The theory of a large class of optical resonators has been developed in a compact form by the means of raising and lowering differential operators (commonly used in quantum mechanics). The theory is applicable to any cavity for which paraxial ray theory may be applied successfully and where losses, aperturing, and aberrations can be ignored. The resonator need not be planar (so that image rotation may occur), the optical elements may be astigmatic and the optic axis incompletely defined (such as when dispersive prisms are used). A discussion of existence and uniqueness of paraxial (pencillike) modes is provided, including the modification of the theory when degeneracies are present. It is proved that unstable cavities do not possess paraxial modes.
Ernest E. Bergmann, "Optical Resonators with Paraxial Modes," Appl. Opt. 11, 113-119 (1972)