Improved mode properties of unstable resonators with tapered reflectivity mirrors and shaped apertures

The use of tapered reflectivity mirrors and shaped apertures in unstable resonators is shown to be an effective method for improving the mode properties. Mode intensity and phase profiles are smoothed and the mode discrimination ratio is increased. Results are presented illustrating the importance of diffracted waves from sharp mirror edges in determining these mode properties. A simple expression for estimating the diffractive contribution is given and is used to determine optimum mirror designs. Shaped mirrors and mirrors having amplitude and phase reflectivity tapers are studied. The concept of equivalent Fresnel zones is used to gain physical insight into the mode properties.