  In this letter, to the best of our knowledge, a new type of hollow-core
anti-resonant fiber (HC-ARF) design using hybrid silica/chalcogenide cladding
is presented for single-polarization, high-birefringence, and endlessly
single-mode operation at 2 $\mu$m wavelength. We show that the inclusion of a
chalcogenide layer in the cladding allows strong suppression of
$x$-polarization, while maintaining low propagation loss and single-mode
propagation for $y$-polarization. The optimized HC-ARF design includes a
combination of low propagation loss, high-birefringence, and
polarization-extinction ratio (PER) or loss ratio of 0.02 dB/m,
1.2$\times$10$^{-4}$, >550 respectively, while the loss of the $x$-polarization
is >20 dB/m. The proposed fiber may also be coiled to small bend radii while
maintaining low bend-loss of $\approx$ 0.01--0.1 dB/m, and can potentially be
used as polarization filter based on the different gap separations and bend
conditions.
