5.7 Sample Numerical Results

We present in this section selected numerical results obtained by various rigorous methods which have been discussed in this review. These results illustrate how changing various parameters affects the resonant frequencies of various modes of open and shielded DRs. This section should also help the reader interpret the data presented in research papers and to alert him or her to the diverse notation used by various authors in classifying the modes. For more results the reader is referred to the papers listed in the bibliography at the end of this chapter.

The data presented in Figs. 5.5 through 5.9 are for a ring resonator in free space (see Fig. 5.4 for the geometry) and were obtained by DeSmedt [37] by the perturbational approach discussed in Sec. 5.5. The pillbox resonator case is included in these results as a special case when b/a = 0. These data show the dependence of the resonant wave number and the Q factor on the aspect ratio L/(2a) and the (normalized) size of the inner hole b/a. The solid lines pertain to the TE _{01 ?} (magnetic dipole) mode and the dashed lines to the TE _{011+ ?} (magnetic quadrupole) mode. Figure 5.5 gives the zero-order normalized resonant wave number k ₀a, and Figs. 5.6 and 5.7 give, respectively, the first and second corrections (see (5.111b)). The zero-order Q factor is shown in Fig. 5.8, and the first correction (see (5.114)) in Fig. 5.9.

Figure 5.5: Zero-order resonant...