Field Analysis of Pillbox Resonator with Radiation Loss Utilizing Finite-Element Beam Propagation Method Formulation

To deal with the radiation from an axially symmetric pillbox resonator embedded in LiNbO₃ substrate, an eigenvalue equation is derived from the expression of the finite-element beam propagation method in a cylindrical coordinate system. By solving the eigenvalue equation iteratively, the field distributions and the angular phase constants of the pillbox resonator are evaluated. The iterative scheme of solving the eigenvalue equation is an extension of our previous direct solution method which was described for a lossless case. The results obtained by this method are compared with those obtained analytically, and excellent agreement is found.