The modes of single defect 2-D photonic bandgap(PBG) slab cavities are studied theoretically by using 3-D finite difference time domain(FDTD). We analyzed the characteristics of several resonant modes, such as mode profile, field direction and quality factors under the different cladding conditions and slab thickness.
In the free-standing structures that the above and below claddings of the slab are air, a two-dimensional monopole mode is proposed and analyzed as a candidate for a nondegenerate PBG cavity mode. This monopole mode formed in a single defect triangular PBG cavity is truly nondegenerate and remains nindegenrate in the sense that intoduction of asymmetry does not result in splitting of the mode. Several methods to tune the resonant frequency of the mode are studied. The radii, positions, and shape of the nearest neighbor air hole are varied in this analysis using the 3-D FDTD calculations. The quality factor of the monopole mode formed in a slab waveguide structure is found to be larger than that of the dipole mode in the nearest elliptical air-hole around the cavity. Also the radiation loss mechanisms of monopole and dipole modes were analyzed from the vertical distribution of electric field.
The loss mechanism of cavity modes in the several cladding conditions of photonic crystal slab single defect cavity is investigated. It is described that the low Q factor of <20,000 of the dipole and monopole mode can be explained as the high overlap of radiation losses. It has been demonstrated by analyzing quality factors and the distribution of electric field the nondegenerate hexapole mode has characteristic of a very small radiation loss, and exhibits a very high quality factor of >100,000 in the free-standing triangular photonic crystal slab. Also in the asymmetric cladding of air and oxide the quality factor of hexapole mode as large as about 10000, which correspond to 30% compared to that of the free-standing PBG structure. The high quality factor of >30,000 in the symmetric oxide cladding has been achieved when the slab thickness is equal to $0.8a. In conclusion, it has been shown the nondegenerate hexapole mode has the highest quality factor among the triangular PBG single defect slab cavity modes.