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 paper, the authors demonstrate a continuous-wave fiber optical parametric oscillator with a tuning range of 240 nm around 1550 nm, and derive expressions for the threshold power of singly and doubly resonant oscillators that include the full frequency dependence of the complex Raman susceptibility.
Abstract: We demonstrate a continuous-wave fiber optical parametric oscillator with a tuning range of 240 nm around 1550 nm. We show that key to the operation of this device is the combined interaction of the Raman and Kerr nonlinearities and derive expressions for the threshold power of singly and doubly resonant oscillators that include the full frequency dependence of the complex Raman susceptibility.
36 citations
01 Aug 2013
36 citations
TL;DR: In this article, the non-linear behavior of a slender beam carrying a lumped mass subjected to principal parametric base excitation is investigated, where the dimension of the beam-mass system and the position of the attached mass are so adjusted that the system exhibits 3 ǫ: 1 internal resonance.
Abstract: The non-linear behaviour of a slender beam carrying a lumped mass subjected to principal parametric base excitation is investigated. The dimension of the beam–mass system and the position of the attached mass are so adjusted that the system exhibits 3 : 1 internal resonance. Multi-mode discretization of the governing equation which retains the cubic non-linearities of geometrical and inertial type is carried out using Galerkin’s method. The method of multiple scales is used to reduce the second-order temporal differential equation to a set of first-order differential equations which is then solved numerically to obtain the steady-state response and the stability of the system. The linear first-order perturbation results show new zones of instability due to the presence of internal resonance. For low amplitude of excitation and damping Hopf bifurcations are observed in the trivial steady-state response. The multi-branched non-trivial response curves show turning point, pitch-fork and Hopf bifurcations. Cascade of period and torus doubling, crises as well as the Shilnikov mechanism for chaos are observed. This is the first natural physical system exhibiting a countable infinity of horseshoes in a neighbourhood of the homoclinic orbit.
35 citations
TL;DR: In this paper, the authors derived the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic currents pump, and monochrome flux pump and showed that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms.
Abstract: Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance.
35 citations
TL;DR: In this article, a double multiple scales method is applied to reduce the original QP oscillator to an autonomous system performing two successive reduction, and the problem for approximating QP solutions of the original system is then transformed to the study of stationary regimes of the induced autonomous system.
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.
35 citations