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medium is metallic when α is an odd number. In Eq. (7), the translation matrix 

and the column vector v$_{α}$ = [ a$_{α}$, b$_{α}$ ] giving some constant amplitudes. Note that a$_{α}$ is independent of a$_{K}$ given in Eq. (5) and they should not be confused. Also, 

where ϵ$_{1}$ = ϵ$_{m}$ and ϵ$_{2}$ = ϵ$_{d}$ are the relative dielectric constants of the metallic medium and the dielectric material, respectively. For other slabs we use the recurrence relation ϵ$_{α}$$_{+2}$ = ϵ$_{α}$ ; here ϵ$_{α}$ at α = 0 does not refers to its value in vacuum but ϵ$_{d}$ and it is not necessarily the unity. In Eq. (9) the real-valued wave vector onto a plane parallel to the metallo-dielectric interface has a squared modulus k 2 ‖ = k 2 x + β $^{2}$. Finally since material losses are neglected, the dielectric constant of the plasma-like material ϵ$_{m}$ < 0 and that of the insulator ϵ$_{d}$ > 0 are also real-valued parameters. 

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We also take advantage of spatial symmetries from the layered system in Fig. 1. In particular, we use that the relative dielectric constant is a real and even function ϵ ( − y $^{′}$) = ϵ ( y $^{′}$), being y ′ = y − y$_{α}$$_{−}$$_{1}$$_{/}$$_{2}$ a spatial coordinate centered in the middle point of the domain R$_{α}$ , y$_{α}$$_{−}$$_{1}$$_{/}$$_{2}$ = ( y$_{α}$ + y$_{α}$$_{−}$$_{1}$ ) / 2. Given a wavefield h$_{x}$ ( x, y $^{′}$) that satisfies Eq. (4), the fields h ∗ $_{x}$( x, y $^{′}$) and h$_{x}$ ( x, − y $^{′}$) are also solutions of the wave equation. From the series expansion of Eq. (5), therefore, we infer that h$_{K}$ ( − y $^{′}$) and h ∗ $_{K}$( y $^{′}$) are periodic functions both associated with the same Bloch (real) number − K , so that there should be a constant of proportionality between them. Provided ϕ is the argument of h$_{K}$ ( y ′ = 0) we find that 

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As a consequence h$_{K}$ is hermitian under the normalization h$_{K}$ ( y ′ = 0) = 1. However this is not necessarily true when h$_{K}$ ( y = 0) = 1. In the later case it yields for instance that the amplitude of the periodic function | h$_{K}$ | evaluated on every surface y = y$_{α}$ reaches the unit. 

The continuity at the interfaces of the wavefields h$_{x}$ given in Eq. (5), h$_{z}$ , e$_{x}$ and e$_{z}$ [that is continuity of ϵ − $^{1}$∂$_{y}$ h$_{x}$ as inferred from Eqs. (2a) and (2c)], together with the periodicity of h$_{K}$ determine the waveform of each Bloch mode and its dispersion behaviour. Using the 

