FIG. 1: (Color online) Geometry for studying waves in layered superconductors. The interface z = 0 divides the layered superconductor from an insulator with dielectric constant ε$_{ext}$ . The electromagnetic field inside the layered superconductor is determined by the dis- tribution of the gauge invariant phase difference ϕ ( x, z, t ) of the order parameter between neighboring layers. This phase difference can be described by a set of coupled sine-Gordon equations (see review [5]). In the continuum and linear approximation, ϕ ( x, z, t ) can be excluded from the set of equations for electromagnetic fields, and the electrodynamics of layered superconductors can be described in terms of an anisotropic frequency-dependent dielectric permittivity with components ε$_{c}$ (Ω) and ε$_{ab}$ (Ω) across and along the layers, re- spectively [2]. In Ref. [9], the effect of spatial dispersion in ε$_{c}$ , related to the capacitive interlayer coupling, was taken into account. Here we do not consider this effect because it is only important for a very narrow frequency range near ω$_{J}$ [9]. In the limit s/d ≪ 1, the equations for ε$_{c}$ (Ω) and ε$_{ab}$ (Ω) can be written as Here we introduce the dimensionless parameters Ω = ω/ω$_{J}$ , ν$_{ab}$ = 4 πσ$_{ab}$/εω$_{J}$ γ $^{2}$, and ν$_{c}$ = 4 πσ$_{c}$/εω$_{J}$ . The relaxation frequencies ν$_{ab}$ and ν$_{c}$ are proportional to the averaged quasi- 4 ε$_{c}$ (Ω) = ε ( 1 − 1 Ω 2 + iν$_{c}$ 1 Ω ) , ε$_{ab}$ (Ω) = ε ( 1 − 1 Ω $_{2}$γ 2 + iν$_{ab}$ 1 Ω γ 2 ) . (2)