Strong-field optoelectronics in solids

Perturbative optical nonlinearities induced by static electric fields 1 have proven useful in visualizing dynamical function in systems including operating circuits 2 , 3 , electric and magnetic domain walls 4 , and biological matter 5 , and in controlling light for applications in silicon photonics 6 . 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 7 , 8 paves the way for realizing active optics in the extreme ultraviolet and will allow imaging of operating electronic circuits 9 , of Si-photonic devices 10 and of other functional materials 11 , 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. Near-infrared femtosecond laser pulses are sent to a Si or ZnO crystal to generate high-harmonic waves via static or transient field-induced optical nonlinearities. The beam profile of the high-harmonic emission is controlled by electronic methods.