  Composite dark matter (DM) comprised of electrically charged constituents can
interact with the electromagnetic field via the particle's dipole moment. This
interaction results in a dispersive optical index of refraction for the DM
medium. We compute this refractive index for atomic dark matter and more
strongly bound systems, modeled via a harmonic oscillator potential. The
dispersive nature of the index will result in a time lag between high and low
energy photons simultaneously emitted from a distant astrophysical observable.
This time lag, due to matter dispersion, could confound potential claims of
Lorentz invariance violation (LIV) which can also result in such time lags. We
compare the relative size of the two effects and determine that the dispersion
due to DM is dwarfed by potential LIV effects for energies below the Planck
scale.
