Finite difference time domain recursive convolution for second order dispersive materials

The finite-difference-time-domain method has been applied to frequency-dependent dispersive materials through an efficient recursive discrete convolution with results given for first-order dispersive materials including polar liquids (Debye) and cold plasmas. The recursive convolution utilizes the exponential behavior of the first-order time-domain susceptibilities. Alternatively a differential approach, valid for both first- and second-order dispersion relations, has been demonstrated. In the present work, the extension of the recursive convolution approach to second-order dispersion relations is discussed. The extension is very straightforward, with the only added computational burden being a complex recursive accumulation variable. The method has been applied to second-order dispersion relations for magnetized plasmas and ferrites with good accuracy, and appears simpler and more efficient than the differential methods.<>