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We propose a novel negative-curvature hollow-core fiber structure with double trigonal-symmetrical anti-resonant elements implementing single-mode or polarization-maintaining transmission for high-power laser delivery in the 1 µm wavelength window. For the single-mode fiber, the single-mode performance with a higher-order modes extinction ratio (HOMER) as high as 4.65*10⁴ is achieved, and it remains >1*10⁴ with a large fault tolerance proportion of tubes size, which can increase the flexibility of fiber fabrication. For another polarization-maintaining fiber, an ultra-low confinement loss of 0.005 dB/m is obtained for polarization-maintaining transmission by optimizing the refractive index of the two transverse glass tubes, while the polarization extinction ratio and HOMER remain both >1*10³. This is the first birefringent negative-curvature hollow-core fiber with a loss below 0.01 dB/m in the 1 µm wavelength window.