Formation of effective energy carriers in donor or acceptor lattice disturbances at the band-gap edges of photonic crystals

The effect of a long-range, slowly varying, modulation of the refractive index of a photonic crystal is investigated. It is shown that the Bloch modes are modified by essentially being modulated by an envelope function which adapts to the long-range dielectric function perturbation. This envelope function obeys a simple linear Schroedinger equation of classical (non-quantum) origin. Close to a band extremum, at a gap edge, the envelope functions can be interpreted as wave functions of relativistic particles possessing a finite rest mass. These effective energy carriers come as two species, referred to as “effective photons” (for positive band curvatures) or “photonic holes” (for negative band curvatures). The energy transfer through the chirped structure can be viewed as resulting from the migration of these particles under forces implied by the long-range dielectric function modulation.