We study the interaction of electromagnetic waves in layered media with textured interfaces. Experimental results of a solar cell grown on a sinusoidal back reflector are compared with a theoretical model using an expansion into diffraction modes. We assume the validity of the Rayleigh hypothesis and show that the continuity equations extend the coupling only to neighboring orders for the case of sinusoidal textures. This approach includes all essential aspects of the coupling process and it requires only a moderate amount of mathematical complexity. Our modeling results correctly reproduce the absorption of the periodically textured solar cell for both polarization directions. The absorption phenomena underlying the light-trapping process can thus be studied with a small number of parameters like period, depth, and film thickness.