  Topological physics in photonic systems have attracted great attentions in
recent years. In this work, we theoretically study the one and two dimensional
photonic quasicrystal resonator lattices characterized by the first and second
Chern number, which show exotic boundary states within the photonic energy band
gap. In particular, the second Chern number protected edge states has opened up
new possibilities for realizing topological physics of dimensions higher than
three in photonic systems, which is highly sought for. Such photonic systems
can be easily experimentally realized in regular photonic crystal with
dielectric rods in air, by varying the radius of the rods, so we propose
experiments realizing our predictions.
