Development of a Theoretical Framework for Non-Linear Optical Response in Nigerian Mineral-Derived Crystal Systems for Photonic Device Applications

Background: Nigeria's diverse mineral deposits include optically active crystal systems whose non-linear optical properties for photonic applications have not been theoretically described or experimentally exploited. A comprehensive theoretical framework for these materials would unlock new indigenous photonic device possibilities. Aim: This study developed and validated a theoretical framework describing non-linear optical response in selected Nigerian mineral-derived crystal systems, focusing on tourmaline and beryl families from the North East mineral belt. Methods: The theoretical framework combined density functional perturbation theory with time-dependent DFT to compute second and third-order non-linear optical susceptibilities. Crystal samples were grown from purified Nigerian mineral sources by hydrothermal techniques and characterised by single-crystal X-ray diffraction. Z-scan measurements validated theoretical predictions for second harmonic generation and two-photon absorption coefficients. Results: Second harmonic generation coefficients of the Nigerian tourmaline system exceeded those of lithium niobate by 14% in specific crystallographic orientations. Two-photon absorption cross-sections matched theoretical predictions within 9%. Phase-matching conditions were identified at 1064 nm pump wavelength. Conclusion: Nigerian mineral-derived crystals exhibit competitive non-linear optical properties and the developed framework provides a reliable design tool for photonic device engineering. Indigenous crystal growth programmes for photonic applications are strongly recommended. Keywords: non-linear optics, crystal systems, photonic devices, Nigeria minerals, density functional theory.