transfer matrix elements for layered media [21] we may obtain in a rather simple way the dispersion equation. Let us give the corresponding analysis briefly. Experienced readers may ignore the rest of the present section thus going to Sec. III directly. Eq. (7) provides the complex waveform of h$_{K}$ appropriately. However, in order to sim- plify the application of continuity conditions of the fields, we also establish an equivalent definition, at y ∈ R$_{α}$ , where the new column vector v ′ α = [ a ′ $_{α}$, b ′ $_{α}$]. Note that the matrix P$_{α}$ = T$_{α}$ ( y$_{α}$$_{−}$$_{1}$ − y$_{α}$ ) representing a translation between the boundaries of R$_{α}$ . Thus the continuity of the p-polarized fields at y = y$_{α}$ holds when where the transmission matrix given as a direct application of the Bloch theorem. As a consequence, considering the continuity of the fields at y = y$_{α}$ given in (13) and that at y = y$_{α}$$_{+1}$ , Eq. (15) leads to the matrix equation where Eq. (12) is also used at ( α + 1) and ( α + 2). The computation of the matrix M$_{α}$ leads to 6   A$_{α}$ B$_{α}$ C$_{α}$ D$_{α}$   = P − 1 α $_{+2}$D − 1 α $_{+2}$D$_{α}$$_{+1}$ P − 1 α $_{+1}$D − 1 α $_{+1}$D$_{α}$ . (17) M$_{α}$v$_{α}$ = exp ( iKp ) v$_{α}$ , (16) v$_{α}$$_{+2}$ = exp ( iKp ) v$_{α}$ , (15) D$_{α}$ =   1 1 k$_{yα}$ ϵ$_{α}$ − k$_{yα}$ ϵ$_{α}$   . (14) D$_{α}$v$_{α}$ = D$_{α}$$_{+1}$v ′ α $_{+1}$, (13) v ′ α = P$_{α}$v$_{α}$ , (12) h$_{K}$ ( y ) = exp ( − iKy ) T$_{α}$ ( y − y$_{α}$$_{−}$$_{1}$ ) v ′ α (11) A. Dispersion equation and isofrequency curves On other hand, imposing the periodicity condition h$_{K}$ ( y$_{α}$$_{+2}$ ) = h$_{K}$ ( y$_{α}$ ) we also find Consequently, the field amplitudes corresponding to the slab labelled as ( α + 1) may be determined by means of those amplitudes of the adjacent slab α as v$_{α}$$_{+1}$ = P − 1 α $_{+1}$D − 1 α $_{+1}$D$_{α}$ v$_{α}$ .