title: Theoretical study of photonic band gaps in woodpile crystals.
abstract: 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 microm 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.
authors.affiliation: FOM-Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands. gralak@amolf.nl
authors.forename: Boris
authors.initials: B
authors.lastname: Gralak
authors.forename: Michiel
authors.initials: M
authors.lastname: de Dood
authors.forename: Gérard
authors.initials: G
authors.lastname: Tayeb
authors.forename: Stefan
authors.initials: S
authors.lastname: Enoch
authors.forename: Daniel
authors.initials: D
authors.lastname: Maystre