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The coherent superposition of orthogonal modes can result in transverse offsets, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for first and second order moments, the beam quality and the Rayleigh length for the superposition of Hermite-Gauss modes are derived. The Courant-Snyder formalism, which was originally developed in the context of charged particle optics, is applied to propagate andoi:10.3204/pubdb-2021-02534 fatcat:xsdxevew5rhednec6yj5lyahc4