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, 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 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 5 h$_{K}$ ( − y $^{′}$) exp( − iϕ ) = [ h$_{K}$ ( y $^{′}$) exp( − iϕ )] ∗ . (10) k$_{yα}$ =    √ ( ω/c ) 2 ϵ$_{α}$ − k 2 $_{‖}$, ( ω/c ) 2 ϵ$_{α}$ ≥ k 2 ‖ i k 2 ‖ − ( ω/c ) 2 ϵ$_{α}$, ( ω/c ) 2 ϵ$_{α}$ < k 2 ‖ (9) T$_{α}$ ( y ) =   exp ( ik$_{yα}$y ) 0 0 exp ( − ik$_{yα}$y )   , (8) 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.