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Over the past 15 years, several groups have engineered media that are bothstrongly dispersive and roughly transparent for some finite bandwidth.Relationships and intuitive models that are satisfactory when it is reasonableto neglect dispersion may then fail. We analyze three such cases of failure.  First, a simple generalization of the Abraham and Minkowski momenta todispersive 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 formsare experimentally relevant for the case of the Abraham momentum, but not forthe Minkowski momentum. We show how dispersion modulates the displacement of asphere embedded in a dispersive medium by a pulse.  Second, pulse transformation in a nonstationary medium is modulated by thepresence of dispersion. Using an explicit description of the kinetics ofdispersive nonstationary inhomogeneous media, we show how the group velocitycan modulate pulse response to a change in the refractive index and how Dopplershifts may become large in a dispersive medium as the velocity of the Dopplershifting surface approaches the group velocity. We explain a simple way to useexisting technology to either compress or decompress a given pulse, changingits bandwidth and spatial extent by several orders of magnitude while otherwisepreserving its envelope shape.  Finally, we note that the nature of a single optical cavity quasimode dependson intracavity dispersion. We show that the quantum field noise associated witha single cavity mode may be modulated by dispersion. For a well-chosen mode ina high-Q cavity, this can amount to either an increase or a decrease in totalvacuum field energy by several orders of magnitude. We focus on the "whitelight cavity," showing that the quantum noise of an ideal white light cavitydiverges as the cavity finesse improves.

Dispersion, Controlled Dispersion, and Three Applications