  We characterize planar electric terahertz metamaterials fabricated on thin,
flexible substrates using terahertz time-domain spectroscopy.
Quasi-three-dimensional metamaterials are formed by stacking multiple
metamaterial layers. Transmission measurements reveal resonant band-stop
behavior that becomes stronger with an increasing number of layers. Extracted
metamaterial dielectric functions are shown to be independent of the number of
layers, validating the effective medium approximation. Limitations of this
approximation are discussed.
