Nonlinear Optical Properties of Graphene Oxide Colloids Under a Low-Power Laser Irradiation at 532 nm

The nonlinear optical properties of a graphene oxide (GO) suspension dispersed in deionized water were examined at 532 nm using under continuous-wave laser excitation using the Z-scan technique. Open- and closed- aperture configurations were employed to characterize the nonlinear absorption coefficient (β), nonlinear refractive index (n₂), and thermo-optic coefficient (dn/dT). The open-aperture response displayed a symmetric valley centered at the focal position, characteristic of two-photon absorption (TPA), and analysis of the data yielded β = (2.7±0.01) × 10⁻³ cm/W. The closed-aperture traces showed a pronounced asymmetric peak–valley profile, indicating a negative refractive nonlinearity associated with self-defocusing. To identify the physical origin of this behavior, the experimental data were analyzed using four theoretical frameworks: the Sheik-Bahae, thermal thin-lens, aberrant thermal lens, and Fresnel–Kirchhoff diffraction integral models. Although the Sheik-Bahae approach provided an effective nonlinear refractive index of n₂ = −(3.77±0.05) × 10⁻⁷ cm²/W, its local Kerr approximation was unable to adequately describe the observed response. Incorporating thermal diffusion significantly improved the agreement between theory and experiment. The Fresnel–Kirchhoff model produced the best fit, yielding n₂ = −(1.16±0.02) × 10⁻⁷ cm²/W and dn/dT = −(2.71±0.1) × 10⁻⁶ K⁻¹. Comparison with previously reported data confirms that the measured nonlinear parameters are consistent with the range reported for graphene-based colloidal systems under continuous-wave excitation. The results demonstrate that the optical nonlinearity of the GO suspension is dominated by a nonlocal thermo-optic mechanism and highlight the importance of diffraction-based analysis for reliable extraction of nonlinear optical parameters.