ABSTRACT
This chapter investigates resonators, i.e., certain spatial cavities filled with a linear medium whose μa and εa are independent of the field strength and invariable in time. The potential component of the magnetic field is usually omitted from the formulation of standard electrodynamic problems because magnetic flux density lines are always closed. However, this is the case for fields in an infinite space. Even in the case of homogeneous boundary conditions the analytical solution to is possible only for a few cases, particularly if the surface bounding the cavity is a coordinate surface, so that the Fourier separation of variables is applicable. For cavities bounded by a coordinate surface, the Fourier method can be used also for solving the scalar equations subject to the homogeneous boundary conditions to construct a set of potential vector eigenfunctions.
