Tetsuyuki Ochiai

Research Center for Functional Materials,
National Institute for Materials Science (NIMS)
Japan

Bulk-edge correspondence in open photonic systems

Radiation fields are real-valued. This implies that their frequencies are positive-definite, regardless of their spatial profiles, either localized or extended. The "work function" for photons is thus completely absent between photonic media (such as photonic crystal) and outer media. Suppose that there is a topologically nontrivial photonic system with open boundary. We expect that the system has gapless boundary states, in accordance with the bulk-edge correspondence. However, such boundary states are embedded in the radiation continuum of the outer medium (e.g. air), so that the states become leaky unless they are outside the light cone. We considered this situation in [1], and found the bulk-edge correspondence works provided that the blurring (in frequency) of the leaky boundary states is taken into account. We revisit this problem in a more ideal situation than in [1], and demonstrate that the bulk-edge correspondence certainly works. The key ingredients here are the transfer-matrix formalism and the Krein-Friedel-Lloyd formula for the optical density of states.

[1] T. Ochiai and M. Onoda, Phys. Rev. B 80, 155103 (2009).