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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. In order to have high cavity powers in GW detectors, it is necessary to suppress the parametric instability and to reduce the loss in the arm caused by point absorbers by damping the resonant conditions of harmful higher order optical modes (HOOM). This can be achieved effectively by using non spherical mirrors in symmetric Fabry–Perot (FP) cavities by increasing roundtrip losses of HOOMs Ferdous F et al 2014 Phys. Rev. A 90 033826; Matsko A et al 2016 Phys. Rev. D 93 083010. FP 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 present here a general method to design non spherical non-identical mirrors in non-symmetric FP cavities to damp HOOMs. The proposed design allows us to suppress the loss of the arm power caused by point absorbers on test masses. [ABSTRACT FROM AUTHOR]