Improved Sensitivity for Future Gravitational-Wave Detectors with Novel Toroidal Mirrors for Robust Loss Mitigation

As the Laser Interferometer Gravitational-Wave Observatory (LIGO) project nears the end of its fourth observing run, it is critical to look toward future upgrades to its current facility in pursuit of better sensitivity targets. One of the ways that this is achieved is by reducing sources of loss within the interferometer in LIGO. Our project focuses on reducing mode mismatch-induced losses between the coupled cavities in LIGO, which negatively impacts the quantum squeezing performance and the sensitivity. Non-zero angles of incidence on the curved SRC mirrors lead to an astigmatic mode in SRC which is mismatched to coupled cavities. We explore modifying the mirrors in LIGO's SRC from spherical to toroidal mirrors to reduce mismatch and improve quantum-noise-limited sensitivity. Using these new toroidal mirrors, we search the optical parameter space for optimal SRC mirror RoC's for reduced astigmatism. This optimization also allows for exploration of more robust SRC designs which would be more error-tolerant towards common manufacturing and positioning errors.