Symplectic Finite-Difference Time-Domain Method for Maxwell Equations

We introduce a symplectic finite-difference time-domain method for electromagnetic field simulation. Our method can successfully solve Maxwell equations involving conductor loss, which cannot be solved by the symplectic integration methods that have been presented in previous works. A class of high-order symplectic schemes for computing the time-dependent electric and magnetic fields are derived on the basis of an s-stage symplectic partitioned Runge–Kutta method. We present numerical results to illustrate the validity and accuracy of the algorithm.