One-dimensional photonic crystal: The Kronig-Penney model

We formulate the photonic band-structure problem for a one-dimensional photonic crystal in terms of the reflection and transmission coefficients, obtaining a transcendental photonic band equation. The reflection and the transmission coefficients may be evaluated by using the standard transfer-matrix method. The structure of the equation reveals the existence of gaps, analogous to the Kronig-Penney model in the electronic band-structure problem. As an example, the photonic band equation is solved for the simple case of the “Kronig-Penney” dielectric structure, consisting of alternating slabs of refractive indices n₁ and n₂.