An alternative formulation of the Small Perturbation Method (SPM) in solving electromagnetic scattering from multi-layer random rough surfaces to resolve singularities in spectral integrals is presented. Non-monotonic permittivity changes will allow a multi-layer structure with flat interfaces to support guided modes. The presence of these guided modes translates to poles in the zeroth order Green's function of the media for the surface fields. The poles appear in the first and second order perturbation solutions based on a iterative procedure. Thus, evaluating the spectral integrals to obtain the spatial fields becomes problematic. The Sommerfeld integration path instead of real line integrals is introduced by analytic continuation of the integrand into complex spectral space. It is verified that this alternative spectral integration method is valid for both monotonic and non-monotonic cases.
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