According to quantum mechanics, everything moves like a wave but exchanges energy and momentum like a particle. The three most important kinds of waves in solids are light waves, sound wave, and electron waves. This section describes light waves. When light exchanges energy or momentum like a particle, those particles are called photons. A discussion of photons is found in the online notes on photons.
Notes on the quantization of electromagnetic fields
Kittel Appendix C: Quantization of Elastic Waves
Light in a layered material
Online book on photonic crystals: Photonic Crystals:
Molding the Flow of Light, John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade
Quantisierung des klassischen elektromagnetischen Feldes, E. Schachinger
Planck, Max (1901). "On the Law of Distribution of Energy in the Normal Spectrum", Annalen der Physik 4: 553.
Landau and Lifshitz, Statistical Physics, Part 1, Pergamon Press, 1980
The Brillouin zone applet