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Gravitational-wave (GW) laser interferometers such as Advanced LIGO transduce spacetime strain into optical power fluctuation.
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In the Hanford detector, a slight optical antispring is observed, with ξ 2 ≃ − ( 7 Hz ) 2 \xiup^{2}\simeq-($7\text{\,}\mathrm{Hz}$)^{2} or ϕ ≃ 90.5 ° \phiup\simeq$90.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ , but this is not considered for the simulations in this work
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In this work, we use the convention that the servo goes unstable if G ( f ) = + 1 G(f)=+1 . If instead the opposite convention is used [instability occurs for G ( f ) = − 1 G(f)=-1 ], then the response function R ( f ) R(f) has the form [ 1 + G ( f ) ] / C ( f ) [1+G(f)]/C(f)
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