Programmable on-chip nonlinear photonics

Nonlinear photonics uses coherent interactions between optical waves to engineer functionality that is not possible with purely linear optics. Traditionally, the function of a nonlinear-optical device is determined during design and fixed during fabrication. In this paper, we present a photonic device with highly programmable nonlinear functionality: an optical slab waveguide with an arbitrarily reconfigurable two-dimensional distribution of $\chi^{(2)}$ nonlinearity. The nonlinearity is realized using electric-field-induced $\chi^{(2)}$ in a $\chi^{(3)}$ material. The programmability is engineered by massively parallel control of the electric-field distribution within the device using a photoconductive layer and optical programming with a spatial light pattern. To showcase the versatility of our device, we demonstrated spectral, spatial, and spatio-spectral engineering of second-harmonic generation by tailoring arbitrary quasi-phase-matching (QPM) grating structures in two dimensions. Second-harmonic light was generated with programmable spectra, enabled by real-time in situ inverse design of QPM gratings. Flexible spatial control was also achieved, including the generation of complex waveforms such as Airy beams and the simultaneous engineering of spectral and spatial features. This allowed us to create distinct spatial light profiles across multiple wavelengths. The programmability also allowed us to demonstrate in situ, real-time compensation of fluctuations in pump laser wavelength. Our work shows that we can transcend the conventional one-device--one-function paradigm, expanding the potential applications of nonlinear optics in situations where fast device reconfigurability is not merely practically convenient but essential -- such as in programmable optical quantum gates and quantum light sources, all-optical signal processing, optical computation, and structured light for sensing.