Original Contributions to the Theory of Non-Linear Optical Absorption in Two-Dimensional Graphene-Based Nanomaterials Synthesized from Nigerian Biomass

Two-dimensional graphene and graphene oxide nanomaterials synthesized from biomass precursors exhibit nonlinear optical properties that are attracting intense research interest for applications in ultrafast photonic switches, optical limiters, and saturable absorbers. This research makes original theoretical and experimental contributions to understanding the nonlinear optical absorption mechanisms in graphene-based nanomaterials synthesized through pyrolysis of Nigerian agricultural waste biomass including rice husk from Kebbi State and sugarcane bagasse from Kogi State. A theoretical model of the nonlinear absorption coefficient incorporating both saturable absorption and two-photon absorption contributions is developed from the electronic band structure of defect-containing graphene using the tight-binding Hamiltonian extended to include disorder and oxygen functional group perturbations characteristic of biomass-derived graphene oxide. Many-body effects on optical response are incorporated through a self-consistent field Hamiltonian approach. The theoretical model is parameterized and validated against nonlinear transmission measurements performed using the Z-scan technique with 800 nm femtosecond laser pulses at the National Laser Centre, Abuja. Experimentally measured nonlinear absorption coefficients for biomass-derived reduced graphene oxide ranged from 0.8 to 4.2 cm/GW as a function of reduction temperature, showing strong dependence on the sp2 carbon domain size confirmed by Raman D/G ratio analysis. The theoretical model correctly predicts the experimentally observed sign change of nonlinear absorption from saturable to two-photon-dominated behavior as sp2 domain size increases beyond a critical threshold. Original analytical expressions for the critical domain size threshold are derived and represent a new contribution to nonlinear optical theory for disordered two-dimensional materials. Keywords: nonlinear optics, graphene, biomass synthesis, Z-scan, two-photon absorption