We present detailed numerical simulations of a class of material systems that strongly discriminate light based primarily on the angle of incidence, over a broad range of frequencies, and independent of the polarization. Unique properties of these systems emerge from exploring photonic crystals whose constituents have an anisotropic dielectric response.National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Grant no. DMR-0819762)United States. Dept. of Energy. Office of Basic Energy Sciences (S3TEC grant no. DE-SC0001299)Massachusetts Institute of Technology. Energy Initiative