Hamiltonian Formalism for the Plane Waves Propagating in Periodically Layered Media

Application of the Floquet theorem and the propagator matrix method reduces this problem of the plane wave propagating in periodically layered media, to investigation of properties of stationary envelopes consisting of the plane waves of different modes propagating up- and downwards. The Floquet multipliers movement with the change in frequency can be described by using the Hamiltonian formalism. This description allows us to obtain new results in addition to those based on the symmetry of the dispersion equation. We explain the interchanging of propagation and attenuation zones, their structure at small incidence angles and the presence of wide propagation zone at low frequencies.