  In this paper, a novel sixth order energy-conserved method is proposed for
solving the three-dimensional time-domain Maxwell's equations. The new scheme
preserves five discrete energy conservation laws, three momentum conservation
laws, symplectic conservation law as well as two divergence-free properties and
is proved to be unconditionally stable, non-dissipative. An optimal error
estimate is established based on the energy method, which shows that the
proposed method is of sixth order accuracy in time and spectral accuracy in
space in discrete $L^{2}$-norm. The constant in the error estimate is proved to
be only $O(T)$. Furthermore, the numerical dispersion relation is analyzed in
detail and a fast solver is presented to solve the resulting discrete linear
equations efficiently. Numerical results are addressed to verify our
theoretical analysis.
