A high efficiency finite difference time-domain method based on high order compact scheme is shown.It not only improves accuracy,but also has the advantages of fewer grid nodes,lower memory consumes and CPU time.Numerical simulations of electromagnetic wave propagation in a lossless waveguide and photonic crystals fibers are realized.They prove efficiency and accuracy of the algorithm.

Euler-Hamilton equations are provided using Hamiltonian function of Maxwell's equations.High order symplectic schemes of three-dimensional time-domain Maxwell's equations are constructed with symplectic integrator technique combined with high order staggered difference.The method is used to analyzing stability and numerical dispersion of high order time-domain methods and symplectic schemes with matrix analysis and tensor product.It confirms accuracy of the scheme and super ability compared with other time-domain methods.