Solitons and Squeezing.- 13.1 The Hamiltonian and Equations of Motion of a Dispersive Waveguide.- 13.2 The Quantized Nonlinear Schrodinger Equation and Its Linearization.- 13.3 Soliton Perturbations Projected by the Adjoint.- 13.4 Renormalization of the Soliton Operators.- 13.5 Measurement of Operators.- 13.6 Phase Measurement with Soliton-like Pulses.- 13.7 Soliton Squeezing in a Fiber.- 13.8 Summary.- Problems.- Solutions.- 14. Quantum Nondemolition Measurements and the "Collapse" of the Wave Function.- 14.1 General Properties of a QND Measurement.- 14.2 A QND Measurement of Photon Number.- 14.3 "Which Path" Experiment.- 14.4 The "Collapse" of the Density Matrix.- 14.5 Two Quantum Nondemolition Measurements in Cascade.- 14.6 The Schrodinger Cat Thought Experiment.- 14.7 Summary.- Problems.- Solutions.- Epilogue.- Appendices.- A.1 Phase Velocity and Group Velocity of a Gaussian Beam.- A.2 The Hermite Gaussians and Their Defining Equation.- A.2.1 The Defining Equation of Hermite Gaussians.- A.2.2 Orthogonality Property of Hermite Gaussian Modes.- A.2.3 The Generating Function and Convolutions of Hermite Gaussians.- A.3 Recursion Relations of Bessel Functions.- A.4 Brief Review of Statistical Function Theory.- A.5 The Different Normalizations of Field Amplitudes and of Annihilation Operators.- A.5.1 Normalization of Classical Field Amplitudes.- A.5.2 Normalization of Quantum Operators.- A.6 Two Alternative Expressions for the Nyquist Source.- A.7 Wave Functions and Operators in the n Representation.- A.8 Heisenberg's Uncertainty Principle.- A.9 The Quantized Open-Resonator Equations.- A.10 Density Matrix and Characteristic Functions.- A.10.1 Example 1. Density Matrix of Bose-Einstein State.- A.10.2 Example 2. Density Matrix of Coherent State.- A.11 Photon States and Beam Splitters.- A.12 The Baker-Hausdorff Theorem.- A.12.1 Theorem 1.- A.12.2 Theorem 2.- A.12.3 Matrix Form of Theorem 1.- A.12.4 Matrix Form of Theorem 2.- A.13 The Wigner Function of Position and Momentum.- A.14 The Spectrum of Non-Return-to-Zero Messages.- A.15 Various Transforms of Hyperbolic Secants.- A.16 The Noise Sources Derived from a Lossless Multiport with Suppressed Terminals.- A.17 The Noise Sources of an Active System Derived from Suppression of Ports.- A.19 The Heisenberg Equation in the Presence of Dispersion.- References.

Stochastic Processes in Physics, Chemistry, and Biology

Abstract: Stochastic Transport and Brownian Motion.- Directed Current Without Dissipation: Reincarnation of a Maxwell-Loschmidt Demon.- Molecular Motors and Stochastic Models.- Nonlinearly Coupled Chemical Reactions.- Thermodynamics of Isothermal Brownian Motors.- Rocking Ratchets at High Frequencies.- Defect Dragging in Periodic Structures.- Conduction in an Inhomogeneous Medium.- Theory and Control of Multiple Hopping in Activated Surface Diffusion.- Brownian Motion in a d-Dimensional Space with Fluctuating Friction.- Active Motion of Brownian Particles.- Diffusion in Granular Gases of Viscoelastic Particles.- Stochastic Resonance and Phase Synchronization.- Scaling of Noise and Constructive Aspects of Fluctuations.- Stochastic Resonances in Underdamped Bistable Systems.- Stochastic Resonance in a System of Coupled Asymmetric Resonators.- Optimizing Information Transmission in Model Neuronal Ensembles: The Role of Internal Noise.- Stochastic Resonance with Images and Spatially Correlated Stochastic Patterns.- Adiabatic and Non-adiabatic Resonances in Excitable Systems.- The Lighthouse Model of a Neural Net with Delay.- Noise-enhanced Phase Coherence in Ensembles of Stochastic Resonators.- Estimation of Synchronization from Noisy Data with Application to Human Brain Activity.- Nonequilibrium Thermodynamics and Dynamical Complexity.- Noise-Induced Phase Transitions and Reactive Processes.- Noise-Induced Order in Extended Systems: A Tutorial.- Linear Instability Mechanisms of Noise-Induced Phase Transitions.- Parametric Resonance Revisited.- On Noise-Induced Transitions in Nonlinear Oscillators.- The Kramers Oscillator Revisited.- Reactive Processes in Low Dimensions: Statistical and Dynamical Aspects.- On-Off Intermittency and Stochastic Stability in Nematics Driven by Multiplicative Noise.- Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates.- Experimental Studies of Noise-Induced Phenomena in a Tunnel Diode.- Quantum Mechanical Model of Proton Transfer in a Fluctuating Potential Field of the Active Site of ?-Chymotrypsin.- Large Fluctuations and Noise in Chaotic Systems.- A Gentle Introduction to the Integration of Stochastic Differential Equations.- Controlling Large Fluctuations: Theory and Experiment.- Fluctuational Escape from a Chaotic Attractor.- Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium.- Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems.- Peculiarities of Nonhyperbolic Chaos.- Information of Open Systems.- Structure Formation.- Nonlinear Spatiotemporal Patterns in Globally Coupled Reaction-Diffusion Systems.- Segregation Effects in Randomly Mixed Diffusion-Controlled Binary Reactions.- Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia.- Stochastic Field Equation for Amorphous Surface Growth.- Epitaxial Growth with Elastic Interaction: Layer and Cluster Growth.- Stochastic Evolution of a Discrete Line: Numerical Results.- Structures in Planetary Rings- Stability and Gravitational Scattering.

