Parametric Oscillatory Instability Research Articles

Influence of Young’s modulus temperature dependence on parametric instability in Advanced LIGO interferometer

We discuss the influence of Young’s modulus temperature dependence on the number of parametrically unstable modes in a Fabry-Perot cavity of Advanced LIGO interferometer. Some unstable modes may be suppressed by changing the mirror’s temperature due to temperature dependence of Young’s modulus. Varying the temperature of the mirrors we can change their frequencies of the elastic modes; it, in turn, can change the number of unstable modes, leading to nonlinear effect of parametric oscillatory instability. Preliminary estimations of the optimal values of the temperature variations for some elastic modes are made to reduce the number of unstable modes. The applications of this method in cryogenic detectors like LIGO Voyager or Einstein Telescope are proposed.

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.

A maser based on dynamical backaction on microwave light

The work of Braginsky introduced radiation pressure dynamical backaction, in which a mechanical oscillator that is parametrically coupled to an electromagnetic mode can experience a change in its rigidity and it's damping rate. The finite cavity electromagnetic decay rate can lead to either amplification or cooling of the mechanical oscillator, and lead in particular to a parametric oscillatory instability, associated with regenerative oscillations of the mechanical oscillator, an effect limiting the circulating power in laser gravitational wave interferometers. These effects implicitly rely on an electromagnetic cavity whose dissipation rate vastly exceeds that of the mechanical oscillator, a condition naturally satisfied in most optomechanical systems. Here we consider the opposite limit, where the mechanical dissipation is engineered to dominate over the electromagnetic one, essentially reversing role of electromagnetic and mechanical degree of freedom. As a result, the electromagnetic field is now subject to dynamical backaction: the mechanical oscillator provides a feedback mechanism which modifies the damping rate of the electromagnetic cavity. We describe this phenomenon in the spirit of Braginsky's original description, invoking finite cavity delay and highlighting the role of dissipation. Building on previous experimental work, we demonstrate this dynamical backaction on light in a superconducting microwave optomechanical circuit. In particular, we drive the system above the parametric instability threshold of the microwave mode, leading to maser action and demonstrate injection locking of the maser, which stabilizes its frequency and reduces its noise.

Suppression of parametric oscillatory instability in third generation gravitational wave detectors

We discuss one possible method for suppression of the nonlinear effect of a parametric oscillatory instability in a Fabry–Perot cavity of the next generation of gravitational wave detectors by determination of optimal radii of curvature of interferometers' mirrors. Varying the radii of curvature of the mirrors we can change the frequencies of the optical modes of the Fabry–Perot resonators and distributions of optical fields in optical modes, which, in turn, can change the number of unstable modes, leading to parametric oscillatory instability. The determination of the optimal values of the radii of curvature of mirrors to reduce the number of unstable modes by thermal lensing is fulfilled.

Parametric oscillatory instability in gravitational wave laser detectors

The nonlinear effect of parametric oscillatory instability in the gravitational wave laser detector (antenna) is considered as a factor that considerably reduces the sensitivity of the device. It is shown that in an antenna with a circulating power above a certain threshold value, excitation of Stokes optical modes occurs in Fabry-Perot resonators and of test mass elastic modes. Parametric oscillatory instability in gravitational wave interferometers of the second (LIGO, Virgo, LCGT, GEO-600) and third (ET — Einstein Telescope) generation with different types of pumps is examined. The effect discussed has been observed not only in gravitational wave laser interferometers, but also many times in other opto-mechanical systems. All current methods for suppressing parametric oscillatory instability in gravitational wave interferometers are also discussed, both passive and active.

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.

The effect of a laser beam displacement on parametric oscillatory instabilities for Advanced LIGO

The arm cavities of real gravitational wave detectors can show small deviations like a tilt or a spatial shift between the cavity mirrors. These deviations lead to a separation of the optical mode centres with respect to the mirrorʼs centre. In this Letter we perform the computation of parametric instable modes considering the described displacement. We further analyse the possibility of parametric oscillatory instability in the Advanced LIGO interferometer for the case of a displaced arm cavity. Our results reveal an additional number of optical and elastic mode combinations due to a displacement that can give rise to the undesirable effect of parametric oscillatory instability.

