Toward optomechanical parametric instability prediction in ground-based gravitational wave detectors

David E. Cohen; Annalisa Allocca; Gilles Bogaert; Paola Puppo; Thibaut Jacqmin

doi:10.1364/AO.437695

Applied Optics
Vol. 60,
Issue 27,
pp. 8540-8549
(2021)
•https://doi.org/10.1364/AO.437695

Toward optomechanical parametric instability prediction in ground-based gravitational wave detectors

David E. Cohen, Annalisa Allocca, Gilles Bogaert, Paola Puppo, and Thibaut Jacqmin

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David E. Cohen, Annalisa Allocca, Gilles Bogaert, Paola Puppo, and Thibaut Jacqmin, "Toward optomechanical parametric instability prediction in ground-based gravitational wave detectors," Appl. Opt. 60, 8540-8549 (2021)

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Abstract

Increasing laser power is essential to improve the sensitivity of interferometric gravitational wave detectors. However, optomechanical parametric instabilities can set a limit to that power. It is of major importance to understand and characterize the many parameters and effects that influence these instabilities. Here, we model with a high degree of precision the optical and mechanical modes involved in these parametric instabilities, such that our model can become predictive. As an example, we perform simulations for the Advanced Virgo interferometer (O3 configuration). In particular, we compute mechanical mode losses by combining both on-site measurements and finite element analysis with unprecedented levels of detail and accuracy. We also study the influence on optical modes and parametric gains of mirror finite size effects, and mirror deformations due to thermal absorption. We show that these effects play an important role if transverse optical modes of orders higher than four are involved in the instability process.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (7)

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Advanced Virgo FEA Parameters
IM Coating^a
${T a}_{2} O_{5}$ High index layer overall thickness( $t_{H}^{I M}$ )	2080 nm
$S i O_{2}$ Low index layer overall thickness( $t_{L}^{I M}$ )	727 nm
Loss angle ( $ϕ_{C I M}$ )	$1.1 \cdot 10^{- 4} f^{0.05}$
EM Coating^a
$T a_{2} O_{5}$ High index layer overall thickness ( $t_{H}^{E M}$ )	3766 nm
$S i O_{2}$ Low index layer overall thickness ( $t_{L}^{E M}$ )	2109 nm
Loss angle ( $ϕ_{C E M}$ )	$2.2 \cdot 10^{- 4} f^{0.01}$
TM Suprasil
Young’s modulus	72.251 GPa
Poisson ratio	0.16649
Density	$2201 k g . m^{- 3}$
Loss angle ( $ϕ_{S u p r a s i l}$ )	$7.6 \cdot 10^{- 12} f^{0.11}$
Ear and Anchors HCB [21]
Young’s modulus	72.9 GPa
Poisson ratio	0.17
Density	$2201 k g . m^{- 3}$
Thickness	60 nm
Loss angle ( $ϕ_{H C B}$ )	0.1
IM and EM Properties
Mass	42 kg
Thickness	200 mm
Diameter	350 mm
Flats	50 mm

Arm lengths	2999.8 m
Transmittance NI	13770 ppm
Transmittance NE	4.4 ppm
Transmittance WI	13750 ppm
Transmittance WE	4.3 ppm
Transmittance PR	48400 ppm
Round trip loss	75 ppm
Distance from BS to NI	6.0167 m
Distance from BS to WI	5.7856 m
Distance from BS to PR	6.0513 m
Laser wavelength	1064 nm
Gouy phase of PR cavity	1.8 mrad

Advanced Virgo FEA Parameters
IM Coating^a
${T a}_{2} O_{5}$ High index layer overall thickness( $t_{H}^{I M}$ )	2080 nm
$S i O_{2}$ Low index layer overall thickness( $t_{L}^{I M}$ )	727 nm
Loss angle ( $ϕ_{C I M}$ )	$1.1 \cdot 10^{- 4} f^{0.05}$
EM Coating^a
$T a_{2} O_{5}$ High index layer overall thickness ( $t_{H}^{E M}$ )	3766 nm
$S i O_{2}$ Low index layer overall thickness ( $t_{L}^{E M}$ )	2109 nm
Loss angle ( $ϕ_{C E M}$ )	$2.2 \cdot 10^{- 4} f^{0.01}$
TM Suprasil
Young’s modulus	72.251 GPa
Poisson ratio	0.16649
Density	$2201 k g . m^{- 3}$
Loss angle ( $ϕ_{S u p r a s i l}$ )	$7.6 \cdot 10^{- 12} f^{0.11}$
Ear and Anchors HCB [21]
Young’s modulus	72.9 GPa
Poisson ratio	0.17
Density	$2201 k g . m^{- 3}$
Thickness	60 nm
Loss angle ( $ϕ_{H C B}$ )	0.1
IM and EM Properties
Mass	42 kg
Thickness	200 mm
Diameter	350 mm
Flats	50 mm

Arm lengths	2999.8 m
Transmittance NI	13770 ppm
Transmittance NE	4.4 ppm
Transmittance WI	13750 ppm
Transmittance WE	4.3 ppm
Transmittance PR	48400 ppm
Round trip loss	75 ppm
Distance from BS to NI	6.0167 m
Distance from BS to WI	5.7856 m
Distance from BS to PR	6.0513 m
Laser wavelength	1064 nm
Gouy phase of PR cavity	1.8 mrad

Abstract

Data Availability

Cited By

Figures (13)

Tables (2)

Equations (7)

Applied Optics