Wave propagation in one-dimensional optical quasiperiodic systems

One-dimensional quasiperiodic optical systems are studied, using a Schrodinger-like equation with a potential V(x) = 2 lambda (1) cos x+2 lambda (2) cos alphax as an approximation to the wave equation in the slowly-varying wave approximation. It is shown that small changes in the parameter alpha produce major changes in the band structure of the system. For certain values of alpha, the band structure consists of many "thin bands" and allows the possibility of dense multiplexing. The propagation of "noisy optical waves" that contain many frequencies with a thermal distribution is also studied with a thermodynamic model. Quantities like the thermodynamically averaged group velocity and the thermodynamically averaged inverse effective mass are introduced in order to quantify the complex relation between the frequency and wave vector in these systems.