Aspherical laser resonators: An analogy with quantum mechanics

We develop an analogy between the transverse modes of a class of aspherical laser resonators and the eigenstates of the stationary Schrödinger equation with a potential well directly related to the mirror profile. Using a perturbation method, the equivalence is shown to be valid for a short cavity length in comparison with the Rayleigh range of the fundamental mode, i.e., the most practical situation. Numerical examples with mirror profiles corresponding to a Pöschl-Teller potential confirm the validity of the model. The analysis also includes higher-order corrections for the case of a longer resonator length. The analogy with quantum mechanics should be useful for designing laser resonators with a high discrimination against higher-order transverse modes.