Parametric amplification of metric fluctuations during reheating in two field models

Abstract: We study the parametric amplification of super-Hubble-scale scalar metric fluctuations at the end of inflation in some specific two-field models of inflation, a class of which is motivated by hybrid inflation. We demonstrate that there can indeed be a large growth of fluctuations due to parametric resonance and that this effect is not taken into account by the conventional theory of isocurvature perturbations. Scalar field interactions play a crucial role in this analysis. We discuss the conditions under which there can be nontrivial parametric resonance effects on large scales.

Quasi-phase-matched optical parametric oscillation with periodically poled stoichiometric LiTaO(3).

Abstract: We have demonstrated, for the first time to our knowledge, periodic poling of a 2-mm-thick near-stoichiometric LiTaO3 substrate and its operation in a nanosecond optical parametric oscillator. Because the coercive field of stoichiometric LiTaO3 is ∼2 kV/mm, which is approximately one tenth that of the conventional congruent field, periodic poling of thicker stoichiometric substrates was successfully performed by means of an electric-field poling process at room temperature. The performance of a parametric oscillator with a 1-mm-thick sample was compared with that of the oscillator with the periodically poled congruent oscillator. The stoichiometric device exhibited better performance.

Parametric resonance in microelectromechanical structures

Abstract: MEM structures which may be driven at parametric frequencies to provide stable operation and to permit precise switching between stable and unstable operations by very small changes in the drive frequency or by very small changes in the characteristics of the structure itself so as to provide improved control and sensing are disclosed. The techniques of the present invention are applicable to a wide variety of microstructures, including parallel plate linear actuators, reduction and augmentation actuators, linear force comb actuators, and in particular to torsional scanning probe z-actuators having an integrated tip. These devices incorporate capacitive actuators, or drivers, for producing mechanical motion, and more particularly comb-type actuator structures which consist of high aspect ratio MEM beams fabricated as interleaved fixed and movable capacitor fingers. The capacitive actuator structures can be used either for sensing displacements or inducing motion, the capacitive plates of the fixed and movable fingers allowing a wide range of motion and high amplitudes without failure. Such micromechanical torsional resonators obey the Mathieu equation, and are driven by a suitable driving force such as an AC driver to resonate at frequencies other than their natural frequencies of resonance with a sharp transition between stable and unstable operation. The devices may be switched between stable and unstable operation by very small changes in the physical characteristics, or parameters, of the devices and/or by small changes in the frequency or amplitude of the driving force.

Optical parametric oscillator far below threshold: Experiment versus theory

Abstract: The theory of the optical parametric oscillator is examined and compared to the experiment in the regime of far below threshold. It is found that the output state has no difference from spontaneous parametric down-conversion except that the bandwidth of down-conversion is reduced to that of the resonator and the conversion rate is enhanced by cavity resonance. The reduction of the bandwidth of the down-converted fields makes it possible for a direct measurement of the time interval distribution between two down-converted photons. The observed distributions are well explained by the theory. Such a narrow-band two-photon source will find wide applications in quantum information processing.

High-power optical parametric oscillation in large-aperture periodically poled KTiOPO(4).

