High-order modes of spoof surface plasmon polaritons (SPPs) on the periodically corrugated metal surfaces are investigated theoretically with the modal expansion method. An analytical expression for the condition of existence of high-order modes is presented. The properties of high-order modes such as dispersion and field pattern are analyzed detailedly, from which it seems that the propagation of spoof SPPs along the corrugated metal surface is mainly based on the coupling between the open groove cavities.
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