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Advanced LIGO and other ground-based interferometric gravitational-wave detectors use high laser power to minimize shot noise and suspended optics to reduce seismic noise coupling. This can result in an opto-mechanical coupling which can become unstable and saturate the interferometer control systems. The severity of these parametric instabilities scales with circulating laser power and first hindered LIGO operations in 2014. Static thermal tuning and active electrostatic damping have previously been used to control parametric instabilities at lower powers but are insufficient as power is increased. Here we report the first demonstration of dynamic thermal compensation to avoid parametric instability in an Advanced LIGO detector. Annular ring heaters that compensate central heating are used to tune the optical mode away from multiple problematic mirror resonance frequencies. We develop a single-cavity approximation model to simulate the optical beat note frequency during the central heating and ring heating transient. An experiment of dynamic ring heater tuning at the LIGO Livingston detector was carried out at 170 kW circulating power and, in agreement with our model, the third order optical beat note is controlled to avoid instability of the 15 and 15.5 kHz mechanical modes. We project that dynamic thermal compensation with ring heater input conditioning can be used in parallel with acoustic mode dampers to control the optical mode transient and avoid parametric instability of these modes up to Advanced LIGO’s design circulating power of 750  kW. The experiment also demonstrates the use of three mode interaction monitoring as a sensor of the cavity geometry, used to maintain theg-factor product tog₁g₂= 0.829 ± 0.004.

 

Abstract KAGRA, the underground and cryogenic gravitational-wave detector, was operated for its solo observation from February 25 to March 10, 2020, and its first joint observation with the GEO 600 detector from April 7 to April 21, 2020 (O3GK). This study presents an overview of the input optics systems of the KAGRA detector, which consist of various optical systems, such as a laser source, its intensity and frequency stabilization systems, modulators, a Faraday isolator, mode-matching telescopes, and a high-power beam dump. These optics were successfully delivered to the KAGRA interferometer and operated stably during the observations. The laser frequency noise was observed to limit the detector sensitivity above a few kilohertz, whereas the laser intensity did not significantly limit the detector sensitivity. 

This paper analytically and numerically investigates misalignment and mode-mismatch-induced power coupling coefficients and losses as a function of Hermite–Gauss (HG) mode order. We show that higher-order HG modes are more susceptible to beam perturbations when, for example, coupling into optical cavities: the misalignment and mode-mismatch-induced power coupling losses scale linearly and quadratically with respect to the mode indices, respectively. As a result, the mode-mismatch tolerance for the${\mathrm{H}\mathrm{G}}_{3,3}$mode is reduced to a factor of 0.28 relative to the currently used${\mathrm{H}\mathrm{G}}_{0,0}$mode. This is a potential hurdle to using higher-order modes to reduce thermal noise in future gravitational-wave detectors.