A layer-by-layer periodic dielectric structure with a large photonic band gap is presented. It consists of a layer-by-layer approximation to the triply periodic bicontinuous level set D surface structure having diamond (Fd3m) symmetry. The structure retains the ease of fabrication of the standard woodpile while increasing the maximum quality factor of the gap by 28%. Photonic band gap properties of this structure were calculated using the plane-wave method and its band gap optimized at a fixed index contrast of 3.6:1.
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