A crystal is a periodic arrangement of atoms or molecules. If a small basic building block of atoms or molecules is repeated spatially, a crystal lattice will be formed. As is well known, semiconductor materials have a bandgap between the valence and conduction energy bands. Electrons are forbidden to occupy any energy level within the bandgap. Similarly, if the dielectric constant of a material changes periodically in space, the material is referred to as a photonic crystal. A photonic crystal possesses a forbidden frequency band in which propagation of electromagnetic waves is prohibited. According to the number of directions in which dielectric materials exhibit periodicity, one-, two-, or three-dimensional photonic crystal structures are possible. Scattering of light by photonic crystals can produce many of the analogous phenomena for photons to the atomic potential acting on electrons.
The photonic bandgap (PBG) can be defined as a range of frequencies for which photons are forbidden to travel through a photonic crystal in any direction of propagation. In analogy to electrons in a crystal, electromagnetic waves propagating in a structure with periodically varying dielectric constants are organized into photonic bands. For certain crystal structures, that have high enough dielectric contrast ratios, these photonic bands are separated by (photonic) gaps in which propagating states are forbidden.
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