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

Aubrey G. J. Nyiri, Michael J. Waters, James M. Rondinelli

TL;DR

This work addresses the challenge of fairly comparing SHG performance across materials with different band gaps by validating a band-gap–dependent upper bound on $|χ^{(2)}|$ and introducing a normalized descriptor $\hat{d} = \frac{2}{ξ} d_{ij}^{\mathrm{max}} E_g^4$ (with $ξ = 17370~\mathrm{pm\,V^{-1}\,eV^{4}}$). It demonstrates that $|χ^{(2)}|$ scales roughly as $E_g^{-4}$ and that $\hat{d}$ remains approximately uniform across a wide range of $E_g$, enabling unbiased cross-material screening and interpretable machine-learning labels. The descriptor shows strong transferability across DFT functionals (LDA, PBE vs HSE) and correlates with conventional SHG metrics, supporting its use for rapid, band-gap–aware material discovery from large ab initio NLO databases. Limitations arise at low band gaps due to dataset biases, but within application-relevant windows, $\hat{d}$ provides a practical, physics-informed filter to accelerate the identification of high-performance NLO materials from mid-IR to deep-UV ranges.

Abstract

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 $χ^{(2)}$ 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 $χ^{(2)}$ 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.

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

TL;DR

This work addresses the challenge of fairly comparing SHG performance across materials with different band gaps by validating a band-gap–dependent upper bound on and introducing a normalized descriptor (with ). It demonstrates that scales roughly as and that remains approximately uniform across a wide range of , enabling unbiased cross-material screening and interpretable machine-learning labels. The descriptor shows strong transferability across DFT functionals (LDA, PBE vs HSE) and correlates with conventional SHG metrics, supporting its use for rapid, band-gap–aware material discovery from large ab initio NLO databases. Limitations arise at low band gaps due to dataset biases, but within application-relevant windows, provides a practical, physics-informed filter to accelerate the identification of high-performance NLO materials from mid-IR to deep-UV ranges.

Abstract

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 spans several orders of magnitude and strongly depends on the band gap . To address this, we empirically validate a theoretical upper bound on using new databases of \textit{ab initio}-computed nonlinear optical (NLO) properties. We then formulate a normalized descriptor, , which expresses the NLO response of a material relative to the band gap-dependent physical limit. We show that exhibits a similar distribution across a wide range of band gap energies. This universality supports the use of 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.

Paper Structure

This paper contains 8 sections, 3 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Results and Discussion
  4. Theoretical Upper Bound Assessment
  5. SHG Performance Descriptor
  6. Transferability
  7. Limitations
  8. Conclusion

Figures (3)

  • Figure 1: The HSE/scissor-corrected dataset (left) and the PBE dataset (right) plotted against the TTP theoretical upper bound given by \ref{['eq:chi2_upper_bound']}. The entries at the Pareto front generally track the shape of the upper bound curve.
  • Figure 2: The (a) normalized SHG response $\hat{d}$ and the (b) maximum SHG tensor component $d_{ij}^{\mathrm{max}}$ plotted against the band gap for the PBE dataset, with experimental data for several reference materials includedzhang2020bera2010. Background colors represent the approximate band gap ranges for the four application wavelength regimes for NLO materials for SHGxie2023. This illustrates the effectiveness of \ref{['eq:d_hat_simplified']} in scaling the SHG response to an approximately uniform scale across the range of band gaps.
  • Figure 3: The linear relationships between $\hat{d}$ for (a) HSE and LDA-computed data and between (b) HSE and PBE-computed data, supported by $R^2$, Spearman's $\rho_s$, and MAE values.