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In this work, we present a dispersive finite-difference time-domain (FDTD) algorithm using a four-pole complex rational function (CRF). For the sake of a better curve fitting of the four-pole CRF dispersion model, we use a particle swarm optimization technique. We also discuss an efficient memory storage strategy using a state-space approach. The numerical aspects of four-pole CRF-FDTD, the numerical accuracy and the numerical stability, are investigated in detail. Numerical examples are used to validate four-pole CRF-FDTD and numerical stability issues are discussed in detail. We also discuss the computational accuracy and the computational efficiency of an arbitrary $N$-pole CRF-FDTD. [ABSTRACT FROM PUBLISHER]