Perturbative optical nonlinearities induced by static electric fields1 have proven useful in visualizing dynamical function in systems including operating circuits2,3, electric and magnetic domain walls4, and biological matter5, and in controlling light for applications in silicon photonics6. Here, we extend field-induced second-harmonic generation to the non-perturbative regime. We demonstrate that static or transient fields up to terahertz (THz) frequencies applied to silicon and ZnO crystals generate even-order high harmonics. Images of the even harmonics confirm that static fields delivered with conventional electronics control the spatial properties of the high-harmonic emission. Extending our methodology to higher-harmonic photon energies7,8 paves the way for realizing active optics in the extreme ultraviolet and will allow imaging of operating electronic circuits9, of Si-photonic devices10 and of other functional materials11,12, with higher spatio-temporal resolution than perturbative methods. For THz spectroscopy, our method has the bandwidth to allow measurement of attosecond transients imprinted on THz waveforms.