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We design a novel slow-light silicon photonic crystal waveguide which can operate over an extremely wide flat band for ultrafast integrated nonlinear photonics. By conveniently adjusting the radii and positions of the second air-holes rows, a flat slow-light low-dispersion band of 50 nm is achieved numerically. Such a slow-light photonic crystal waveguide with large flat low-dispersion wideband will pave the way for governing the femtosecond pulses in integrated nonlinear photonic platforms based on CMOS technology.

A practical direct-view scheme for generating arbitrary high-order cylindrical vector (HCV) beams by cascading vortex half-wave plates (VHPs) is presented. The combination of odd number 2n-1 VHPs for n≥1 can realize (m2n-1-m2n-2+…+m1)-order CV beams, in which m is the order number of VHP and the corresponding subscript 2n-1 represents the arrangement number of VHPs, and the cascading of even number 2n ones can obtain (m2n-m2n-1+…+m2-m1)-order CV beams. All 1-12 order CV beams, including the high-order anti-vortex CV (ACV) beams, are generated only by selectively cascading the VHPs with m=1, 3 and 8. The polarization properties of the generated HCV beams are investigated by measuring the corresponding Stokes parameters. It is experimentally demonstrated that arbitrary HCV beams are effectively achieved by the proposed method. The order numbers of CV beams can be greatly expanded by cascading limited types of VHPs.

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