Calculus of Variations Applied to Boundary Condition of Gangbuster Metasurface

In this letter, the calculus of variations is applied to boundary condition of the gangbuster metasurface based on assumed current distribution. In the theory, the radiated field from the periodic gangbuster metasurface can be deposed into a series of Floquet's modes, which results in an integral equation about the surface current density. Furthermore, due to smaller periodicity than the operation wavelength, the zero-order reflection coefficient can be derived through its surface current distribution. Especially, the reflection coefficient is variably stable for the induced current distribution. In this case, an approximate sine current distribution is provided, yielding a high-accuracy expression of the reflection coefficient. Finally, the simulated results of the periodic metallic cut-lines support the proposed theory, regardless of the geometrical size and incidence angle. The theory provides a simple and accurate approach for the average boundary condition of the metasurface, greatly avoiding the difficulty of obtaining an accurate induced current of the metasurface under the incident field.