Dispersion, controlled dispersion, and three applications
type: CreativeWork
description: Causality dictates that all physical media must be dispersive. (We will call a medium dispersive if its refractive index varies with frequency.) Ordinarily, strong dispersion is accompanied either by strong absorption or strong gain. However, over the past 15 years several groups have demonstrated that it is possible to have media that are both strongly dispersive and roughly transparent for some finite bandwidth. In these media, group and phase velocities may differ from each other by many orders of magnitude and even by sign. Relationships and intuitive models that are satisfactory when it is reasonable to neglect dispersion may then fail dramatically. In this dissertation we analyze three such cases of failure. Before looking at the specific cases, we review some basic ideas relating to dispersion. We review some of the geometric meanings of group velocity, touch on the relationship between group velocity and causality, and give some examples of techniques by which the group velocity may be manipulated. We describe the interplay between group velocity and energy density for non-absorbing dispersive media. We discuss the ideas of temporary absorption and emission as dictated by an instantaneous spectrum. We then apply these concepts in three specific areas. First, non-dispersive formulations for the momentum of light in a medium must be adjusted to account for dispersion. For over 100 years, there has been a gradual discussion of the proper form for the per-photon momentum. Two forms, each of which has experimental relevance in a \'dispersionless\' medium, are the Abraham momentum, and the Minkowski momentum. If $\\omega$ is the angular frequency, $n$ is the refractive index, $\\hbar$ is Planck\'s constant, and $c$ is the speed of light, then these reduce in a dispersionless medium to per-photon momenta of $\\hbar \\omega/(nc)$, and $n\\hbar \\omega/c$ respectively. A simple generalization of the two momenta to dispersive media entails multiplying each per-photon …
abstract: Causality dictates that all physical media must be dispersive. (We will call a medium dispersive if its refractive index varies with frequency.) Ordinarily, strong dispersion is accompanied either by strong absorption or strong gain. However, over the past 15 years several groups have demonstrated that it is possible to have media that are both strongly dispersive and roughly transparent for some finite bandwidth. In these media, group and phase velocities may differ from each other by many orders of magnitude and even by sign. Relationships and intuitive models that are satisfactory when it is reasonable to neglect dispersion may then fail dramatically. In this dissertation we analyze three such cases of failure. Before looking at the specific cases, we review some basic ideas relating to dispersion. We review some of the geometric meanings of group velocity, touch on the relationship between group velocity and causality, and give some examples of techniques by which the group velocity may be manipulated. We describe the interplay between group velocity and energy density for non-absorbing dispersive media. We discuss the ideas of temporary absorption and emission as dictated by an instantaneous spectrum. We then apply these concepts in three specific areas. First, non-dispersive formulations for the momentum of light in a medium must be adjusted to account for dispersion. For over 100 years, there has been a gradual discussion of the proper form for the per-photon momentum. Two forms, each of which has experimental relevance in a \'dispersionless\' medium, are the Abraham momentum, and the Minkowski momentum. If $\\omega$ is the angular frequency, $n$ is the refractive index, $\\hbar$ is Planck\'s constant, and $c$ is the speed of light, then these reduce in a dispersionless medium to per-photon momenta of $\\hbar \\omega/(nc)$, and $n\\hbar \\omega/c$ respectively. A simple generalization of the two momenta to dispersive media entails multiplying each per-photon …
author: Bradshaw, Douglas Harris
language: English
date published: 2010-06-25T07:00:00Z
date modified: 2026-07-24T05:26:35Z
provider: University of New Mexico
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of New Mexico

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property ID: Handle
value: http://hdl.handle.net/1928/10856