The extension of the Jones matrix formalism to higher-order transverse modes using N x N matrices presented in a previous paper  is applied to laser resonators. The resonator discussed in detail has a TEM01* Hermite-Gaussian mode, an axially symmetric polarizer combined with an axially symmetric phase shifter as a rear mirror and a folding mirror with conventional polarization dependent reflectivity and phase shift. The analysis reveals some useful regimes, where the output polarization is close to radial or azimuthal and the sensitivity to variations in the phase shift of the folding mirror is minimized.
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