Photons

The quantization of the electromagnetic field is not traditionally covered at this point in a solid state course. Nevertheless, the derivation is both beautiful and useful for understanding the quantization of fields in solids. Since this topic is not discussed in the book, the reading for this subject is a set of online notes.

Outline
• Photons in vacuum
• Review of Maxwell's unification of electromagnetism with optics      W
• Quantization of the normal mode solutions to the wave equation      W
• Thermodynamic properties of light
• Planck's radiation law      W
• Wien's displacement law      W
• Stefan-Boltzmann law      W
• Internal energy density      W
• Specific heat      W
• Radiation pressure      W
• Entropy      W
• Table summarizing the results of the quantization of the wave equation
• Light in one-dimensional layered material
• Photonic crystals      W
• Empty lattice approximation
• Plane wave method
• Table of photonic crystals

Reading
• The quantization of electromagnetic fields, see also: Kittel Appendix C: Quantization of Elastic Waves
• Light in a layered material

For the exam
• You should know how to calculate the density of states D(k) in 1, 2 and 3 dimensions.
• You should know how to calculate the macroscopic properties (like the specific heat) of a gas of noninteracting photons. You should be able to explain how to calculate the quantities listed in the table summarizing the results of the quantization of the wave equation.
• You should know that when the speed of light is a periodic function, that gaps can appear in the dispersion relation. There are frequencies which get reflected out of a photonic crystal.

Student presentations
• Planck Strahlungsgesetz und Verteiling - Reinhold Hetzel, 2008
• Quantization of the wave equation in 1, 2, and 3 dimensions - Benjamin Kollmitzer, 2008
• 1-D Photonische Kristalle - Antonius Dorda, 2009
• Thermodynamic properties of bosons - Elias Assman, 2009

Resources
Table summarizing the results of the quantization of the wave equation
Table of photonic crystals
Quantisierung des klassischen elektromagnetischen Feldes, E. Schachinger