INFLUENCE OF WEAK DISSIPATION ON THE PHOTONIC BAND-STRUCTURE OF PERIODIC COMPOSITES

We study dissipation in an otherwise perfect photonic crystal. A pertu rbational calculation (for small dissipation) leads to formulas for th e imaginary part of the eigenfrequency (if the wavevector is real) and for the imaginary part of the wave vector (if the frequency is real). We also calculate the density of states (DOS) in the vicinity of a ba nd edge omega(c) of a complete photonic band gap. There is a smoothing effect, namely, the density of states becomes finite inside the gap. In this region the DOS is inversely proportional to (omega - omega(c)) (1/2) (three-dimensional periodicity) or to (omega - omega(c)) (two-di mensional periodicity). We also present a semiquantitative argument wh ich suggests that, inside the band gap, the importance of finite cryst al size is considerably less than that of absorption.