We suggest a geometrical framework in which to discuss periodic layered structures in the unit disk. Bandgaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of… (More)
The action of any lossless multilayer is described by a transfer matrix that can be factorized in terms of three basic matrices. We introduce a simple trace criterion that sorts the multilayers into three classes, each of whose properties are closely related to one (and only one) of the three basic matrices.
We re-elaborate on the recent basic result that the action of any multilayer is equivalent to a proper Lorentz transformation. As a consequence, we propose simple optical measurements that can serve as an analogue computer for simulating special relativity. Special attention is paid to the question of the Wigner rotation, showing that it can be easily… (More)