Suppression of instability of output beam of thin-disk lasers caused by the air-wedge effect based on resonator design

•The method of forced convection can remove hot air in front of the thin disk element and reduce the air wedge effect.•The special resonator can eliminate angular misalignment introduced by the air wedge and improve the stability of laser beam obviously.•The ABCD matrix with positional misalignment and angular misalignment is effective to describe the influence of air wedge.