  An efficient finite-difference time-domain (FDTD) algorithm is built to solve
the transverse electric 2D Maxwell's equations with inhomogeneous dielectric
media where the electric fields are discontinuous across the dielectric
interface. The new algorithm is derived based upon the integral version of the
Maxwell's equations as well as the relationship between the electric fields
across the interface. It is an improvement over the contour-path
effective-permittivity algorithm by including some extra terms in the formulas.
The scheme is validated in solving the scattering of a dielectric cylinder with
exact solution from Mie theory and is then compared with the above contour-path
method, the usual staircase and the volume-average method. The numerical
results demonstrate that the new algorithm has achieved significant improvement
in accuracy over the other methods. Furthermore, the algorithm has a simple
structure and can be merged into any existing FDTD software package very
easily.
