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In this paper, the propagation characteristics of spoof surface plasmon polaritons (SPPs) on infinitely thin corrugated metal strips are theoretically analyzed. Compared with the situations of infinitely thick lateral thickness, the infinitely thin lateral thickness leads to lower plasma frequency according to the analyses. The propagation lengths and the binding capacity of the spoof SPPs are evaluated based on the derived dispersion equation. The effects of different lateral thicknesses are also investigated. At the end, a surface wave splitter is presented using infinitely thin corrugated metal strip. Other functional planar or flexible devices can also be designed using these metal strips in microwave or terahertz regimes.