Higher Order Mode Generation for Optical Damping of Parametric Instabilities in LIGO

During the most recent observation run of the Laser Interferometer Gravitational-Wave Observatory (LIGO), the detector suffered multiple lock losses due to parametric instabilities (PIs) driven by higher-order modes (HOMs) in the interferometer arm cavities. Currently, certain PIs are mitigated by the thermal compensation system (TCS), which shifts the resonant frequency of the HOMs to stable positions. However, as arm power increases, PIs become increasingly disruptive, and the TCS method is no longer viable. A more robust method is optical damping, which involves injecting a HOM with the opposite phase to dampen the PI-coupled target mode. In this project, we aim to generate target HOMs for injection into the cavities. We first developed a script implementing the Gerchberg-Saxton algorithm for phase mask generation, typically achieving over 95% beam overlap after approximately 20-30 iterations. We then built a tabletop setup using a spatial light modulator with two phase masks on its screen; the first allows amplitude shaping, while the second corrects phase. In the future, we will characterize the generated beam profiles with a phase camera, then inject them into a reference cavity to assess mode coupling.