First-Principles Electronic Structure Calculations of Nonlinear Optical Properties in low-dimensional materials

Nonlinear optical phenomena in quantum materials offer a powerful platform for compact frequency conversion and integrated photonics. We present first-principles calculations of the second- and third-order nonlinear optical susceptibilities, χ2 and χ3, in three classes of systems: rare-earth-doped i-MAX phases, carbon nanotubes (CNTs), and defect-engineered hexagonal boron nitride (h-BN). For i-MAX materials, we use density functional theory (DFT) to investigate how rare-earth dopants modify the electronic structure, break inversion symmetry, and enhance the χ2 response through dopant-induced hybridization. For CNTs, we apply the Bethe–Salpeter equation (BSE) formalism to accurately capture excitonic resonances and their effects on χ2 and two-photon absorption, revealing substantial exciton-enhancement of nonlinearities. For h-BN, we examine the roles of point defects and substitutional dopants in creating mid-gap states and enabling otherwise-forbidden nonlinear resonant processes. Our results show that these three material platforms exhibit complementary tunability of nonlinear coefficients. We compare their performance with that of conventional nonlinear crystals and discuss their applications as promising candidates for next-generation integrated nonlinear photonic devices operating in the near-to mid-infrared frequency range.