  Understanding the dispersive properties of photonic crystals is a fundamental
and well-studied problem. However, the introduction of singular permittivities
and damping complicates the otherwise straightforward theory. In this paper, we
study photonic crystals with a Drude-Lorentz model for the permittivity,
motivated by halide perovskites. We demonstrate how the introduction of
singularities and damping affects the spectral band structure and show how to
interpret the notion of a "band gap" in this setting. We present explicit
solutions for a one-dimensional model and show how integral operators can be
used to handle multi-dimensional systems.
