Square spiral photonic crystals: robust architecture for microfabrication of materials with large three-dimensional photonic band gaps.

Abstract

We provide a blueprint for microfabricating photonic crystals with very large and robust three-dimensional photonic band gaps (PBG's). These crystals are based on interleaving polygonal spiral posts and can be efficiently manufactured on a large scale in a one-step process using the recently introduced technique of glancing angle deposition. We classify various families of spiral photonic crystals based on (i) the parent three-dimensional (3D) point lattice to which they are most closely related, (ii) the crystallographic axis of the parent lattice around which the spiral posts wind, and (iii) the set of points of the parent lattice which the spiral arms connect or nearly connect. We obtain optimal geometries for the spiral photonic crystals by detailed mapping of the size and location of the PBG within a multidimensional parameter space which characterizes the shape of each spiral post. For the optimum PBG, the spiral arms and elbows may deviate significantly from the points of the original point lattice. The largest 3D PBG's are obtained for square spiral posts that wind around the [001] axis of diamond (or face centered cubic) lattice and in which the spiral arm segments approximately connect either the fifth or first nearest-neighbor points of the parent lattice. In the case of silicon posts (with a dielectric constant of 11.9) in an air background, whose arm segments nearly connect fifth nearest-neighbor point of the diamond lattice, the full PBG can be as large as 16% of the gap center frequency. For the corresponding air posts in a silicon background, the maximum PBG is 24% of the gap center frequency. We compute both the total electromagnetic density of states and the electromagnetic field distributions near the PBG. It is suggested the PBG in an optimized structure is highly tolerant to various forms of disorder that may arise during the manufacturing process.