Analytical solution for photonic band-gap crystals using Drude conductivity

An analytical solution for the photonic band-gap of semiconductor structures in the terahertz (THz) frequency range is discussed. In analogy with the Kronig–Penney model for electronic band-gaps in periodic potentials, Maxwell’s equations for the propagation of light in the photonic crystal are transformed into an equivalent form of Schrödinger’s equation. In the THz frequency range, the refractive index of the semiconductor is well represented by a frequency-dependent Drude model. We thus find a Kronig–Penney type solution for the photonic band-gap crystal.