Why are the eigenmodes of stable laser resonators structurally stable?

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Optical resonators are usually examined wave optically. We consider geometrical imaging in stable canonical resonators. We show that, with important exceptions related to eigenmode degeneracy, stable resonators generally image all transverse planes into each other. This insight leads to an intuitive understanding of important properties of the corresponding eigenmodes, most notably their well-known structural stability, i.e., the property that the eigenmodes retain their shape on propagation.