  Maxwell equations describe the propagation of electromagnetic waves and are
therefore fundamental to understanding many problems encountered in the study
of antennas and electromagnetics. The aim of this paper is to propose and
analyse an efficient fully discrete scheme for solving three-dimensional
Maxwell's equations. This is accomplished by combining time exponential
integrator and Fourier pseudospectral methods. Fast computation is implemented
in the scheme by using the Fast Fourier Transform algorithm which is well known
in scientific computations. An optimal error estimate which is not encumbered
by the CFL condition is established and the resulting scheme is proved to be of
spectral accuracy in space and infinite-order accuracy in time. Furthermore,
the scheme is shown to have multiple conservation laws including discrete
energy, helicity, momentum, symplecticity, and divergence-free field
conservations. All the theoretical results of the accuracy and conservations
are numerically illustrated by two numerical tests.
