  Over the past 15 years, several groups have engineered media that are both
strongly dispersive and roughly transparent for some finite bandwidth.
Relationships and intuitive models that are satisfactory when it is reasonable
to neglect dispersion may then fail. We analyze three such cases of failure.
  First, a simple generalization of the Abraham and Minkowski momenta to
dispersive media entails multiplying each per-photon momentum by $n/n_g$, where
$n$ is the refractive index and $n_g$ is the group index. The resulting forms
are experimentally relevant for the case of the Abraham momentum, but not for
the Minkowski momentum. We show how dispersion modulates the displacement of a
sphere embedded in a dispersive medium by a pulse.
  Second, pulse transformation in a nonstationary medium is modulated by the
presence of dispersion. Using an explicit description of the kinetics of
dispersive nonstationary inhomogeneous media, we show how the group velocity
can modulate pulse response to a change in the refractive index and how Doppler
shifts may become large in a dispersive medium as the velocity of the Doppler
shifting surface approaches the group velocity. We explain a simple way to use
existing technology to either compress or decompress a given pulse, changing
its bandwidth and spatial extent by several orders of magnitude while otherwise
preserving its envelope shape.
  Finally, we note that the nature of a single optical cavity quasimode depends
on intracavity dispersion. We show that the quantum field noise associated with
a single cavity mode may be modulated by dispersion. For a well-chosen mode in
a high-Q cavity, this can amount to either an increase or a decrease in total
vacuum field energy by several orders of magnitude. We focus on the "white
light cavity," showing that the quantum noise of an ideal white light cavity
diverges as the cavity finesse improves.
