Light in periodically stratified media

A pedagogical presentation of the propagation of electromagnetic waves in stratified media is given. The usual 2 × 2 matrix analysis is simplified and generalized. A Bloch factor eigenvalue equation is obtained, valid for all periodic stratifications. The implications of the band structure of an infinite periodic structure for reflection by a finite structure are demonstrated. Some features of the reflectivity are shown to be universal. In the long-wave limit, a periodic stratification with an arbitrary dielectric function profile ∊(z) within a unit cell is shown to be equivalent to a homogeneous anisotropic medium, with ordinary and extraordinary dielectric constants given by ∊o = 〈∊〉 and ∊e−1 = 〈∊−1〉.