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Characteristics of vector beams in mid-infrared waveband are analyzed numerically in an As2Se3 photonic crystal fiber (PCF) with small central hollow core (SCHH), including the mode fields, confinement loss, effective refractive index and chromatic dispersion. In the PCFs with the SCHH diameter d0 of 0-1.5 μm, the confinement losses of the four vector beams (HE11, TM01, TE01, and HE21) are smaller than 1.0 dB/m for the wavelengths up to ~5 μm. For the SCHH diameter d0 of 0.5-1.5 μm, the field enhancement of the HE11 mode occurs in the SCHHs in the central area for the wavelengths ≤ 5 μm. This happens because the evanescent light penetrates into the SCHH. With d0 increasing, the effective refractive index separations (δneff) between the HE11 mode and high-order modes (TM01, TE01, and HE21) decreases, while the δneff among the high-order modes increases. At the wavelength of 5 μm, the δneff of HE11-TE01, TE01- HE21, and HE21-TM01 is 0.03098, 0.03960, and 0.06867, respectively, when d0 is 1.5 μm. The second ZDWs of TE01, HE21 and TM01 mode are blueshifted with the increase of d0, but they are longer than 5 μm. The negative dispersion regions of the high-order modes (TE01, HE21, and TM01) are much wider than the HE11 modes. With the increase of d0, the HE11 mode dispersion curves have no obvious change, while the high-order modes (TE01, HE21, and TM01) dispersion curves become steep at the longer wavelength, the TM01 mode changes most obviously, and the depression appears. To demonstrate the application of the PCF, super-continuum generation pumped by the four vector modes are simulated and analyzed. Our simulated results will be useful for the optical applications in mid-infrared waveband, such as the generation of cylindrical vector mode and orbital angular momentum (OAM) and the particle manipulation by optical fields.
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