Theoretical study of photonic bandgaps in woodpile crystals

We investigate numerically the existence of photonic band gaps in woodpile crystals. We present a numerical method specifically developed to solve Maxwell's equations in such photonic structures. It is based upon a rigorous mathematical formulation and leads to a considerable improvement of the convergence speed as compared to other existing numerical methods. We tested our method by comparing the calculated reflectivity with measurements on an actual sample, i.e., a silicon woodpile photonic crystal designed for 1.5 µm wavelength. Excellent agreement is obtained, provided the main structural imperfections of the sample are taken into account. We show that the existence of photonic band gaps in woodpile crystals requires an index contrast higher than 2.05±0.01. The effects of imperfections of such structures with an index contrast equal to 2.25 are also investigated. Thus, the relative band gap width falls from 3.5% to 2.2% with structurals imperfection similar to those of the sample.