  CMB polarization provides a unique window into cosmological inflation; the
amplitude of the B-mode polarization from last scattering is uniquely sensitive
to the energetics of inflation. However, numerous systematic effects arising
from optical imperfections can contaminate the observed B-mode power spectrum.
In particular, systematic effects due to the coupling of the underlying
temperature and polarization fields with elliptical or otherwise asymmetric
beams yield spurious systematic signals. This paper presents a non-perturbative
analytic calculation of some of these signals. We show that results previously
derived in real space can be generalized, formally, by including infinitely
many higher-order corrections to the leading order effects. These corrections
can be summed and represented as analytic functions when a fully Fourier-space
approach is adopted from the outset. The formalism and results presented in
this paper were created to determine the susceptibility of CMB polarization
probes of the primary gravitational wave signal but can be easily extended to
the analysis of gravitational lensing of the CMB.
