We proposed a quantitative theory based on the surface plasmon polariton (SPP) coupled-mode model for SPP-Bragg reflectors composed of N periodic defects of any geometry and any refractive index profile. A SPP coupled-mode model and its recursive form were developed and shown to be equivalent. The SPP absorption loss, as well as high-order modes in each defect and possible radiation loss, is incorporated without effort. The simple recursive equations derived from the recursive model bridge the reflectance and the transmittance of N periodic defects to those of a single one, resulting in that the computational cost of the geometry optimization or the spectra calculation for N periodic defects is reduced into that for a single one. The model predictions show good agreement with fully vectorial computation data on the reflectance and the transmittance. From the recursive model, the generalized Bragg condition is proposed, which is verified by SPP-Bragg reflectors of various structures. The quantitative theory and the generalized Bragg condition proposed will greatly simplify the design of SPP-Bragg reflectors.
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