In this paper, we investigate an accurate and efficient method for nonlinear Maxwell's equation. DG method and Crank-Nicolson scheme are employed for spatial and time discretization, respectively. A semi-explicit extrapolation technique is adopted for the linearization of the nonlinear term. Since the proposed scheme is semi-implicit, only a linear system needs to be solved at each time step. Optimal convergent order of $ O(\tau^2+h^{p+\frac{1}{2}}) $ is proved under time step size condition $ \tau\leq h^{d/4} $. Finally, 2D and 3D numerical examples are provided to validate the theoretical convergence rate.
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