Structure of cavity modes with general astigmatism

The modes in an optical cavity between two astigmatic mirrors have a twisted structure when the mirror axes are not aligned. We use operator techniques to obtain a full characterization of these modes. The method is exact in the paraxial limit. The structure of the modes is completely determined by the geometry of the resonator. This geometry is given by the separation between the mirrors, their radii of curvature, and the relative orientation of their symmetry axes. The fundamental mode has elliptical Gaussian intensity profiles and the intersections of a nodal plane with a transverse plane normal to the axis can be ellipses or hyperbolae. The symmetry axes of the intensity curves and the nodal curves are not aligned. At the mirrors, the higher-order modes have a Hermite-Gaussian structure. Their analytical form can be generated from the fundamental mode by using raising operators that generalize the operators that are known in the description of the quantum harmonic oscillator. In the interior region of the resonator, admixture of Laguerre-Gaussian structures can arise, resulting in vortices.