A Normalized Descriptor for Unbiased Screening of Second-Order Nonlinear Optical Materials

Second-order nonlinear optical materials enable frequency doubling of light (second-harmonic generation, SHG), which is essential for optoelectronic applications ranging from materials characterization to quantum technologies. However, comparing SHG performance across materials remains challenging as the second-order nonlinear susceptibility $\chi^{(2)}$ spans several orders of magnitude and strongly depends on the band gap $E_g$. To address this, we empirically validate a theoretical upper bound on $\chi^{(2)}$ using new databases of \textit{ab initio}-computed nonlinear optical (NLO) properties. We then formulate a normalized descriptor, $\hat{d}$, which expresses the NLO response of a material relative to the band gap-dependent physical limit. We show that $\hat{d}$ exhibits a similar distribution across a wide range of band gap energies. This universality supports the use of $\hat{d}$ as a robust, generalizable descriptor for data-driven and chemistry-informed machine learning models of NLO response, enabling accelerated materials discovery and optimization across broad application frequencies.