We rigorously analyze the dispersion function and the curvature of the dispersion surface of a photonic

crystal to explore the fundamental limit of its angular sensitivities. With insight gained from group theory, we

fi nd that symmetry induced degeneracy gives rise to a singular dispersion surface curvature and a nonvanishing

group velocity simultaneously. Near such a singularity, high angular sensitivities can be achieved at low optical

loss. This phenomenon exists generally in most common two-dimensional and three-dimensional photonic

crystal lattices, although it occurs only for certain photonic bands as dictated by symmetry.