Considerations on parametric instability in Fabry–Perot interferometer

We evaluate the parametric phenomenon for the main optical mode coupled to other resonant waves excited by acoustic interaction with the mirrors of a Fabry–Perot. We apply this to the arm cavity of a gravitational wave antenna. Under certain assumptions we find that the amplitude of these parasitic modes is expressed by analytic solutions that are always damped. We analyze both the zero detuning and the detuned case and solve the equations. The form of the solution shows that for equally spaced and excited cavity modes the instability is expressed by a threshold condition, which is well approximated for LIGO arm resonator parameters.     

The effect of parametric oscillatory instability in a Fabry-Perot cavity of the Einstein telescope

The nonlinear effect of a parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope is investigated. Unstable combinations of elastic and optical modes are calculated for two possible configurations of the third-generation gravitational-wave detector. The results are compared with those for the LIGO gravitational-wave interferometer.     

Parametric oscillatory instability in a Fabry–Perot cavity of the Einstein Telescope with different mirror's materials

We discuss the parametric oscillatory instability in a Fabry–Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are deduced. The results are compared with the results for gravitational wave interferometers LIGO and LIGO Voyager.     

Numerical calculations of elastic modes frequencies for parametric oscillatory instability in Advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric oscillatory instability. We propose accuracy estimations through use of analytical solutions based on Chree-Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric oscillatory instability.     

Parametric oscillatory instability on axially-symmetrical test mass elastic modes in Advanced LIGO interferometer

We discuss the importance of accurate calculation of axially-symmetrical elastic modes frequencies and forms in test masses (mirrors) of Advanced LIGO interferometer using the method of superposition to analyse the effect of parametric oscillatory instability. This method consists in possibility to construct analytical expressions for partial solutions of media motion equation in the cylindrical coordinates which allow to satisfy all zero boundary conditions. Obtained results allow to predict more exactly (in comparison with numerical calculations) the number of combinations of optical and elastic modes that can create undesirable effect of parametric oscillatory instability.     

Elastic modes frequencies in the mirrors with “ears” for parametric oscillatory instability in advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors with suspension “ears” in advanced LIGO interferometer to enable precise predictions of parametric oscillatory instability problem. We show that “ears” of test masses produce additional shift of elastic modes frequencies which is larger than relaxation rate of optical modes. These shifts may increase the possibility of parametric oscillatory instability.     

Statistical properties for a class of nonlinear squeezed states

Theoretical investigations of dynamical behavior in optical parametric oscillators (OPO) have generally assumed that the cavity detunings of the interacting fields are controllable parameters. However, OPOs are known to experience mode hops, where the system jumps to the mode of lowest cavity detuning. We note that this phenomenon significantly limits the range of accessible detunings and thus may prevent instabilities predicted to occur above a minimum detuning from being evidenced experimentally. As a simple example among a number of instability mechanisms possibly affected by this limitation, we discuss the Hopf bifurcation leading to periodic behavior in the monomode mean-field model of a triply resonant OPO and show that it probably can be observed only in very specific setups.     

Effect of parametric oscillatory instability in axially symmetric modes of test masses in gravitational antennas LIGO

We demonstrate the importance of using the method of superposition for the precise calculation of frequencies and forms of axially symmetric elastic modes of test masses in gravitational antennas LIGO for detailed analysis of the effect of parametric oscillatory instability. The method allows one to construct analytical expressions for particular solutions to the medium equations of motion in cylindrical coordinates, which allow one to satisfy all zero boundary conditions. The obtained results allow considerably more reliable methods (as compared to meshing methods) to be used for predicting the number of combinations of optical and elastic modes that lead to the undesirable effect of the parametric oscillatory instability.     

Generation of Optical and Mechanical Squeezing in the Linear‐and‐Quadratic Optomechanics

Generation of strong stationary optical and mechanical squeezing is proposed for the linear‐and‐quadratic optomechanical system, where two cavity modes induce linear and quadratic optomechanical couplings, respectively. Through the linearization treatment, linearized coupling between cavity mode and mechanical mode and the mechanical parametric amplification process are achievable and controllable by independent driving lasers. Optical and mechanical squeezing are generated following different mechanisms. Optical squeezing works in the strong coupling regime, and mechanical amplification would push the system close to instability threshold, which could deeply improve ponderomotive squeezing even significantly beyond the 3 dB squeezing limit. Mechanical squeezing is generated based on the reservoir engineering method, where parametric amplification induces the squeezing transformation of mechanical mode; and linearized coupling, which operates in the red‐sideband and weak coupling limits, induces the ground‐state cooling of transformed mechanical mode. Finally, the original mechanical mode would be squeezed, which could also exceed 3 dB limit.     

