On the accuracy of the beam-wave theory of the open resonator

Some fundamental defects of the beam-wave theory of an open resonator are discussed. In addition to the nonsphericity of the equiphase surfaces, and the approximateness of the solution to the wave equation, the article points out that the boundary condition entertained over the whole surface of each mirror is not correct for spherical mirrors when dealing with Cartesian components of the transverse electric field. The article shows that this boundary condition error is no less serious than the other two defects, at least for the fundamental mode p = l = 0. Corrections based on perturbation theory are applied, and a substantial error is found to remain after the corrections, but the residual error appears to be independent of the radial mode number.