Abstract
Suppose that a composite is constructed from two phases and that we propagate an electromagnetic signal through it. The velocity of the signal in the composite depends on the microstructure. What microstructures are associated with the maximum and minimum speeds of the electromagnetic signal? Here we show that the group velocity of a pulse can be higher in the composite than in either of the two phases. We derive sharp bounds for the relative increase and decrease in the group velocity of the electromagnetic signal in the composite and give the associated optimal microstructures. We also find that a pulse in a composite can have substantially smaller dispersion and, at the same time, substantially larger group velocity than pulses traveling in the pure phases.
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