The goal of NSF's LIGO gravitational wave detectors is to explore the Universe by observing the astronomical gravitational waves that were first described by Einstein over a century ago. LIGO is currently observing a gravitational wave event about once every two weeks. This award is to develop improved mirrors for the laser-based detector that will allow more observations of gravitational waves, both more frequently and from astronomical sources that are rarer and/or farther away. Gravitational wave observations will help us better understand the universe, and specifically current mysteries including the source of dark matter, the nature of dark energy and the expansion of the Universe, and whether Einstein’s description of gravity continues to work at very high strengths like immediately around a black hole. Developing better mirrors for LIGO will also advance the technology used for mirrors in related precision timing technologies and lasers. This can help with a number of precision measurement techniques useful in many fields and applications. The PIs will train students in STEAM research areas.<br/><br/>This award is part of the effort to reduce coating thermal noise, the limitation to LIGO’s sensitivity which dominates the lowest noise mid-frequency band. For LIGO's A# upgrade and the future Cosmic Explorer detector crystalline GaAs/AlGaAs coatings are being developed because they have the best thermal noise properties known and have optical properties commensurate with the best current coatings. With AlGaAs coatings the predicted event rate for LIGO A# will increase by 3-4 times over the previous A+ upgrade. This contrasts with 1.5-2 times the event rate increase expected with ion beam-deposited amorphous oxide coatings. Such improved sensitivity will deliver a signal-to-noise ratio (SNR) of more than 200 for binary black hole sources like GW150914 and more than 300 for binary neutron star sources like GW170817. This will allow for better determinations of black hole spin, better tests of alternative theories of gravity, improvement in our knowledge of the nuclear equation of state from neutron star mergers, and a better explanation of objects in the mass gap between black holes and neutron stars.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.