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Optimal superluminal systems

We demonstrate that significant effects in the "superluminal propagation"of light-pulses cannot be observed without involving systems whose gain explodes outside the pulse spectrum. We explicitly determine the minimum norm of the gain to attain given superluminal effects and the transfer function of the corresponding optimal system. The gain-norms which would be required with the most efficient systems considered up to now (dispersive media, photonic barriers) to attain the same effects are shown to exceed the minimum by several orders of magnitude. We finally estimate the largest superluminal advances which could be attained in a realistic experiment.