  In photonics, band degeneracies at high-symmetry points in wavevector space
have been shown to exhibit rich physical phenomena. However, obtaining
degenerate bands away from such points is highly nontrivial. In this work, we
achieve complex band degeneracy in a photonic crystal structure over a region
of momentum space. We show that this band degeneracy corresponds to
polarization-independent transmission, which can be harnessed for nonlocal
metasurface design. Moreover, we find that the band degeneracy manifests as a
topological singularity in the structural parameter space of the system. Our
work highlights the importance of topological concepts in the design of
polarization-independent photonic structures.
