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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. 

## A. Dispersion equation and isofrequency curves 

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 

<img src='content_image/361153.jpg'>

<img src='content_image/361152.jpg'>

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 

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$_{α}$ . 

<img src='content_image/361151.jpg'>

<img src='content_image/361150.jpg'>

On other hand, imposing the periodicity condition h$_{K}$ ( y$_{α}$$_{+2}$ ) = h$_{K}$ ( y$_{α}$ ) we also find 

<img src='content_image/361149.jpg'>

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 

<img src='content_image/361147.jpg'>

<img src='content_image/361148.jpg'>

