  We present a non-staggered method for the Maxwell equations in adaptively
refined grids. The code is based on finite volume central scheme that preserves
in a discrete form both divergence-free property of magnetic field and the
Gauss law. High spatial accuracy is achieved with help of non-oscillatory
extrema preserving piece-wise or piece-wise-quadratic reconstructions. The
semi-discrete equations are solved by implicit-explicit Runge-Kutta method. The
new adaptive grid Maxwell's solver is examined based on several 1d examples,
including the an propagation of a Gaussian pulse through vacuum and partially
ionised gas. Two-dimensional extension is tested with a Gaussian pulse incident
on dielectric disc. Additionally, we focus on testing computational accuracy
and efficiency.
