Topic
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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TL;DR: In this article, a quantum theory of non-degenerate phase-sensitive amplification in a χ(3) nonlinear medium is presented, where the nonzero response time of the nonlinearity determines the quantum-limited noise figure of the parametric amplification, as well as the limit on quadrature squeezing.
Abstract: We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a χ(3) nonlinear medium. The nonzero response time of the Kerr (χ(3)) nonlinearity determines the quantum-limited noise figure of χ(3) parametric amplification, as well as the limit on quadrature squeezing. This nonzero response time of the nonlinearity requires coupling of the parametric process to a molecular vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency nondegenerate and frequency degenerate χ(3) parametric amplifiers operated as phase-sensitive amplifiers. We also present results for frequency nondegenerate quadrature squeezing. We show that our nondegenerate squeezing theory agrees with the degenerate squeezing theory of Boivin and Shapiro as degeneracy is approached. We have also included the effect of linear loss on the phase-sensitive process.
40 citations
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TL;DR: A package of simulation programs is developed suited for examining the phenomenon of paramagnetic resonance in a linear system, which simulates the parametric excitation of the rotary oscillations of a mechanical torsion-spring pendulum whose moment of inertia is subject to periodic variations.
Abstract: Computer simulation experiments are especially good tools for helping students understand basic principles of physics. In this a, I have developed a package of simulation programs called Physics of Oscillations. One of its programs is suited for examining the phenomenon of paramagnetic resonance in a linear system. The program simulates the parametric excitation of the rotary oscillations of a mechanical torsion-spring pendulum whose moment of inertia is subject to periodic variations. I discuss the conditions and characteristics of parametric resonance, including paramagnetic regeneration. Instructors and their students can also use the Physics of Oscillations package to explore other problems, such as ranges of frequencies within which parametric excitation is possible and stationary oscillations on the boundaries of these ranges. The simulation experiments complement the analytical study of the subject in a manner that is mutually reinforcing.
40 citations
TL;DR: In this paper, the nonlinear transverse vibration of an axially moving beam subject to two frequency excitation was analyzed by adopting the direct method of multiple scales, the governing nonlinear integro-partial differential equation for transverse motion was reduced to a set of nonlinear first order ordinary partial differential equations which are solved either by means of continuation algorithm or via direct time integration.
Abstract: This study analyses the nonlinear transverse vibration of an axially moving beam subject to two frequency excitation. Focus has been made on simultaneous resonant cases i.e. principal parametric resonance of first mode and combination parametric resonance of additive type involving first two modes in presence of internal resonance. By adopting the direct method of multiple scales, the governing nonlinear integro-partial differential equation for transverse motion is reduced to a set of nonlinear first order ordinary partial differential equations which are solved either by means of continuation algorithm or via direct time integration. Specifically, the frequency response plots and amplitude curves, their stability and bifurcation are obtained using continuation algorithm. Numerical results reveal the rich and interesting nonlinear phenomena that have not been presented in the existent literature on the nonlinear dynamics of axially moving systems.
40 citations
TL;DR: In this paper, the response of two-degree-of-freedom systems with quadratic nonlinearities to a combination parametric resonance in the presence of two to one internal resonances is investigated.
40 citations