  Cosmological Birefringence (CB) is a phenomenon, caused by parity violating
modifications to electrodynamics, whereby the linear polarisation angle of
light changes as photons traverse a vacuum. It is possible to use a number of
different analysis techniques to constrain this effect using Cosmic Microwave
Background (CMB) polarisation observations. We investigate two different
methods of constraining direction dependent birefringence for present and
future CMB experiments including BICEP/Keck, Simons Observatory (SO), and
LiteBIRD . Specifically we compare the constraints placed on anisotropic CB
from a quadratic estimator technique to those derived from estimates of the
$B$-mode power-spectrum for the three different experiments. The constraints
derived from estimates of the $B$-mode power spectrum are found to be
comparable to those derived from quadratic estimator for BICEP/Keck and SO, but
not LiteBIRD due to its larger sky coverage. These forecasted upper bounds for
CB are converted to constraints on primordial magnetic fields and the coupling
between photons and pseudo Nambu-Goldstone bosons. Finally we show that even
with the best constraints on CB, for the respective experiments, the
potentially induced $B$-mode power can act as a significant contaminant in the
prospective measurement of primordial $B$-modes.
