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G. Milton
University of Utah
CAN WAVES TRAVEL FASTER IN A COMPOSITE THAN IN THE CONSTITUENT PHASES?
Authors: Graeme Milton and Knut Solna
Its well known that in a bubbly fluid sound waves travel much
slower (and are much more rapidly damped) than in either air or water alone.
That has had important applications to masking the noise of submarines. Here
we show that the opposite phenomena can also occur. Specifically we show that
the group velocity, which governs the speed of propagation of electromagnetic
signals, can be substantially larger in the composite than in either of the
two isotropic constituent phases. The key point is that the group velocity
depends on both the refractive index and the dispersion (i.e. how the
refractive index changes with frequency.) By combining one phase with high
refractive index and low dispersion, with a second phase with low refractive
index and high dispersion, the composite can be made to exhibit comparatively
low refractive index and low dispersion, and hence a large group velocity.
We find that the speed enhancement is largest in a simple laminate but is
also quite large in other microstructures such as sphere assemblages.
Depending on the assumptions made, these geometries attain the bounds on the
effective group velocity that we derive. The group velocity can also be
smaller in the composite than in either of the two phases.
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