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A unified treatment for the truncation of finite-difference time-domain lattices, applicable to dispersive and conductive media alike, is proposed. The method is based on periodic boundary conditions, hence necessitating that the medium under study be periodic along the direction of truncation. When this condition (which is satisfied in many practical cases) is met, a much simpler but equally effective alternative to the PML is provided by the combination of periodic boundaries with an array-scanning method. The proposed formulation does not need any additional auxiliary variables when applied to dispersive media, unlike the PML. Applications include a Bragg filter and a negative-refractive-index super lens.