Ruler equation for precisely tailoring the resonance frequency of terahertz U-shaped metamaterials

Artificially controlling the spectral response of metamaterials is important for the applications of functional devices. Here, we identify a simple ruler equation for describing the direct relation between the resonance frequencies and geometric parameters in terahertz metamaterials, which can accurately predetermine the eigenmode resonance frequencies of U-shaped metamaterials. Utilizing this ruler equation, we demonstrate the switching of the multi-band resonator which can be customized to work at expectant frequency bands. This ruler equation provides a practical guidance on tailoring the resonance frequency and paves the way for the development of metamaterial-based terahertz functional devices.