Transient Super‐/Sub‐Linear Nonlinearities in Silicon Nanostructures

Nonlinear silicon nano-photonics has recently attracted significant attention due to the plethora of electric and magnetic Mie resonances that offer substantial enhancement of optical nonlinearities. Conventionally, the characterization of nonlinearity and its transient nature rely on intensity-scan methods (z-scan) in the spatial domain and pump-probe techniques in the temporal domain. However, most studied ultrafast nonlinear effects are instantaneous, that is, strongest at zero pump-probe delay, and have a solitary nonlinear power dependency (square, cubic, etc.). Here the authors found that when relaxation lifetime is dependent on pump fluence, transient nonlinearity appears. The effect is exemplified via Auger-based nonlinear carrier dynamics of a nano-silicon Mie-resonator. The Auger-induced transient nonlinearity not only locates at the time delay of several tens of picoseconds, but also displays diverse nonlinearities, including sub-linear, super-linear, and surprisingly full saturation, which features a "crossing point" where the probe scattering is pump-fluence independent. The crossing point exists when the relaxation lifetime is inversely dependent to second power of carrier density. Combining confocal intensity-scan (x-scan) and pump-probe temporal scan, the authors demonstrate that sub-linearity and super-linearity lead to swelled and reduced full-width-at-half-maximum (FWHM) of single-nanostructure images, further confirming the nonlinearity as well as the potential of sub-diffraction microscopy. The results open up a new avenue in nonlinear silicon nano-photonics by adding new degrees of freedom in temporally tuning the types of transient nonlinearities, which are valuable in all-optical signal processing and nano-imaging.