  The IceCube Neutrino Observatory instruments about 1 km$^3$ of deep, glacial
ice at the geographic South Pole using 5160 photomultipliers to detect
Cherenkov light from relativistic, charged particles. Most IceCube science
goals rely on precise understanding and modelling of the optical properties of
the instrumented ice. A peculiar light propagation effect observed by IceCube
is an anisotropic attenuation, which is aligned with the local flow of the ice.
Recent efforts have shown this effect is most likely due to curved photon
trajectories resulting from the asymmetric light diffusion in the birefringent
polycrystalline microstructure of the ice. This new model can be optimized by
adjusting the average orientation, size and shape of the ice crystals. We
present the parametrization of the birefringence effect in our photon
propagation simulation, the fitting procedures and results. The anticipated
potential of calibration instrumentation in the upcoming IceCube Upgrade to
improve on known shortcomings of the current ice modelling is also discussed.
