Perturbative optical nonlinearities induced by static electric fields¹ have proven useful in visualizing dynamical function in systems including operating circuits^2,3, 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 energies^7,8 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 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.

已证明，由静电场¹引起的微扰光学非线性可用于可视化系统中的动力学功能，包括操作电路^2,3，电和磁畴壁⁴和生物物质⁵，以及控制光以用于硅光子学⁶。在这里，我们将场感应的二次谐波产生扩展到非扰动状态。我们证明，应用于硅和ZnO晶体的高达太赫兹（THz）频率的静态或瞬态场会产生偶次高次谐波。偶次谐波的图像证实了常规电子设备传递的静电场控制着高谐波发射的空间特性。将我们的方法扩展到高次谐波光子能量^7,8为在极紫外下实现有源光学系统铺平了道路，并将允许对工作的电子电路⁹，硅光子器件¹⁰以及其他功能材料^11,12进行成像，其时空分辨率高于微扰方法。对于太赫兹光谱，我们的方法具有允许测量印在太赫兹波形上的阿秒瞬变的带宽。