Maxwell's equations in time domain are partial differential equations of hyperbolic type. Finite difference solutions of this type, if properly formulated and discretized, will lead to a step-by-step solution rather than requiring the solution of simultaneous equations. This chapter obtains finite-difference time-domain (FDTD) solution by using central difference approximations for the space and time second-order partial derivatives. In any one time step, a point on a plane wave propagating through a one-dimensional FDTD grid cannot pass through more than one cell. A perfectly matched layer (artificial material) called perfectly matched layer (PML) absorbs an electromagnetic wave (EMW) that enters it. The artificial material properties are designed so that the impedance matching boundary condition is satisfied and no refection occurs. For a highly lossy medium, the exponential decay of waves is so rapid that the use of central difference approximation of the first derivative used in the standard Yee algorithm cannot be easily used.