Optical peculiarities in quasi-sandwiching periodic one-dimensional photonic crystals

Within the Maxwell framework and using the transfer-matrix method, we have determined an exact expression that governs the photonic band structure and the density of states (the group velocity) of one-dimensional superlattices composed of three alternate layers (quasi-sandwiching periodic structure) characterized by three different refractive indexes. We begin by giving the band gap of the quasi-sandwiching period structure. Owing to the advantage of the quasi-sandwiching periodic structure, we develop a specific formula that gives the N-period mode density in terms of the complex transmission coefficient of a unit cell. The specific example of a quarter-wave stack is analyzed.