The rigorous coupled wave approach (RCWA) was implemented to investigate optical absorption in a triple-p-i-n-junction amorphous-silicon solar cell with a 2D metallic periodically corrugated backreflector (PCBR). Both total and useful absorptances were computed against the free-space wavelength $lambda_o$ for both s- and p-polarized polarization states. The useful absorptance in each of the three p-i-n junctions was also computed for normal as well as oblique incidence. Furthermore, two canonical boundary-value problems were solved for the prediction of guided-wave modes (GWMs): surface-plasmon-polariton waves and waveguide modes. Use of the doubly periodic PCBR enhanced both useful and total absorptances in comparison to a planar backreflector. The predicted GWMs were correlated with the peaks of the total and useful absorptances. The excitation of GWMs was mostly confined to $lambda_o < 700$ nm and enhanced absorption. As excitation of certain GWMs could be correlated with the total absorptance but not with the useful absorptance, the useful absorptance should be studied while devising light-trapping strategies.
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