Self-amplified lock of an ultra-narrow linewidth optical cavity

High finesse optical cavities are an essential tool in modern precision laser interferometry. The incident laser field is often controlled and stabilized with an active feedback system such that the field resonates in the cavity. The Pound-Drever-Hall reflection locking technique is a convenient way to derive a suitable error signal. However, it only gives a strong signal within the cavity linewidth. This poses a problem for locking an ultra-narrow linewidth cavity. We present a novel technique for acquiring lock by utilizing an additional weak control signal, but with a much larger capture range. We numerically show that this technique can be applied to the laser frequency stabilization system used in the Laser Interferometric Gravitational-wave Observatory (LIGO), which has a linewidth of 0.8 Hz. This new technique will allow us to robustly and repeatedly lock the LIGO laser frequency to the common mode of the interferometer.