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We use a 1D grating back reflector to study the mechanism of light trapping in solar cells. Experimental results of a full solar cell on a sinusoidal back reflector are compared to a theoretical model using an expansion into grating modes and the Rayleigh hypothesis. By means of the sinusoidal shape, the continuity equations extend the coupling only to neighboring orders. The essential aspects of the coupling process are thus included, but the algorithm requires only a minimum 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.