Abstract: Electric field poling has been employed to fabricate 3-mm-thick periodically poled KTiOPO4 crystal for a high-power optical parametric oscillator. The maximum output power of the singly resonant optical parametric oscillator reached 13 mJ with 45% efficiency when the resonator was pumped with a 2.2-mm-diameter beam from a Q‐switched Nd:YAG laser. The influence of the cavity design on the spectral and spatial qualities of the output parametric radiation is also discussed.

A theoretical and experimental investigation of indirectly excited roll motion in ships

Abstract: The phenomenon of indirectly exciting the roll motion of a vessel due to nonlinear couplings of the heave, pitch and roll modes is investigated theoretically and analytically. Two nonlinear mechanisms that cause large-amplitude rolling motions in a head or following sea are investigated. The first mechanism is internal or autoparametric resonance and the second is parametric resonance. The energy put into the pitch and heave modes by the wave excitations may be transferred into the roll mode by means of nonlinear coupling among these modes; thus, the roll can be indirectly excited. As a result, a ship in a head or following sea can spontaneously develop severe rolling motion. In the analytical approach, the method of multiple scales is used to determine a system of nonlinear first-order equations governing the modulation of the amplitudes and phases of the system. The fixed-point solutions of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found in the case of two-to-one internal resonance. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They demonstrate some of the nonlinear effects, such as the jump phenomenon, the subcritical instability, and the coexistence of multiple solutions. The experimental results are in good qualitative agreement with the results predicted theoretically.

Effect of resonator length on a doubly resonant optical parametric oscillator pumped by a multilongitudinal-mode beam

Abstract: The resonator length of an optical parametric oscillator (OPO) is normally made a short as possible to minimize the signal-buildup time and maximize the output energy. We have found that, when a doubly resonant OPO is pumped by a multilongitudinal-mode beam, its output energy has a significant maximum when its optical length matches that of the pump source, even if this length is much greater than the shortest possible for the OPO. We have observed this effect in a ZnGeP>(2)-based OPO and reproduced it in numerical simulations.

All-optical limiter using gain flattened fibre parametric amplifier

Abstract: An all-optical limiting amplifier that is capable of reducing amplitude fluctuations in 20 Gbit/s data packets is presented. The limiting amplifier is based on a gain flattened two-stage fibre parametric amplifier having a record bandwidth of 15 nm.

Saturated behavior of the gyrotron backward-wave oscillator

Abstract: Physical processes in the gyrotron backward-wave oscillator (gyro-BWO) are investigated theoretically. Results indicate highly current-sensitive field profiles and hence sharply contrasting linear and saturated behaviors. The linear field extends over the entire structure length, whereas the saturated profile depends strongly on the energetics in the internal feedback loop. It is shown that this distinctive feature substantially influences the basic properties of the gyro-BWO including the start-oscillation current, efficiency, power scaling, and stability of tuning.

Measurement of the optical phase relation among subharmonic pulses in a femtosecond optical parametric oscillator.

Abstract: We observed the phase relation among subharmonic pulses generated by a femtosecond optical parametric oscillator (OPO). The ratio of the optical frequencies of the idler, the signal, and the pump pulses was set to 1:2:3. Under these conditions the wavelengths of the second harmonic of the signal pulse and the sum frequency between the pump and the idler pulses are the same. The beat signal between these two pulses represents the phase relationship among the pump, the signal, and the idler. The beat frequency varied when the cavity length of the OPO was changed.

Microlaser-pumped periodically poled lithium niobate optical parametric generator-optical parametric amplifier.

Abstract: For what is believed to be the first time, a single-longitudinal-mode passively Q-switched Nd:YAG microlaser is used to pump a narrow-bandwidth periodically poled lithium niobate (PPLN) optical parametric generator–optical parametric amplifier (OPG–OPA). Before amplification in the OPA, the output of the OPG stage was spectrally filtered with an air-spaced etalon, resulting in spectroscopically useful radiation (bandwidth, ∼0.05 cm-1 FWHM) that was tunable in 15‐cm-1 segments anywhere in the signal range 6820–6220 cm-1 and the idler range 2580–3180 cm-1. The ability to pump an OPG–OPA with compact, high-repetition-rate, intrinsically narrow-bandwidth microlasers is made possible by the high gain of PPLN. The result is a tunable light source that is well suited for use in portable spectroscopic gas sensors.

Extended mode-hop-free tuning by use of a dual-cavity, pump-enhanced optical parametric oscillator

Abstract: We report extended mode-hop-free tuning in a continuous-wave, pump-enhanced optical parametric oscillator (PE-OPO). We employ a dual-cavity configuration to allow independent control of the resonant pump and signal fields, and so we can suppress frequent mode hops in the signal as the pump is tuned in frequency. With the signal field clamped in frequency by an uncoated etalon, the idler field can be scanned smoothly through a range of 10.8 GHz. The PE-OPO outputs can also be tuned coarsely from 1.01 to 1.18 µm in the signal and from 2.71 to 3.26 µm and 4.07 to 5.26 µm in the idler. We find that increased idler absorption only slightly increases the oscillation threshold.

Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator

Abstract: We study the dynamics of the formation of circular domain walls, which are large-intensity structures, in a degenerate optical parametric oscillator. We show that the mean-field and the propagation models predict the same increase in the domain size proportional to t(1/3) .

Suppression of chaos in averaged oscillator driven by external and parametric excitations

Abstract: Controlling chaos in a nonlinear oscillator subjected to external and parametric excitations having incommensurate frequencies is discussed An averaging method is first applied to reduce the original quasi-periodically driven system to a periodically driven one The Melnikov method is applied on the reduced periodically driven system and the Melnikov function is subsequently established The possibility of achieving a suitable system for the control of chaos in the averaged system by introducing a third harmonic parametric component into the cubic term of the original one is investigated

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

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

Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

Abstract: The unitary operator that transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different timescale is found, with and without an inverse-square potential It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given

Thermo-optical effect and saturation of nonlinear absorption induced by gray tracking in a 532-nm-pumped KTP optical parametric oscillator.

Abstract: We present experiments that show that gray tracking modifies the parametric gain and the generated wavelengths of a KTP optical parametric oscillator pumped at 532 nm near degeneracy. These perturbations occur over a limited range of pump intensity. We propose a satisfactory model that takes into account photochromic damage, the thermo-optical effect, and the combined processes of creation and saturation of a two-photon absorber at 532 nm. The temperature dependence of Sellmeier equations of KTP is also established at 20-200 degrees C.

Second harmonic autoresonant control of the l=1 diocotron mode in pure-electron plasmas

Abstract: An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the fundamental frequency, i.e, second harmonic autoresonance. The $l=1$ diocotron mode in pure-electron plasmas, a very high Q nonlinear oscillator, is the focus of the paper. The theory for this oscillator is derived, and compared to experimental results. The results can be generalized to any Duffing-like driven nonlinear oscillator in which the coupling between the drive and the oscillator depends at least weakly on the oscillator amplitude.

Oscillator having a transistor formed of a wide bandgap semiconductor material

Abstract: An oscillator and upconverters and downconverters including the oscillator are provided, wherein the oscillator includes a transistor comprised of a semiconductor material having a wide bandgap for producing RF output signals For example, the transistor can be formed of a semiconductor material, such as GaN, AlGaN, SiC or BN, that has a bandgap of at least 20 eV The oscillator also includes a bias supply for providing a supply voltage and a supply current Additionally, the oscillator has a tank circuit that includes first and second reactances connected to respective terminals of the transistor such that the transistor is unstable and an oscillating RF output signal is produced The tank circuit can also include a varactor connected to a respective reactance and a control input is provided to tune the oscillating RF output signal Upconverters, both saturated and linear, and downconverters are also provided that include the oscillator

Subnormality in the Quantum Harmonic Oscillator

Abstract: This is an invitation to enjoy watching how unbounded subnormality, a rather recent development, gets involved in solving the commutation relation of the quantum harmonic oscillator.

Threshold and linewidth of a mirrorless parametric oscillator

Abstract: We analyze the above-threshold behavior of a mirrorless parametric oscillator based on resonantly enhanced four-wave mixing in a dense atomic vapor. It is shown that, in the ideal limit, an arbitrary small flux of pump photons is sufficient to reach the oscillator threshold. We demonstrate that, due to the large group velocity delays associated with electromagnetically induced transparency, an extremely narrow oscillator linewidth is possible, making a narrow-band source of nonclassical radiation feasible.

Self-pulsing instabilities in an optical parametric oscillator: Experimental observation and modeling of the mechanism

Abstract: We have observed sustained self-pulsing in a continuously pumped, triply resonant, optical parametric oscillator. From the analysis of our experimental data, we conclude that the instability mechanism is different from the Hopf bifurcation predicted by the classical model of parametric interaction. Self-pulsing results from the interplay of a slow variable (temperature) and the optical bistability cycle, leading to a singularly perturbed system. From simple arguments, we propose a minimal dynamical model that reproduces well the observed behaviors.

Pixellike parametric generator based on controlled spatial-soliton formation.

Abstract: We report the observation of a stable matrix of diffraction-limited solitary beams in a monolithic, single-pass, parametric amplifier pumped by a spatially modulated beam.