Method for Calculation of Open Resonators with Regulated Diffraction Output

An open resonator (OR) with round reflectors and near-concentric geometry is analyzed as a resonance system for a free-electron laser. A graphical method for calculation of OR with diffraction coupling is proposed. Apertures and curvature radii of reflectors and the distance between them are calculated as functions of the necessary tuning range. Constant coupling to the load is achieved through changing mirror separation for tuning in the area of unstable geometry. Application of the proposed technique is illustrated for wavelengths shorter than 0.002 m and Fresnel parameters from 0.5 to 2. The possibility of single-mode operation and constant coupling for tuning of more than one octave is demonstrated.