Dispersion, Controlled Dispersion, and Three Applications

Abstract

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.