This Letter proposes a biconical glass rod for generating a cylindrical vector vortex (CVV) beam. Based on the principle of total internal reflection and the cylindrical symmetry structure of the glass rod, a circularly polarized incident beam with a constant phase distribution can be converted into a CVV beam, which possesses both a spatially inhomogeneous polarization and a helical phase distribution. The polarization azimuth of the CVV beam can be tuned with the aid of a polarization rotator composed of two cascade half-wave plates. The design theory is presented, and the feasibility of the design is demonstrated experimentally.
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