In this paper we numerically study the propagation of surface waves guided by a metal-backed dielectric slab with biperiodic metallizations on its surface. Such structures are electromagnetic absorbing screens when the dielectric slab is lossy. In this paper, the surface waves are characterized by their longitudinal and transverse wave numbers, which are deduced from the complex pole locations of the reflection coefficient of the screens. The reflection coefficients can be obtained with a

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... method. These reflection coefficients are generalized to complex incident wave numbers. The poles are isolated in the complex plane with the help of the argument principle and are calculated with a numerical method based on Müller's algorithm. Then the parametric study of the wave numbers of the surface waves shows that the absorption of an electromagnetic wave by the screens at normal incidence is due to a resonance of the real part of the transverse wave number of the excited surface wave. We also show that there exists a Brewster incidence angle for the absorbing screens with suitable metallization array dimensions. This Brewster angle appears when the pole crosses the branch cut of the two-sheeted Riemann space of the reflection coefficient.