Point Absorber Limits to Future Gravitational-Wave Detectors.

High-quality optical resonant cavities require low optical loss, typically on the scale of parts per million. However, unintended micron-scale contaminants on the resonator mirrors that absorb the light circulating in the cavity can deform the surface thermoelastically and thus increase losses by scattering light out of the resonant mode. The point absorber effect is a limiting factor in some high-power cavity experiments, for example, the Advanced LIGO gravitational-wave detector. In this Letter, we present a general approach to the point absorber effect from first principles and simulate its contribution to the increased scattering. The achievable circulating power in current and future gravitational-wave detectors is calculated statistically given different point absorber configurations. Our formulation is further confirmed experimentally in comparison with the scattered power in the arm cavity of Advanced LIGO measured by in situ photodiodes. The understanding presented here provides an important tool in the global effort to design future gravitational-wave detectors that support high optical power and thus reduce quantum noise.

Modeling circulating cavity fields using the discrete linear canonical transform.

Fabry-Perot cavities are central to many optical measurement systems. In high-precision experiments, such as aLIGO and AdVirgo, coupled cavities are often required, leading to complex optical behavior. We show, for the first time to our knowledge, that discrete linear canonical transforms (LCTs) can be used to compute circulating optical fields for cavities in which the optics have arbitrary apertures, reflectance and transmittance profiles, and shape. We compare the predictions of LCT models with those of alternative methods. To further highlight the utility of the LCT, we present a case study of point absorbers on the aLIGO mirrors and compare it with recently published results.

Mode matching error signals using radio-frequency beam shape modulation.

Precise mode matching is needed to maximize performance in coupled cavity interferometers such as Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). In this paper, we present a new mode matching sensing scheme, to the best of our knowledge, that uses a single radio-frequency higher-order-mode sideband and single-element photodiodes. It is first-order insensitive to misalignment and can serve as an error signal in a closed loop control system for a set of mode matching actuators. We also discuss how it may be implemented in Advanced LIGO. The proposed mode matching error signal has been successfully demonstrated on a tabletop experiment, where the error signal increased the mode matching of a beam to a cavity to 99.9%.