The photonic band dispersion and density of states (DOS) are calculated for
the three-dimensional (3D) hexagonal structure corresponding to a distributed
Bragg reflector patterned with a 2D triangular lattice of circular holes.
Results for the Si/SiO2 and GaAs/AlGaAs systems determine the optimal
parameters for which a gap in the 2D plane occurs and overlaps the 1D gap of
the multilayer. The DOS is considerably reduced in correspondence with the
overlap of 2D and 1D gaps. Also, the local density of states (i.e., the DOS
weighted with the squared electric field at a given point) has strong
variations depending on the position. Both results imply substantial changes of
spontaneous emission rates and patterns for a local emitter embedded in the
structure and make this system attractive for the fabrication of a 3D photonic
crystal with controlled radiative properties.Comment: 8 pages, 5 figures; to appear in Phys. Rev.