Engineering band structures and topological invariants by transformation optics

By introducing the transformation optics method to periodic systems, we show the tunability of the band structures by comparing the results from original spaces and transformed spaces. Interestingly, we find the topological invariant Chern number will change sign when the orientation of the Brillouin zone flipped. The new platform we provided for engineering the band diagram and topological invariant might lead to the development of both transformation optics and photonic topological states.