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3D $Z_2$ Topological Nodes in Nonsymmorphic Photonic Crystals: Ultrastrong Coupling and Anomalous Refraction

We propose to simulate 3D Dirac points and line-nodes with nontrivial $Z_2$ topology in nonsymmorphic all-dielectric photonic-crystals with space-time reversal symmetry, which can be realized at infrared and microwave frequencies. Double degeneracy of all Bloch states in high symmetry planes is achieved via nonsymmorphic screw symmetries despite the fundamental obstacle of no Kramers degeneracy in photonic crystals. Two orthogonal screw axes lead to 3D $Z_2$ Dirac points on high symmetry Brillouin zone boundary lines. On the other hand, $Z_2$ line-nodes emerge as protected twofold degeneracy of Bloch bands with opposite mirror parities on the $k_z=0$ plane. The lowest frequency line-node is deterministic because of a degenerate-partner switching mechanism guaranteed by the fundamental properties of Maxwell equations and the nonsymmorphic screw symmetry. A pair of Fermi arcs with opposite chirality due to $Z_2$ topological Dirac points emerge below the light-line on (100) and (010) photonic-crystal-air interfaces. These robust surface states offer an unique opportunity to realize an "open cavity" with strong interaction between quantum emitters and engineered vacuum with nontrivial Berry phases --- an important step toward topological states of strongly interacting bosons. Realistic calculation for resonant coupling between cavity-photons and phonons in boron nitride thin film yields ultrastrong coupling with vacuum Rabi splitting reaching to $23\%$ of photon frequency. We also show that type-II Dirac cones have anomalous valley selective refraction: birefringence with both positive and negative refractions for one valley, while no refraction for the other.