Normalized Descriptor Enables Unbiased Screening of Second-Order Nonlinear Optical Materials across Wide Band Gap Energies

Second-order nonlinear optical materials are crucial for technologies that manipulate light, including frequency doubling used in materials characterisation and optoelectronics, but evaluating and comparing their performance presents a significant challenge. Aubrey G. J. Nyiri, Michael J. Waters, and James M. Rondinelli, all from Northwestern University, now demonstrate a method for objectively assessing these materials by establishing a normalised descriptor that accounts for variations in fundamental properties. The researchers validate this descriptor against extensive databases of computed nonlinear optical properties, revealing a universal distribution across a range of materials. This breakthrough enables more effective data-driven materials discovery and optimisation, promising accelerated development of advanced optical technologies across diverse applications.

Simply maximizing SHG isn’t enough; materials also require appropriate bandgaps for specific applications, such as mid-infrared or deep-UV optics. Normalizing SHG by the bandgap allows researchers to compare materials more effectively and target those with the best combination of NLO activity and transparency. The study details how this normalized SHG is calculated, validates its effectiveness with existing data, and explores its integration into machine learning workflows for materials discovery.

Nonlinear optics studies how materials interact with intense light, leading to phenomena like second harmonic generation, where light frequency is doubled. SHG is crucial for applications like optical frequency conversion and imaging. The bandgap, the energy difference between a material’s valence and conduction bands, determines which wavelengths of light it transmits or absorbs; a larger bandgap allows transmission of higher-energy light. They calculated normalized SHG by dividing the SHG coefficient by the bandgap and validated the metric by demonstrating its correlation with known NLO materials and its ability to rank materials based on overall NLO performance. They also explored machine learning models, such as neural networks, to predict normalized SHG values based on material composition and structure, showing that these models can accurately predict values and screen large databases of materials. The results demonstrate that normalized SHG is a more effective metric for identifying promising NLO materials than simply maximizing SHG or considering bandgap alone.

The normalized SHG values correlate well with known NLO materials, validating the metric’s effectiveness, and machine learning models can accurately predict normalized SHG, enabling high-throughput screening. The study identified several promising NLO candidates and highlights the importance of considering bandgap when searching for NLO materials, as it determines the material’s transparency in the desired wavelength range. This work accelerates materials discovery by providing a targeted metric and workflow for designing materials with specific NLO properties and transparency. Integrating this metric into materials databases facilitates high-throughput screening and discovery, and continued development of machine learning models can further enhance these efforts. Experimental validation of the predicted NLO properties of identified candidates is crucial to confirm their performance. Researchers addressed the challenge of comparing materials with varying second-order nonlinear susceptibilities and band gap energies by compiling data from multiple sources. The team combined data from three studies, each employing different density functional theory (DFT) approximations to calculate both band gap and nonlinear susceptibility, resulting in a dataset of approximately 5,300 entries. To integrate data calculated using different DFT methods, the team constructed a linear regression model to estimate maximum SHG tensor components.

This model achieved a strong correlation with an R² value of 0. 793. To ensure consistency and minimize the influence of resonant effects, the study implemented specific data filtering criteria, restricting materials to those with band gaps exceeding 3 eV. The researchers focused on the maximum SHG tensor component to enable fair comparison across datasets. This meticulous data curation and harmonization formed the foundation for developing a normalized descriptor for SHG performance.

The study also assessed the theoretical upper bound for second-order susceptibility, plotting calculated values alongside the established limit. This assessment revealed deviations from the theoretical bound for several materials, highlighting the material-specific nature of these parameters and emphasizing the need for a generalized descriptor. The merged dataset is provided as supporting information, enabling further investigation and validation by the wider research community.

Normalized Descriptor Reveals Universal Nonlinear Scaling

This work presents a breakthrough in evaluating and comparing second-order nonlinear optical materials, essential for technologies ranging from materials characterization to advanced optics. Scientists addressed the challenge of comparing materials with vastly different nonlinear susceptibilities and band gaps by empirically validating a theoretical upper bound on performance. The team demonstrated that a normalized descriptor exhibits a consistent distribution across a wide range of band gap energies, providing a robust framework for assessing nonlinear optical response. Experiments revealed that the calculated upper bound, based on established theoretical models, accurately reflects the scaling behavior of the materials, particularly those with band gaps exceeding 3 eV.

This consistency supports the use of the bound as a normalization tool, enabling the definition of a band gap-independent metric to evaluate the intrinsic nonlinear optical performance of materials. The team formulated a normalized SHG coefficient, which expresses the maximum coefficient relative to the theoretical upper bound and band gap. This formulation effectively maps the NLO response of a material onto a dimensionless scale, simplifying comparisons. Analysis of a comprehensive dataset identified ten compounds with the largest values of the normalized coefficient, several of which approach or exceed the theoretical upper bound. The team has made a large dataset of experimental values publicly available, facilitating further research and materials discovery.

Normalised Descriptor for Second Harmonic Generation

This research addresses a significant challenge in nonlinear optics: the difficulty in comparing the performance of materials exhibiting second-harmonic generation across different band gaps. Scientists developed a normalized descriptor, which expresses a material’s nonlinear optical response relative to a theoretical upper bound dependent on its band gap. Through validation using extensive datasets of computed nonlinear optical properties, the team demonstrated that the descriptor exhibits a consistent distribution across a wide range of band gaps, establishing its utility as a robust and generalizable metric. The development of this descriptor enables more effective screening of materials for applications requiring second-harmonic generation, accelerating the process of identifying promising candidates.

By framing the nonlinear optical response as a fraction of the theoretical maximum, the descriptor facilitates interpretable comparisons between materials with diverse properties and opens avenues for insightful feature analysis within machine learning models. While acknowledging limitations stemming from dataset biases affecting the upper bound at low band gaps, the researchers highlight its potential to streamline materials discovery workflows. Future work could focus on integrating the descriptor into machine learning frameworks, offering an alternative to current screening methods based on band gap energy or maximum nonlinear susceptibility, and leveraging growing databases of computed properties to enable entirely new approaches to materials design.