Design Rules for Nonlinear Optical Materials: Dimensionality, Interfaces, Topological Band Geometry and Data-Driven Discovery

Abstract

Nonlinear optical (NLO) materials underpin frequency conversion, ultrafast modulation, and light– matter control, yet conventional bulk crystals face practical constraints in tunability and integration. Motivated by the rapid expansion of low-dimensional, interface-engineered, and topology-driven platforms, this review provides a unified perspective on second- and third-order nonlinear responses across material dimensionalities, spanning bulk and bulk-like crystals to two-dimensional (2D) layers, van der Waals heterostructures, and quantum dots. We connect the fundamental framework of nonlinear susceptibilities with key structure–property design rules—particularly symmetry breaking, electronic asymmetry, confinement, and interface effects—and summarize experimental routes used to quantify χ(2) and χ(3). A central theme is the emergence of topology-enabled nonlinear optics, where Berryphase geometry (including Berry curvature and the quantum metric) reshapes NLO design from symmetry–resonance optimization towards symmetry–geometry co-design, enabling robust nonlinear photocurrents and harmonic responses. We further review machine-learning strategies that accelerate screening and inverse design by extracting hidden descriptors and enabling rapid property prediction across large chemical spaces. Finally, we outline near-term opportunities and bottlenecks for translating “hero-material” demonstrations into manufacturable, on-chip nonlinear photonic systems for frequency translation, ultrafast signal processing, and quantum photonics.