Optical cavities with both optimized resonant conditions and high quality
factors are important metrological tools. In particular, they are used for
laser gravitational wave (GW) detectors. It is necessary to suppress the
parametric instability by damping the resonant conditions of harmful higher
order optical modes (HOOM) in order to have high cavity powers in GW detectors.
This can be achieved effectively by using non spherical mirrors in symmetric
Fabry-Perot (FP) cavities by increasing roundtrip losses of HOOMs. Fabry-Perot
cavities in most of the GW detectors have non-identical mirrors to optimize
clipping losses and reduce thermal noise by reducing the beam size on one side
of the cavity facing to the beam splitter and recycling cavities. We here
present a general method to design non spherical non-identical mirrors in
non-symmetric FP cavities to damp HOOMs. The proposed design allows to the
suppress the loss of the arm power caused by point absorbers on test masses.Comment: 12 pages, 10 figure