Electrodynamics on a grid: The finite-difference time-domain method applied to optics and cloaking

Maxwell's curl equations lead to energy transport via electric and magnetic fields because spatial variations of one field lead to a temporal change in the other. The finite-difference time-domain (FDTD) method of calculating electromagnetic fields takes advantage of this interplay of the fields by using a suitable grid and time stepping method. The method is simple and instructive for understanding the genesis of electromagnetic transport phenomena. Reflection, refraction, interference, and diffraction result directly from the linked first-order derivatives of the fields. Extension of the method to include permittivity and permeability tensors with extreme values of these properties allows a wave to be bent around a central region thus cloaking (rendering invisible) any object inside. (c) 2008 American Association of Physics Teachers.