Nonlinear optical response of carbon quantum dots characterized by two-photon absorption and two-photon induced luminescence.

Carbon quantum dots (CQDs) are promising low-toxicity fluorescent probes for two-photon bioimaging, but their practical applications are still limited by the lack of quantitative nonlinear optical parameters, especially the absolute conversion efficiency of two-photon-induced luminescence (TPIL). Here, we systematically investigate the two-photon absorption (TPA) and TPIL responses of commercially available CQDs aqueous solutions with concentrations of 0.2, 0.12, and 0.09 mg/mL. A home-built dual-integrating-sphere I-scan system is used to synchronously study TPA and TPIL under 1030 nm femtosecond excitation with a pulse duration of 40 fs and a repetition rate of 10 kHz. The TPIL intensity exhibits a clear quadratic dependence on the incident laser intensity, confirming its TPA origin. The TPA coefficients are obtained as 0.0031, 0.0030, and 0.0027 cm·GW-1, with corresponding saturation intensities of 69.18, 68.04, and 73.84 GW·cm-2 for 0.2, 0.12, and 0.09 mg/mL CQDs, respectively. The TPIL conversion efficiencies are determined to be 5.01 × 10-4%, 1.83 × 10-4%, and 1.47 × 10-4%. These results provide standardized quantitative parameters for CQD-based two-photon probes and demonstrate an effective approach to measuring luminescent nanomaterials in nonlinear bioimaging.