Laser frequency noise in next generation gravitational-wave detectors

Future ground-based gravitational-wave detectors are slated to detect black hole and neutron star collisions from the entire stellar history of the universe. To achieve the designed detector sensitivities, frequency noise from the laser source must be reduced below the level achieved in current Advanced LIGO detectors. This paper reviews the laser frequency noise suppression scheme in Advanced LIGO, and quantifies the noise coupling to the gravitational-wave readout. The laser frequency noise incident on the current Advanced LIGO detectors is $8 \times 10^{-5}~\mathrm{Hz/\sqrt{Hz}}$ at $1~\mathrm{kHz}$. Future detectors will require even lower incident frequency noise levels to ensure this technical noise source does not limit sensitivity. The frequency noise requirement for a gravitational wave detector with arm lengths of $40~\mathrm{km}$ is estimated to be $7 \times 10^{-7}~\mathrm{Hz/\sqrt{Hz}}$. To reach this goal a new frequency noise suppression scheme is proposed, utilizing two input mode cleaner cavities, and the limits of this scheme are explored. Using this scheme the frequency noise requirement is met, even in pessimistic noise coupling scenarios.