Photonic bandgaps in periodic dielectric structures

Abstract

Photonic bandgaps are defined as frequency intervals for which propagation of electromagnetic waves is forbidden in all 4π steradians within a dielectric structure with a periodic index of refraction. Such structures consist, for example, of dielectric spheres in suspension or air holes in a dielectric material, with a spatial period comparable to the electromagnetic wavelength. The principal feature of periodic structures is their ability to perturb the density of electromagnetic states within the structures. Since photonic bandgap materials can essentially suppress all states, the radiative dynamics within the materials can be strongly modified. By changing the atom-field radiative coupling, photonic bandgap materials could lead to the inhibition of spontaneous emission; if a local defect is introduced within the structure, it will behave like a high- Q microcavity. The existence of bandgaps can be predicted from a classical treatment of the vector wave equation. The use of the plane-wave expansion method can lead to accurate results but introduces two problems related to the dielectric discontinuities and the plane-wave cutoff. Experimental investigations at microwave frequencies have demonstrated many of the properties of photonic bandgap structures.