On the Calculation of the Spectral Bands of One-Dimensional Photonic Crystals

In this work we consider the propagation of transverse electromagnetic waves in one-dimensional photonic crystals consisting of periodic arrays of slabs. On the basis of the Floquet theory we obtain the characteristic function of the periodic medium, which defines the photonic bands of the crystal. The characteristic function is constructed from the monodromy matrices of the slabs. Entries of monodromy matrices are explicitly given as power series of the spectral parameter. The present analysis can be applied not only to homogeneous slabs, but also to slabs with varying refractive indexes. The power series representation of the entries of monodromy matrices leads to an effective numerical method for the calculation of the spectral bands of one-dimensional photonic crystals.