Two types of ultra-high-Q monopole modes are designed in a woodpile three-dimensional photonic crystal. The unit cell size modulation is applied to a woodpile photonic crystal waveguide in a complete photonic band gap. A monopole mode overlapping with a dielectric rod is designed for solid-state sub-wavelength-scale light-matter interaction devices such as nanolasers, cavity-QED and optical switches, whereas another type of monopole mode overlapping with vacuum is designed for optical trapping experiments. For the mode overlapping with vacuum, the mode volume is as small as 0.4 cubic half-wavelengths.
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