Polarization catastrophe in nanostructures doped in photonic band gap materials

In the presence of the dipole-dipole interaction, we have studied a possible dielectric catastrophe in photonic band gap materials doped with an ensemble of four-level nanoparticles. It is found that the dielectric constant of the system has a singularity when the resonance energy lies within the bands. This phenomenon is known as the dielectric catastrophe. It is also found that this phenomenon depends on the strength of the dipole-dipole interaction.