Three-dimensional Green's tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders.

The three-dimensional local density of states (3D LDOS), which determines the radiation dynamics of a point-source, in particular the spontaneous emission rate, is presented here for finite two-dimensional photonic crystals composed of cylinders. The 3D LDOS is obtained from the 3D Green's tensor, which is calculated to high accuracy using a combination of a Fourier integral and the Rayleigh-multipole methods. A comprehensive investigation is made into the 3D LDOS of two basic types of PCs: a hexagonal cluster of air-voids in a dielectric background enclosed by an air-jacket in a fiberlike geometry, and a square cluster of dielectric cylinders in an air background. In the first of these, which has a complete in-plane band gap, the 3D LDOS can be suppressed by over an order of magnitude at the center of the air-voids and jumps sharply higher above the gap. In the second, which only has a TM gap in-plane, suppression is limited to a factor of 5 and occurs at the surface of the cylinders. The most striking band gap signature is the almost complete suppression of the radiation component of the 3D LDOS when the complete in-plane gap is sufficiently wide, accompanied by a burst into the radiation component above the gap.