Abstract
The geometrical-optics properties of a new class of resonators are derived. The resonator magnification is defined by sequential ray positions at one cavity mirror and is assumed to be a function of the transverse coordinate. This function alone is sufficient to determine the geometrical eigenvalues and mode-intensity functions of the cavity. In the opposite sense, if one mode-intensity function is specified, the required magnification function can. be derived. The eigenvalues depend solely on the value of the magnification at the resonator axis. To determine the geometry of the resonator and of the wave front uniquely, additional information must be specified. Mirror-sag formulas are derived for two cases, the self-correcting resonator and the half-symmetric resonator.
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