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The transverse field structure and diffraction loss of the resonant modes ofFabry-P\'erot optical cavities are acutely sensitive to the alignment and shapeof the mirror substrates. We develop extensions to the `mode mixing' methodapplicable to arbitrary mirror shapes, which both facilitate fast calculationof the modes of cavities with transversely misaligned mirrors and enable thedetermination and transformation of the geometric properties of these modes. Weshow how these methods extend previous capabilities by including thepractically-motivated case of transverse mirror misalignment, unveiling richand complex structure of the resonant modes.

Efficient operator method for modelling mode mixing in misaligned optical cavities