
ThreeDimensional Photonic CrystalsThe ideal structure to have is a threedimensionally periodic photonic crystal (simply referred to here as a threedimensional photonic crystal) with a full bandgap in threedimensions. However, the complicated structure apparently required by such crystals has made them difficult to fabricate. An Early DesignIn 1994, we proposed a threedimensional crystal designed specifically to be amenable to fabrication at submicron length scales. [Fan, et. al, APL 65, p. 14661468 (1994)] This structure, shown below, is designed to be fabricated in a layered fashion using two different dielectric materials (say, Silicon and Silicon Dioxide). Staggered channels of the lowerdielectric material pass through the highdielectric substrate, and a triangular lattice of air holes is etched through the whole thing perpendicular to the channels.
We also have a VRML version of the primitive cell of this structure, for readers with VRML viewers. The primitive cell is duplicated (tiled) in three dimensions to form the crystal. A New Layered StructureRecently, we have proposed a new structure for achieving a full threedimensional band gap, shown below. [S. G. Johnson and J. D. Joannopoulos, APL 77, 34903492 (Nov. 2000).] This structure has the unique property that its defect modes (waveguides and cavities) closely mimic those of 2d crystals. [M. L. Povinelli, Steven G. Johnson, Shanhui Fan, and J. D. Joannopoulos, PRB 64, 075313 (2001).]
This structure has three key advantages:
It is the third characteristic that really distinguishes this structure from previous work. The highsymmetry 2d structure of the slabs means that complicated optical networks can be constructed in this crystal by modification of only a single layer. Moreover, the types of defects and defect modes that are used to trap and guide light are strongly analogous to those in the corresponding twodimensional or slab systems. This allows one to leverage the large body of analyses, experiments, and understanding of those simpler structures. In other words, this structure allows you to build a "2d crystal" in 3d, but avoid the inevitable radiation losses that occur without a full 3d gap. The fundamental structure is actually very simple: an fcc lattice (possibly distorted) of air (or lowindex) cylinders in dielectric, oriented along the 111 direction. This results in the layered structure rendered above, and depicted schematically below (in vertical and horizontal crosssections):
Typical parameters, for an undistorted fcc lattice of air cylinders in a dielectric constant of 12 (Si), are: d=a/sqrt(3), x=a/sqrt(2), r=0.293a, and h=0.93a, where a is the fcc lattice constant. This results in a 21% complete threedimensional band gap, centered at a frequency of 0.569 c/a. 