Elegant deduction of three types of recursive convolution (RC) technique in simulation of dispersive material

Recursive convolution (RC) method is widely used in simulation of dispersive material in finite-difference time-domain (FDTD). The method uses inverse Fourier transform to change the constitutive relation between polarization and electric field in frequency-domain to convolution integral form in time domain. The convolution is updated by the recursive method. This paper presents the elegant deduction of the RC method and shows that constant RC (CRC), piecewise linear RC (PLRC) and trapezoidal RC (TRC) are all special cases of a general form. The difference is due to the approximation of electric field in convolution integral. The numerical examinations validate the accuracy and efficiency of the algorithms.