The FDTD Method Of Maxwell Equation Of Nonlinear Medium

Based on the condition that model equation of electromagnetic wave propaga-tion in the medium is found out by coupling Maxwell's equation and the constitutive relation of the medium.This study is focus on the Maxwell's equation in the third-order nonlinear Kerr medium.First of all,We use finite-difference method in space and leapfrog scheme in time to decouple the model equation.Then,We propose discrete implicit scheme and discrete semi-implicit scheme for nonlinear terms.we proved the well-posedness of the model equation and the results of stability and convergence of the two schemes and optimal convergence order are both obtained as(?~2+~2).At last,through numerical experiments the two discrete schemes is verified requiring less computation time than the direct discrete scheme,the validity and accuracy of the two numerical schemes are proved correct as well.