Fast estimation of transverse fields in high-finesse optical cavities

Optical cavities with imperfect geometries have resonant transverse field modes whose spatial descriptions usually deviate from known mathematical functions. Numerical methods are therefore used to approximate the fields inside the cavities, and one method is reviewed that is in current use by groups designing large interferometric systems for gravitational wave detection. The method suffers from a large increase in computational time as the finesse of the cavity is increased. A modified method is presented that cuts down the computational time significantly (by factors of 10–100 in the cases considered) without affecting the accuracy of the results.