| Photonic crystals are dielectric materials containing a periodicity in dielectric constant. The periodic dielectric constant can create a range of forbidden frequencies for electromagnetic waves called a photonic band gap. Photonic band structure calculations are performed for several two-dimensional and three-dimensional photonic crystal geometries. Using a plane wave expansion, Maxwell's equations are solved numerically using a frequency-domain computational method that takes the vector nature of the electromagnetic field into account. Photonic band gaps are found to exist for both two-dimensional and three-dimensional photonic crystal geometries. Specifically, Photonic band gaps are confirmed for both the triangular lattice in two dimensions and for the diamond lattice in three dimensions. For the diamond lattice of spheres of low-dielectric constant embedded in a background of high-dielectric constant, the effects of packing fraction and dielectric constant on photonic band gap width are investigated. |
