| Abstract | Perturbative optical nonlinearities induced by static electric fields have proven useful in visualizing dynamical function in systems including operating circuits, electric and magnetic domain walls, and biological matter, and in controlling light for applications in silicon photonics. 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 energies paves the way for realizing active optics in the extreme ultraviolet and will allow imaging of operating electronic circuits, of Si-photonic devices and of other functional materials, 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. |
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