Band-structure properties of photonic superlattices

The band structure of a one-dimensional periodic array composed of two different layers of dimensions a and b characterized by refractive indices n ₁ and n ₂, respectively, is investigated. Refractive indices may take on positive as well as negative values. Within the Maxwell framework and using a transfer matrix technique for one dimensional periodic eigen-problems, we have determined a general equation, which governs the photonic band structure and the density of states (DOS) of one-dimensional photonic crystals. In addition to the well-known existence of the band gaps, we show that, depending on the width relationship b/a between the layer materials, super-lattices with null photonic band gap may exist and the conditions for such occurrences are established. Furthermore, we have been able to study the so-called 〈n〉 = 0 non-Bragg gap, ground ω₀, for which the average refraction felt by the propagating radiation is null. The text was submitted by the authors in English.