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The finite-difference time-domain (FDTD) technique is employed for the numerical modeling of several synthesized structures with unconventional properties, such as negative refractive index (NRI), negative group delay (superluminal group velocity) and resonance cone formation. The simulated structures are composed of finite arrays of one- and two-dimensional lumped element inclusions, whose presence is accounted for, via the so-called extended FDTD approach. The latter readily allows for the introduction of passive and active circuit architectures in an FDTD mesh. Validation studies are provided, including comparisons with analytical and experimental results, to demonstrate the accuracy of the proposed technique.