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Parametric oscillator

About: Parametric oscillator is a research topic. Over the lifetime, 5836 publications have been published within this topic receiving 95631 citations. The topic is also known as: Parametric excitation.


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Book
22 Nov 1989
TL;DR: In this article, the concept of dynamic stability under constant load finite duration is introduced and the influence of small damping is discussed. But the authors do not consider the effect of small damping.
Abstract: I Concepts and Criteria.- 1 Introduction and Fundamental Concepts.- 2 Simple Mechanical Models.- 3 Dynamic Stability Under Constant Load Finite Duration.- 4 The Influence of Static Preloading.- II Structural Applications.- 5 The Concept of Dynamic Stability.- 6 Two-Bar Simple Frames.- 7 The Shallow Arch.- 8 The Shallow Spherical Cap.- 9 Thin Cylindrical Shells.- 10 Other Strutural Systems.- APPENDIX A.- Parametric Resonance.- APPENDIX B.- Brachistochrone Problems.- APPENDIX C.- The Influence of Small Damping.

259 citations

Book
01 Nov 2000
TL;DR: In this paper, the authors present a model of a single-input single-output (SISO) waveguide with a single source and a single noise matrix, which is used to measure the energy and power of the waveguide.
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.

251 citations

Journal ArticleDOI
TL;DR: It is suggested that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level.
Abstract: This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.

250 citations

Journal ArticleDOI
TL;DR: An analysis of the degenerate parametric amplifier including the quantisation of pump and signal modes is presented in this article, where it is shown that the fluctuations in one quadrature of the signal mode may be reduced at most by a factor of two.

249 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the results of an experimental effort to generate squeezed microwave radiation using the phase-sensitive gain of a Josephson parametric amplifier, which is used for both doubly degenerate and four-photon mode.
Abstract: We present the results of an experimental effort to generate squeezed microwave radiation using the phase-sensitive gain of a Josephson parametric amplifier. To facilitate the interpretation of the experimental results, we first present a discussion of the theory of microwave squeezing via Josephson parametric amplifiers. This is followed by a detailed description of the device fabricated for our experiment. Experimental results are then presented for the device used in both the doubly degenerate or four-photon mode and for the degenerate or three-photon mode. We have observed parametric deamplification of signals by more than 8 dB. We have demonstrated squeezing of 4.2-K thermal noise. When operated at 0.1 K, the amplifier exhibits an excess noise of 0.28 K when referred to the input. This is smaller than the vacuum fluctuation noise level \ensuremath{\Elzxh}\ensuremath{\omega}/2k=0.47 K. The amplifier is thus quieter than a linear phase-insensitive amplifier in principle can be.

247 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202366
2022133
2021123
2020139
2019145
2018135