Third-order optical nonlinearities of graphene from monolayer to multilayers were investigated in the femtosecond regime, and the contribution of interlayer coupling to the nonlinearities was studied. The nonlinear refractive index γ of the order of 10−9 cm2/W and the nonlinear absorption coefficient β of 10−6 cm/W were obtained. By systematically investigating the nonlinear optical properties with the number of layers and comparing the coupling graphene with the decoupling superimposed graphene, we found that the coupling of interlayers has large effect upon the nonlinear refraction. These results provide an effective approach for developing graphene-based nonlinear photonic devices

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A concise, efficient, and practical direct-view scheme is presented to generate arbitrary cylindrical vector (CV) beams, including CV beams, vortex beams, and cylindrical vector vortex (CVV) beams, by a vortex half-wave plate (VHP). Six kinds of first-order and other high-order CV beams, such as azimuthally polarized (AP) beams, antivortex radial polarization mode beams, and three-order AP beams, are formed by simply rotating a half-wave plate. The Stokes parameters and double-slit interference of multitype CV beams are investigated in detail. The polarization parameters, including degree of polarization, polarization azimuth, and ellipticity, are obtained, which demonstrates the efficient generation of CV beams. In addition, the double-slit interference experiment is introduced in the setup, and fringe misplacement and tilt appear for CVV beams, in which the misplacement number M is 2 P + 1 for P ≤ 2 and 2 P − 1 for P ≥ 3 , where P is the polarization order number, and the fringe tilt offset is positively related to the topological charge number l of CVV beams. In addition, new types of VHPs can be formed by cascading two or more VHPs when the types of available VHPs are limited, assisting in more flexible generation of multitype CV beams. It is experimentally demonstrated that arbitrary CV beams with high quality are effectively achieved by the proposed setup, and the double-slit interference method can be utilized to determine and analyze CV beams rapidly and concisely by practical performance, which shows the potential to be implemented as a commercial device.