| Crynodeb: | 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.
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