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Fig. 8.

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Frequency dependences of local spectral density evaluated at the slab axis, S ω v ˘ ω ( x = 0 ) $ S_\omega {\breve{v}}_\omega(x=0) $. A fixed combination [ρi/ρe = 5, kd = π/20] is adopted, whereas a number of values are examined for the steepness parameter μ in different panels. For each μ, a number of values of Λ/d are tested and shown according to the line styles. The magenta arrows in each panel mark the oscillation frequencies of the first two discrete leaky modes ( R Ω 2 DLM $ \Re\Omega^{\mathrm{DLM}}_{2} $ and R Ω 3 DLM $ \Re\Omega^{\mathrm{DLM}}_{3} $) computed for the same set of [ρi/ρe, μ, kd]. All vertical dash-dotted lines correspond to the critical frequency ωcrit = kvAe (see text for more details).

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