  We present an experimental and numerical study of a terahertz metamaterial
with a nonlinear response that is controllable via the relative structural
positioning of two stacked split ring resonator arrays. The first array is
fabricated on an n-doped GaAs substrate and the second array is fabricated
vertically above the first using a polyimide spacer layer. Due to GaAs carrier
dynamics, the on-resonance terahertz transmission at 0.4 THz varies in a
nonlinear manner with incident terahertz power. The second resonator layer
dampens this nonlinear response. In samples where the two layers are aligned,
the resonance disappears and total nonlinear modulation of the on-resonance
transmission decreases. The nonlinear modulation is restored in samples where
an alignment offset is imposed between the two resonator arrays. Structurally
tunable metamaterials can therefore act as a design template for tunable
nonlinear THz devices by controlling the coupling of confined electric fields
to nonlinear phenomena in a complex material substrate or inclusion.
