Numerical simulations of photon trapping in doped photonic crystals doped with multi‐level atoms

Abstract

A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrodinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)