It has been widely recognized that topology is indispensable in distinguishing phases of matter (Nobel 2016). Similarly, new optical material systems are being discovered with non-trivial topologies of their global wave-functions in the parameter space, whose interfaces support novel states of light with ideal transport properties such as the robustness to arbitrarily large disorders and fabrication imperfections. These new degrees of freedoms in photonic bands promise wide exciting opportunities in both fundamental physics and potential applications.

In this talk, I will introduce the underlining principles and show our experimental realizations and theoretical predictions of 2D and 3D photonic crystals with topologically protected interface states, which, in the photonic perspective, are topological waveguides and topological cavities with stably novel properties that cannot be achieved otherwise.