Design of unstable laser resonators with userdefined mode shape

By introducing surface-structured mirrors into stable laser resonators, the generation of user-defined mode profiles and properties has become possible. On a wave-optical basis, we show that there is a general connection between the property of the modes to be phase-conjugated during reflection at the mirrors and their diffraction losses at apertures. This connection makes the design method known for stable resonators with predefined modes unsuitable for the design of such resonators of unstable geometry. An alternative method for the calculation of unstable resonators with user-defined output beam shape is presented and demonstrated by an example design