Influence of weak dissipation on the photonic band structure of periodic composites.

Abstract

We study dissipation in an otherwise perfect photonic crystal. A perturbational calculation (for small dissipation) leads to formulas for the 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 band edge ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ 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 (\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$${)}^{1/2}$ (three-dimensional periodicity) or to (\ensuremath{\omega}-${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$) (two-dimensional periodicity). We also present a semiquantitative argument which suggests that, inside the band gap, the importance of finite crystal size is considerably less than that of absorption. \textcopyright{} 1996 The American Physical Society.