Effect of higher-order waves in parametric oscillatory instability in optical cavities

A new strict proposal for determining radiation pressure coupling to optical resonator devices has been developed. Our evidence shows that the effect of the anti-Stokes wave cannot be neglected. It is shown that Stokes and anti-Stokes frequencies of all orders will participate in the optomechanical effect. Furthermore, we have shown that for the input pump power, there exists a threshold value for instability behavior. Radiation pressure can couple mechanical modes of a cavity to its optical modes, leading to parametric oscillation instability. Here we present an approximate analysis of such a nonlinear effect with Hamilton's least action principle. Loss in every mode has been taken into account through Rayleigh's dissipation function.

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.

Analysis of parametric oscillatory instability in Fabry–Perot cavity with Gauss and Laguerre–Gauss main mode profile

We calculate the parametric instabilities in Fabry–Perot cavities of advanced VIRGO and LIGO interferometers with different main mode profiles. All unstable combinations of elastic and Stokes modes both for the case with TEM 00 and LG 33 as a carriers are deduced.

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.

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 in a signal-recycled LIGO interferometer

The undesirable effect of parametric oscillatory instability in a LIGO (Laser Interferometer Gravitational-Wave Observatory) laser gravitational-wave antenna with a signal-recirculation mirror is analysed in detail. The instability is manifested in excitation of the Stokes optical mode and elastic mechanical mode of the mirror. It is shown that, if the eigenfrequencies of Fabry–Perot resonators in the interferometer arms are different, the parametric instability is quite small due to a small passband band width.

Precursors of parametric oscillatory instability in LIGO interferometer

Abstract The basis of undesirable effect of parametric oscillatory instability in optical interferometer is provided by excitation of the additional (Stokes) optical mode having frequency ω 1 , and the mirror elastic mode, having frequency ω m . It appears when optical energy stored in the main mode, with frequency ω 0 , exceeds a certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω 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.

Analysis of parametric oscillatory instability in signal recycled LIGO interferometer

Analysis of parametric oscillatory instability in signal recycled LIGO interferometer

Analysis of parametric oscillatory instability in signal recycled LIGO interferometer with different arms

Abstract The basis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer is the excitation of the additional (Stokes) optical mode, with frequency ω 1 , and the mirror elastic mode, with frequency ω m , when optical energy stored in the main mode, with frequency ω 0 , exceeds the certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze parametric instability in the general case when eigen frequencies of Fabry–Perot (FP) cavities in arms of interferometer are detuned from each other and show that parametric instability in this interferometer is relatively small due to small bandwidth of interferometer. We propose to “scan” the frequency range where parametric instability may take place by varying the position of signal recycling mirror.

Analysis of parametric oscillatory instability in power recycled LIGO interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with the Fabry–Perot (FP) cavities in the arms. The basis for this effect is the excitation of the additional (Stokes) optical mode with frequency ω 1 and the mirror elastic mode with frequency ω m, when the optical energy stored in the main FP cavity mode with frequency ω 0 exceeds the certain threshold and the frequencies are related as ω 0≃ ω 1+ ω m. The presence of anti-Stokes modes (with frequency ω 1a≃ ω 0+ ω m) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely.

Low quantum noise tranquilizer for Fabry–Perot interferometer

We discuss the possibility to introduce low noise damping produced by light into mechanical oscillator (one of the Fabry–Perot (FP) resonator mirrors is the mechanical resonator). Pumping FP resonator, by light detuned from resonance one can create the positive or negative rigidity in mechanical oscillator. Such a rigidity being introduced with delay (of the order of relaxation time of FP resonator) is equivalent to additional low noise damping. We propose to introduce this damping to tranquilize (to depress) parametric oscillatory instability in FP interferometer (Phys. Lett. A 287 (2001) 331) which is undesirable in laser gravitational wave antennae.

Parametric oscillatory instability in Fabry–Perot interferometer

We present an approximate analysis of a nonlinear effect of parametric oscillatory instability in Fabry–Perot (FP) interferometer. The basis for this effect is the excitation of the additional (Stokes) optical mode with frequency ω 1 and of the mirror's elastic mode with frequency ω m when the optical energy stored in the FP resonator main mode with frequency ω 0 exceeds the certain threshold and the frequencies are related as ω 0≃ ω 1+ ω m . This effect is undesirable in laser gravitational wave antennae because it may create a specific upper limit for the value of energy stored in FP resonator. In order to avoid it the detailed analysis of the mirror's elastic modes and FP resonator optical modes structure is necessary.