Mirror coating-thermal-noise mitigation using multi-spatial-mode cavity readout

We present an approach to mitigating coating thermal noise in optical cavities by using multiple transverse electromagnetic (TEM) spatial modes to read out and stabilize laser frequency. With optimal weightings we synthesize a wider sampling of mirror surfaces, improving the averaging of Brownian thermal fluctuations. We show a thermal noise improvement factor of 1.57, comparable to a mesa beam of a nominal 12 m prototype cavity, and a factor 1.61 improvement over the TEM00 using three modes in a 0.1 m cavity for a practical laboratory experiment, equivalent to cooling mirrors to 120 K from room temperature.