The celebrated Dirac equation is not only the foundation of quantum field theory, but also the parent model of many later advances inphysics. One of  the key notion derived from Dirac equation is the band topology for electrons in various condensed matters. Recently this notion has been extended to bosonic systems, such as in photonics. I will briefly introduce the background, fundamental challenges and recent advances in the search of photonic topological materials. Band degeneracy and topology enriched by both point-group and nonsymmorphic symmetries in all dielectric photonic crystals are emphasized. Microscopic theory on the spin-orbit coupling, angular-momentum---wavevector locking are discussed in details.

Refs:

[1] Wang et al. PRB 93, 235155 (2016)

[2] Xu et al. Optics Express 24, 18059 (2016)

[3] Wang et al. arXiv:1608.02437

[4] Yang et al. arXiv:1610.07780

[5] Wang et al. arXiv:1703.09899

[6] Wang et. al. in preparations