Mode characteristics of hexagonal resonators are numerically simulated by the two-dimensional(2-D) finite-difference time-domain(FDTD) technique.For the hexagonal resonator with the side length of 3 μm and the refractive index of 3.2,the mode quality(Q) factors decrease from 104 to 102 as the resonant wavelength increases from 1.1 to 3.2 μm.The modes have a relatively high Q factor as their even and odd states have different mode wavelengths and different Q factors,i.e.,they are accidentally degenerate modes.The azimuthal mode numbers obtained from mode field distribution for the accidentally degenerate modes satisfy the mode number relation derived from the symmetry characteristics for the split of double-degenerate modes.Furthermore,the numerical results indicate that an output waveguide parallel to one of the sides is the better scheme for directional emission.For the hexagonal resonator with 3 μm side length and 0.3 μm wide output waveguide,the Q factor of 5.05×103 and output efficiency of 33% are obtained at the mode wavelength of 1.29 μm.
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