  We present a novel fully fourth order in time and space {finite difference
method for the time domain Maxwell's equations} in metamaterials. We consider a
Drude metamaterial model for the material response to incident electromagnetic
fields. We consider the second order formulation of the system of partial
differential equations that govern the evolution in time of electric and
magnetic fields along with the evolution of the polarization and magnetization
current densities. Our discretization employs fourth order staggering in space
of different field components and the modified equation approach to obtain
fourth order accuracy in time. Using the energy method, we derive energy
relations for the continuous models, and design numerical schemes that preserve
a discrete analogue of the energy relation. Numerical simulations are provided
in one and two dimensional settings to illustrate fourth order convergence as
well as compare with second order schemes.
