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Plasmonic back reflectors have recently become a promising strategy for realizing efficient organic solar cell (OSCs). Since plasmonic effects are strongly sensitive to light polarization, it is highly desirable to simultaneously achieve polarization-independent response and enhanced power conversion efficiency (PCE) by designing the nanostructured geometry of plasmonic reflector electrode. Here, through a strategic analysis of 2-dimensional grating (2D) and 3-dimensional patterns (3D), with similar periodicity as a plasmonic back reflector, we find that the OSCs with 3D pattern achieve the best PCE enhancement by 24.6%, while the OSCs with 2D pattern can offer 17.5% PCE enhancement compared to the optimized control OSCs. Importantly, compared with the 2D pattern, the 3D pattern shows a polarization independent plasmonic response, which will greatly extend its uses in photovoltaic applications. This work shows the significances of carefully selecting and designing geometry of plasmonic nanostructures in achieving high-efficient, polarization-independent plasmonic OSCs.