Quadratic recursive convolution (QRC) in dispersive media simulation of finite-difference time-domain (FDTD)

Abstract

This paper presents a novel formulation for dispersive media computation in finite-difference time-domain (FDTD). Motivated by conventional recursive convolution (RC) methods in handling convolution integral, the method name quadratic RC (QRC) makes improvement in the approximation of electric field in convolution integral. The electric field is approximated by quadratic function determined by the fields at three time steps at current, next and former. Via quadratic interpolation, the convolution integral result is approximated by the linear combination of three electric fields, rather than two fields in trapezoidal RC (TRC) or piecewise linear RC (PLRC) and one field in constant RC (CRC). Because three electric fields are required for the convolution integral, the method needs two more back level storage of the electric fields to fulfill the recursion process. Numerical demonstrations of Debye and Drude slab's transmission and reflection coefficients demonstrate the efficiency and accuracy of the novel method.