Introduction
The metamaterials have great potential in vacuum electron devices (VEDs) due to their unique characteristics [1], [2]. For example, the metamaterial-loaded waveguide can support the electromagnetic wave transmission below the cut-off frequency and can be as a novel slow wave structure with high interaction impedance [3]. In the metamaterial-based VEDs, the sheet beam transport is one of the most important issues, which has not been discussed at present.