We theoretically investigate a widely-used plasmonic structure composed of a nano-slit aperture surrounded by surface corrugations. A systematical semi-analytical theory in form of two nested coupled-mode models is developed to provide intuitive physical pictures. Based on the theory, figures of merit (FoMs) of the structures designed for normal and for oblique incidence/beaming are defined for the first time to incorporate the interlinks among key structural parameters, making global optimization simple and efficient. Both the theory and the FoMs are quantitatively validated with exhaustive calculations and shown to be highly accurate on performance prediction and structural optimization. With the theory and the FoMs, an efficient, effective and standard recipe is introduced for optimal structure design. We believe this work will help to understand the mechanisms of and to facilitate the design of such a structure in various configurations used in various applications.
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