Spontaneous-emission rates in finite photonic crystals of plane scatterers

Complete band gaps in one-dimensional left-handed periodic structures

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic band gap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete band gap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete band gap.

Spontaneous emission in one-dimensional photonic crystals

We study the spontaneous emission of an atom embedded in a one-dimensional photonic crystal or superlattice using a classical electrodynamic theory of radiation. The rate of emission is a function of the frequency of the emitted photon, the dipole's position and orientation, as well as the geometric and material parameters of the superlattice. The emission spectrum shows an oscillatory behavior which follows the photonic band structure. For TE modes, there are frequency regions where radiative emission is completely prohibited due to the absence of modes with k//>omega/c; the radiation is then TM polarized. In addition to the radiative modes, there are always evanescent modes with k//>omega/c which are waveguided by the dielectric layers. The evanescent contribution to the spontaneous emission is dominant if a dielectric layer is in the near field region of the dipole. For TM modes, emission rates greatly vary for parallel and perpendicular dipole moments. In a photonic crystal with a high filling fraction of the dielectric and perpendicular dipoles located in the low-index layer, the decay rate can be as much as 76 times the free space value for a single atom and 50 times for a gas of atoms. We also find that the rate of emission presents a strong dependence on the atom's position.