Subsurface layer statistical resonance

When considering the scattering of waves by a layered medium with a rough surface, the correlator Q=⟨E(ω)E(ω)⟩ is usually studied (here E and ω are the electric field of the reflected wave and the circular frequency, correspondingly). Generally, it can be expanded in a power series of the reflection coefficients V _i of inner boundaries. For the case of strong scattering the terms Q_i1 proportional to the first powers of V_i become as a rule exponentially small by the scattering parameter Δ=(σ/λ)², with σ and λ being the mean square roughness height and the wave length accordingly. Only if more general correlators P are considered, then the values P_i1 prove to be not exponentially small when some resonance conditions are satisfied. We refer to this phenomena as to the subsurface layer statistical resonance. For the first time, we found that the phenomena exist in the two cases: of small jump of the dielectric constant at the medium boundary and of large-scale roughness for normal incidence of wave. In this report we generalise the last case for oblique incidence of wave. It is shown, that the resonance takes place in a specular direction for the two frequency correlator P=⟨E(ω₁)E(ω₂)⟩ with the resonance condition ω_1,2=ω_2,1(√(ε-sin² θ)/cosθ-1). Here ε and θ are the layer dielectric constant and the incident angle, accordingly. The resonance width and amplitude are studied and discussed