Photonic band effects in a two-dimensional array of dielectric spheres in the millimeter-wave region

The transmission and phase-shift spectra for millimeter electromagnetic waves are obtained for a two-dimensional (2D) square lattice array made of ${\mathrm{Si}}_3{\mathrm{N}}_4$ spheres of diameter $\simeq 3.2$ mm. The results are compared with the theoretical 2D photonic-band structures that take account of the lifetime effect due to the radiative energy decay. It is found that the incidence-angle dependence of the observed transmission spectra is in excellent agreement with the calculated in-plane dispersion curves of the photonic bands and that the frequency dependence of the phase shift agrees well with the calculated lifetime-broadened density of states. The radiative lifetimes of the photonic bands are estimated to be about ten times longer than those of whispering gallery modes of an isolated sphere, though the magnitudes depend rather strongly on the wave vector and band index.