Saturation of spatial self-phase modulation in Ta 4 C 3 nanosheets and its application to all-optical switching

In conventional studies of spatial self-phase modulation (SSPM), the maximum number of far-field self-diffraction rings N max is generally assumed to scale linearly with the optical intensity I . However, under relatively high intensities, a saturation behavior emerges in the N max ∼ I relationship, which introduces inaccuracies in the characterization of the nonlinear refractive index. To address this, we develop the SSPM theory of intense laser beams passing through media with saturated Kerr-like nonlinearity. Experimentally, we investigate the SSPM behavior of Ta 4 C 3 MXene nanosheets—selected for their excellent dispersion stability and pronounced interaction with visible light—under varying laser intensities. For comparison and validation, the SSPM responses of graphene oxide (GO) and black phosphorus (BP) are also systematically examined. Theoretical simulations and experimental measurements indicate that as the laser intensity increases, both the maximum number of rings N max and the maximum ring radius R max increase sublinearly rather than linearly, eventually approaching saturation. Through N max ∼ I nonlinear fitting, the effective third-order nonlinear susceptibility and saturation intensity are accurately determined for the three types of nanosheets. Furthermore, based on the saturation of SSPM in nanosheets, an all-optical switching application is developed alongside a corresponding theory. The experiment observes that the maximum number of self-diffraction rings of the signal laser exhibits nonlinear saturation with increasing control laser intensity, which is consistent with theoretical predictions. This work not only enables the precise simultaneous characterization of both the third-order nonlinear susceptibility and saturation intensity in two-dimensional (2D) nanomaterials, but also provides theoretical guidance and experimental evidence for the application of SSPM saturation in all-optical nonlinear photonic devices.