Point defect geometries in inverted opal photonic crystals

We study point defect geometries in inverted opal photonic crystals that can be easily fabricated by means of colloidal self-assembly. Two broad classes of defects are considered: substitutional and interstitial. Substitutional point defects are found to introduce a usable defect band into the photonic band gap. This can be done by using a silica sphere of radius between $0.33a$ and $0.35a$ (where $a$ is the lattice constant). The state is triply degenerate. Reflectance and local density of states calculations are performed to verify the existence and frequency of this defect. The point defect can be made by precoating shrunk silica spheres with a thin layer of silicon. Such a defect can be used as a microcavity for localizing light at a point, with a quality factor $Q$ that is limited primarily by the proximity of the defect to the surface of the photonic crystal and other such defects.

Figure 1

(Color) Two different styles of point defects (adapted from [26]).

Figure 2

(Color) Band structure of photonic crystal with point defect mode. Defect calculation performed with $3\times 3\times 3$ supercell, with a (48,48,48) basis set, for shrunk silica sphere radius of $0.35a$. The $3\times 3\times 3$ supercell calculation for the defect-produced band structure with multiple folding of bands, and as such the band diagram for that calculation is not edifying to show. The most important result from that calculation, namely, the defect state frequency, was extracted, and this piece of information was incorporated into the above nonsupercell band structure.

Figure 3

(Color) Reflectance spectrum of photonic crystal, with and without point defect. The dipole source is polarized in the [110] direction. The computational cell used had dimensions of $56\times 97\times 411$ grid points, corresponding to 40 grid points per lattice constant. The photonic crystal slab was seated on a silicon substrate. A $2\times 2$ supercell was used, and the simulation was run for $79195$ time steps. (Inset shows magnified version of reflectance dip due to defect.)

Figure 4

Local density of states of photonic crystal, with point defect. We followed the Gilat-Raubenheimer method, using eight evenly spaced $k$ points in the irreducible Brillouin zone.