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A robust generalized analytical expression for resonance frequencies of plasmonic nanoresonators, which consists of folded rectangular structures, is proposed based on a circuit route. The formulation is rigorously derived from the lumped circuit analogue of the plasmon resonance in a rectangular metallic nanorod. Induced by the nonhomogeneous charge distributions in the plasmonic resonators of rectangular end-caps, the electromagnetic forces drive the harmonic oscillations of free electrons in the plasmonic nanoresonators, generating intrinsically nonlinear shape-dependent LC resonance responses. Even for the plasmonic nanoresonators with much larger structure sizes than the skin depths, the significant frequency deviations due to the phase-retardation behavior can still be adequately described by the generalized expression. Moreover, for a large range of plasmonic nanoresonators with various folded rectangular geometries, sizes and materials, the generalized analytical expression gives the underlining physics and provides accurate predictions, which are perfectly verified by a series of numerical simulations. Our studies not only offer quantitative insights of nearly any plasmonic nanoresonators based on folded rectangular geometries, but also reveal potential applications to design complex plasmonic systems, such as periodic arrays with embedded rectangular nanoresonators.

The Generalized Analytical Expression for the Resonance Frequencies of Plasmonic Nanoresonators Composed of Folded Rectangular Geometries