Hybrid Gaussian Mode Formation Due to the Common Dielectric Mirror

Electromagnetic Gaussian modes in axially symmetric resonant cavities can be grouped into families indexed by the transverse order, $N$. In paraxial theory, all of the modes in each family are degenerate. In real cavities, however, the modes within a family have slightly different frequencies, with the frequency splitting scale being $O(\theta^2)$, where $\theta$ is the spread angle of the fundamental Gaussian mode. When the spectral width of a cavity is small enough to resolve this frequency splitting, the resulting cavity eigenmodes may be hybrid mixtures of Laguerre-Gauss (LG) modes. In a plano-concave cavity with conducting mirrors, all of the modes are LG modes. If the planar mirror is replaced with a dielectric mirror, the typical eigenmodes for $N > 1$ are hybrid quasi-TE and quasi-TM modes. These hybrid modes have unusual cross sections that are neither like LG modes or Hermite-Gauss modes. Hybrid modes cannot have well defined orbital angular momentum or spin angular momentum. We present a successful perturbation theory in $\theta^2$ which predicts the properties of the hybrid modes based on the TE and TM reflection phases of the planar mirror.