Floquet multipliers for Bloch waves in absorptive and non-absorptive photonic crystals

Floquet multipliers are analysed for the Bloch waves representing light propagation in both absorptive and non-absorptive one-dimensional photonic crystals. In particular, the dependence of the multipliers in the complex plane on frequency (wavenumber) of the propagating light is studied. As a result, the ambiguity in assigning a proper multiplier to the direct/backward Bloch wave in the allowed bands of non-absorptive crystals is resolved. The results will serve to clarify the relation between the Bloch wavenumber and the multipliers. This facilitates a proper parameterization of the transfer matrix for absorptive crystals, as well as for the bandgaps of non-absorptive crystals.