The hexapole mode still has characteristics of the general single-cell mode, e.g., a large value and small mode volume. However, unlike the general single-cell hexapole mode, the hexapole mode created by a sphere can have several resonant wavelengths with an individual azimuthal mode number in the sphere at the -plane, as shown in Fig. 3. For example, the resonance of a hexapole mode is observed at 1357, 1463, 1591, and 1748 nm in the bandgap when the sphere with a 1000-nm radius and 2.91-refractive index makes contact with the slab. Each mode shows the field at the edge of the sphere like the whispering guided mode,22–24 as shown in the mode profile of the cross-section of the -plane [Fig. 3(b)]. The modes can be classified by the number of oscillations in the circumference of the sphere, called the azimuthal mode number. In this case, the azimuthal mode numbers of each mode are 9, 8, 7, and 6. Therefore, the proposed cavity is free to choose the resonant wavelength when the cavity is coupled with an emitter because the resonant wavelength is selected in a large region from 1357 to 1748 nm with the same hexapole mode as the PC. The resonant wavelength decreases when the azimuthal mode number increases.24 Therefore, the hexapole mode excited in the proposed cavity can have four resonant wavelengths distributed from 1357 to 1748 nm over a broad photonic bandgap spectrum while horizontal electric field profiles are maintained. Here, the index of 2.91 of sphere (index of chalcogenide glass) is chosen for the presented four hexapole modes to be well-localized horizontally.