Understanding the interaction of light with a highly scattering material is essential for optical microscopy of optically thick and heterogeneous biological tissues. Ensemble-averaged analytic solutions cannot provide more than general predictions for relatively simple cases. Yet, biological tissues contain chiral organic molecules and many of the cells' structures are birefringent, a property exploited by polarization microscopy for label-free imaging. Solving Maxwell's equations in such materials is a notoriously hard problem. Here we present an efficient method to determine the propagation of electro-magnetic waves in arbitrary anisotropic materials. We demonstrate how the algorithm enables large scale calculations of the scattered light field in complex birefringent materials, chiral media, and even materials with a negative refractive index.