A linear polarization field on the sphere can be uniquely decomposed into an E-mode and a B-mode component. These two components are analytically defined in terms of spin-2 spherical harmonics. Maps that contain filtered modes on a partial sky can also be decomposed into E-mode and B-mode components. However, the lack of full sky information prevents orthogonally separating these components using spherical harmonics. In this paper, we present a technique for decomposing an incomplete map into E and B-mode components using E and B eigenmodes of the pixel covariance in the observed map. This method is found to orthogonally define E and B in the presence of both partial sky coverage and spatial filtering. This method has been applied to the Bicep2 and the Keck Array maps and results in reducing E to B leakage from ΛCDM E-modes to a level corresponding to a tensor-to-scalar ratio of .

We present measurements of polarization lensing using the 150 GHz maps, which include all data taken by the BICEP2andKeck Array Cosmic Microwave Background polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution (~ 0 . 5), the excellent sensitivity (∼3μK-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales (  ℓ 700). From the auto-spectrum of the reconstructed potential, we measure an amplitude of the spectrum to be) and reject the no-lensing hypothesis at s 5.8 , which is the highest significance achieved to date using an EB lensing estimator. Taking ). We perform a series of null tests and consistency checks to show that these results are robust against systematics and are insensitive to analysis choices. These results unambiguously demonstrate that the B modes previously reported by BICEP/Keck at intermediate angular scales350) are dominated by gravitational lensing. The good agreement between the lensing amplitudes obtained from the lensing reconstruction and B-mode spectrum starts to place constraints on any alternative cosmological sources of B modes at these angular scales.