FDTD for three-dimensional propagation in a magnetized ferrite

In the standard Yee FDTD algorithm, the constitutive parameters /spl epsi/, /spl mu/ and /spl sigma/ are assumed to be constant with respect to frequency for all media located in the computational space. Modifications to the Yee algorithm are required to allow for modeling of propagation in dispersive media. Luebbers and Hunsberger (1992) demonstrated that, because of the exponential nature of the time domain susceptibility functions of Debye and Lorentz materials, the convolution relating the time domain electric field and the electric flux density can be performed efficiently using recursion. Their approach has therefore come to be known as the recursive convolution method. The recursive convolution approach was applied in Melon et al. (1994) to lossless ferrites for a two dimensional problem with the biasing field parallel to the z axis. This approach requires four convolutions per magnetic field component. In the formulation presented here an arbitrary direction for the biasing field is allowed and a maximum of three complex numbers per cell is required. Update equations for both total and scattered field forms have been derived.