The waveguide based on the honeycomb photonic crystal has propagating modes for both the TE and TM polarizations. The group index-normalized frequency curves are U-shaped for the two polarizations. The average group index of the TE mode is approximately 3, while the average group index of the TM mode is over 10, which implies that the TM mode is a slow light mode. With the shift value 0 <= (delta)x <= 0.025a, the group index is over 10 and the normalized delay-bandwidth product is from 0.316 to 0.349, which is ideal for the slow light mode of the TM polarization. In the group velocity dispersion of the waveguide, there is a very large "zero" dispersion region for both the TM and TE modes, which is far larger than that of other photonic crystal waveguides. The TM mode of this kind of waveguide structure is a slow light mode with wide bandwidth and a large "zero" dispersion region.
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