Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most topological photonic structures can be understood by solving the eigenvalue problem of Maxwells equations for a static linear system. Here, we extend topological phases into dynamically driven nonlinear systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs and show it is necessarily non-Hermitian. We then define topological invariants associated with Floquet bands using non-Hermitian topological band theory, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Furthermore, we show that topological phase transitions between Floquet Chern insulators and normal insulators occur at synthetic Weyl points in a three-dimensional parameter space consisting of two momenta and the driving frequency. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven nonlinear optical systems and their optoelectronic applications, and our method of inducing Floquet topological phases is also applicable to other wave systems, such as phonons, excitons, and polaritons.
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