Lagrangian approach for analysis of radiation pressure induced parametric instability in micro-resonators

We introduce a new scheme for determining radiation pressure coupling to microresonator devices. It is shown that for the input pump powers there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to it's optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such nonlinear effect with Hamilton's least action principle. Our Lagrangian includes no interaction term, but interaction between optical and mechanical modes has been taken into account through integration limit.     

Dynamical parametric instability of carbon nanotubes under axial harmonic excitation by nonlocal continuum theory

Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.     

衰荡腔复杂模拍效应的实验研究

利用光参量振荡器产生的脉冲光研究了衰荡腔在不同条件下的衰减信号,实验表明,衰荡腔的输出信号会呈现复杂的调制。这些现象,有些可利用在谐振腔本征模理论基础上导出的公式来解释,另外一些可能是由于像散和畸变引起的腔的横膜分裂,从而导致复杂的模拍效应,对实验结果进行了分析和解释。     

Parametric excitation of oscillatory states and symmetry in phase space

We study the excitation of nonlinear dissipative oscillator under influence of a monochromatic force at the level of a few quanta. With this purpose we consider an optical parametric oscillator combined with phase-modulation in which the oscillatory mode is excited through down-conversion process under a monochromatic laser field. The temporal Rabi oscillations of Fock states as well as the properties of oscillatory mode in phase space are studied with use of the Wigner functions.     

Precursors of parametric oscillatory instability in LIGO interferometer

The basis of undesirable effect of parametric oscillatory instability in optical interferometer is provided by excitation of the additional (Stokes) optical mode having frequency ω₁${\omega }_1$, and the mirror elastic mode, having frequency ωm${\omega }_m$. It appears when optical energy stored in the main mode, with frequency ω₀${\omega }_0$, exceeds a certain threshold and the frequencies are related as ω₀?ω₁+ωm${\omega }_0?{\omega }_1+{\omega }_m$. We analyze the time evolution of parametric instability which allows predicting the characteristics of precursors of parametric instability. Observation of such precursors may help avoid parametric instability.     

Entanglement of Coupled Optomechanical Systems Improved by Optical Parametric Amplifiers

A scheme to generate the stationary entanglement of two distant coupled optical cavities placed optical parametric amplifiers is proposed. We study how the optical parametric amplifiers can affect the entanglement behaviors of the movable mirrors and the cavity fields. With the existence of optical parametric amplifiers, we show that larger stationary entanglement of optical and mechanical modes can be obtained and the entanglement increases with the increasing parametric gain. Especially, the degree of entanglement between the two cavity fields is more pronouncedly enhanced. Moreover, for a fixed parametric gain, the entanglement of distant cavity optomechanical systems increases as the input laser power is increased.     

Perfect photon absorption based on the optical parametric process

The perfect photon absorption is studied in a cavity quantum electrodynamics(CQED) system, in which an optical parameter amplifier(OPA) is coupled to the cavity mode. This makes it possible to control the optical phase to realize the perfect photon absorption. It is found that in the presence of one and two injected fields, the perfect photon absorption is present in these two cases and can be controlled by adjusting the parametric phase. Moreover, different from the previous predictions of perfect photon absorption in atomic CQED systems, the perfect photon absorption can be changed significantly by the relative phase. Our work provides a new platform to use the parametric processes to make an available way to control the behaviors of photons and to take advantage of the optical phase to achieve the perfect photon absorption.     

Stable operation of a cw optical parametric oscillator near the signal-idler degeneracy

The frequency stability of a cw optical parametric oscillator (cw OPO) near the signal-idler degeneracy has been studied. The strong tendency of a near-degenerate OPO to mode hop has been suppressed by using a bulk Bragg grating as a spectral filter in the OPO cavity. An experimental demonstration of stable parametric oscillation in a single longitudinal mode of the OPO cavity is reported, together with the capability of tuning the signal-idler difference frequency from 1 to 4 THz. The OPO has potential use in cw terahertz generation.     

Synchrotron instability for long pulses in free electron laser oscillators

We consider the mode evolution of the optical field in free electron laser oscillators. Periodic boundary conditions are employed to solve the coupled equations for the electrons and optical field. At high optical powers we find a universal sideband instability related to electron synchrotron motion. We discuss the suppression of this instability by use of a dispersive optical cavity.     

Entanglement of movable mirror and cavity field enhanced by an optical parametric amplifier

A scheme to generate entanglement in a cavity optomechanical system filled with an optical parametric amplifier is proposed. With the help of the optical parametric amplifier, the stationary macroscopic entanglement between the movable mirror and the cavity field can be notably enhanced, and the entanglement increases when the parametric gain increases.Moreover, for a given parametric gain, the degree of entanglement of the cavity optomechanical system increases with increasing input laser power.