We report a B-mode power spectrum measurement from the cosmic microwave background (CMB) polarization anisotropy observations made using the SPTpol instrument on the South Pole Telescope. This work uses 500 deg² of SPTpol data, a five-fold increase over the last SPTpol B-mode release. As a result, the bandpower uncertainties have been reduced by more than a factor of two, and the measurement extends to lower multipoles: 52<<2301. Data from both 95 and 150 GHz are used, allowing for three cross-spectra: 95 GHz × 95 GHz, 95 GHz × 150 GHz, and 150 GHz × 150 GHz. B-mode power is detected at very high significance; we find P(BB<0)=5.8×10^-71, corresponding to a 18.1σ detection of power. With a prior on the galactic dust from Planck, WMAP and BICEP2/Keck observations, the SPTpol B-mode data can be used to set an upper limit on the tensor-to-scalar ratio, $r<0.44$ at 95% confidence (the expected 1σ constraint on r given the measurement uncertainties is 0.22). We find the measured B-mode power is consistent with the Planck best-fit ΛCDM model predictions. Scaling the predicted lensing B-mode power in this model by a factor Aₗₑₙₛ, the data prefer Aₗₑₙₛ=1.17±0.13. These data are currently the most precise measurements of B-mode power at >320.
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