A new framework for atom-resolved decomposition of second-harmonic generation in nonlinear-optical crystals

TL;DR

This paper introduces a novel, rigorous atom-resolved framework for analyzing second-harmonic generation in nonlinear optical crystals, revealing the hierarchical and cooperative atomic contributions to SHG.

Contribution

The work develops a general AIM-based formalism for atom-resolved optical property decomposition, applied to six UV and deep-UV nonlinear crystals, providing new microscopic insights.

Findings

Two-center atomic contributions dominate SHG in studied crystals.

The framework reveals the significant role of anionic frameworks and cation sublattices.

Cooperative effects between different atomic motifs influence SHG responses.

Abstract

In this work, we develop a new framework for computing atom-resolved contributions to optical properties based on atoms-in-molecules (AIM) schemes. The formalism is independent of the specific AIM method and is made rigorous by partitioning momentum matrix elements into atomic contributions while exactly satisfying the relevant sum rules. We apply it to second-harmonic generation (SHG) in six representative UV and deep-UV nonlinear-optical crystals, namely $\beta$-\ce{BaB2O4} (BBO), \ce{LiB3O5} (LBO), \ce{CsB3O5} (CBO), \ce{CsLiB6O10} (CLBO), \ce{KBe2BO3F2} (KBBF), and \ce{LiCs2PO4} (LCPO). The atom-triplet decomposition reveals a clear hierarchy for the largest SHG component of each crystal. In general, two-center terms provide the leading contribution, one-center terms remain comparatively small, and fully three-center terms supply an important secondary contribution. A motif-triplet decomposition further indicates behavior dominated by the anionic framework in KBBF and LBO. In BBO, CBO, and CLBO, contributions from the anionic framework and the cation sublattice act cooperatively, although the cation contribution is crystal dependent. Moreover, cooperative contributions from the phosphate framework and the Cs sublattice are also observed in LCPO, where the O-Cs contribution is particularly significant. These results may provide a new perspective for understanding the microscopic origin of SHG in nonlinear-optical materials.