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Robert T. Thompson

Publications and source records attributed to Robert T. Thompson.

14 recordsLinked to original sources
arXiv2018

Covariant electrodynamics in linear media: Optical metric

While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including between accelerating frames -- that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary time-like observer. In terms of those medium parameters I derive an explicit expression for the Finsler-like optical metric of birefringent media and show how it reduces to a Riemann-like optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.

gr-qc↗
arXiv2017

Covariant kinematics of light in media and a generalized Raychaudhuri equation

There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating through arbitrary dielectric media in curved space-times are derived, allowing for analysis and tracing of congruences of light through media that may smoothly vary in character between vacuum, positively refracting, and negatively refracting; or null, timelike, and spacelike with respect to the background metric. The kinematics are then used to generalize the Raychaudhuri equation -- an important tool in general relativity that describes the focus of a congruence. These results will be useful for the analysis of optical devices, particularly those designed using transformation optics, and serve as theoretical tools to study generalized concepts in general relativity.

gr-qc↗
arXiv2016

On Spacetime Transformation Optics: Temporal and Spatial Dispersion

The electromagnetic implementation of cloaking, the hiding of objects from sight by diverting and reassembling illuminating electromagnetic fields has now been with us ten years, while the notion of hiding events is now five. Both schemes as initially presented neglected the inevitable dispersion that arises when a designed medium replaces vacuum under transformation. Here we define a transformation design protocol that incorporates both spacetime transformations and dispersive material responses in a natural and rigorous way. We show how this methodology is applied to an event cloak designed to appear as a homogeneous and isotropic but dispersive medium. The consequences for spacetime transformation design in dispersive materials are discussed, and some parameter and bandwidth constraints identified.

physics.optics↗
arXiv2016

Cartographic distortions make dielectric spacetime analog models imperfect mimickers

It is commonly assumed that if the optical metric of a dielectric medium is identical to the metric of a vacuum space-time then light propagation through the dielectric mimics light propagation in the vacuum. However, just as the curved surface of the Earth cannot be mapped into a flat plane without distortion of some surface features, so too is it impossible to project the behavior of light from the vacuum into a dielectric analog residing in Minkowski space-time without introducing distortions. We study the covariance properties of dielectric analog space-times and the kinematics of a congruence of light in the analog, and show how certain features can be faithfully emulated in the analog depending on the choice of projection, but that not all features can be simultaneously emulated without distortion. These findings indicate conceptual weaknesses in the idea of using analog space-times as a basis for transformation optics, and we show that a certain formulation of transformation optics closely related to analog space-times resolves these issues.

gr-qc↗
arXiv2016

Fresnel-Fizeau drag: Invisibility conditions for all inertial observers

It was recently shown [Halimeh et al. arXiv:1510.06144 (to appear in Phys. Rev. A)] that as a result of the Doppler effect, inherently dispersive single-frequency ideal free-space invisibility cloaks in relative motion to an observer can only cloak light whose frequency in the cloak frame coincides with the operational frequency of the cloak, although an infinite number of such rays exist for any cloak motion. In this article, we show analytically and through ray-tracing simulations that even though this relationship can be relaxed by simplifying the ideal invisibility cloak into a broadband amplitude cloak, Fresnel-Fizeau drag uncloaks the phase of light in the inertial frame of the cloak thereby compromising its amplitude cloaking in all other inertial frames. In other words, only an invisibility device that perfectly cloaks both the amplitude and the phase of light in its own inertial frame will also (perfectly) cloak this light in any other inertial frame. The same conclusion lends itself to invisible objects that are not cloaks, such as the invisible sphere.

physics.optics↗
arXiv2016

Invisibility cloaks in relativistic motion

We consider an ideal invisibility cloak which is illuminated by monochromatic light and which moves in vacuum at constant relativistic velocity with respect to the common inertial frame of light source and observer. We show that, in general, the moving cloak becomes detectable by image distortions and by generating a broad frequency spectrum of the scattered light. However, for many special combinations of incident light frequency, wave vector of light, and cloak velocity, ideal cloaking remains possible. It becomes non-reciprocal though. This means that light rays emitted by the light source arrive at the observer as though they have travelled through vacuum, but they take completely different paths after being retro-reflected at the observer position.

physics.optics↗
arXiv2015

Shrinking cloaks in expanding spacetimes: the role of coordinates and the meaning of transformations in Transformation Optics

The fully covariant formulation of transformation optics is used to find the configuration of a cloaking device operating in an expanding universe modelled by a Friedmann-Lemaître-Robertson-Walker spacetime. This spacetime cloak is used as a platform for probing the covariant formulation of transformation optics, thereby rigorously enhancing the conceptual understanding of the theory. By studying the problem in both comoving and physical coordinates we explicitly demonstrate the preservation of general covariance of electrodynamics under the transformation optics procedure. This platform also enables a detailed study of the various transformations that arise in transformation optics. We define a corporeal transformation as the "transformation" of transformation optics, and distinguish it from coordinate and frame transformations. We find that corporeal transformations considered in the literature have generally been restricted to a subset of all possible corporeal transformations, providing a potential mechanism for increased functionality of transformation optics.

physics.optics↗
arXiv2012

General Relativistic Contributions in Transformation Optics

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space-time, such as Earth orbit. This raises the question of what, if any, role does space-time curvature play in determining transformation media? Transformation optics has been based on a three-vector representation of Maxwell's equations in flat Minkowski space-time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space-times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important.

physics.optics↗
arXiv2011

Generalized Transformation Optics of Linear Materials

We continue the development of a manifestly 4-dimensional, completely covariant, approach to transformation optics in linear dielectric materials begun in a previous paper. This approach, which generalizes the Plebanski based approach, is systematically applicable for all transformations and all general linear materials. Importantly, it enables useful applications such as arbitrary relative motion, transformations from arbitrary non-vacuum initial dielectric media, and arbitrary space-times. This approach is demonstrated for a resulting material that moves with uniform linear velocity. The inverse problem of this covariant approach is shown to generalize Gordon's "optical metric".

physics.optics↗
arXiv2011

Dielectric Analog Space-Times

We generalize the notion of a dielectric analog Schwarzschild black hole model to analog models of arbitrary space-times; in particular, the approach is not restricted to static space-times. This is done by establishing a correspondence between electrodynamics on a curved, vacuum manifold, with electrodynamics in a general linear dielectric residing in Minkowski space-time. The mapping is not unique, allowing for some freedom in the specification of equivalent materials, which could be useful for exploiting recent developments in the production of metamaterials. Some examples are considered, with special attention paid to the dielectric analog of the exterior Kerr geometry, which is found to be reproducible with regular, linear, dielectrics.

gr-qc↗
arXiv2010

A Completely Covariant Approach to Transformation Optics

We show that the Plebanski based approach to transformation optics overlooks some subtleties in the electrodynamics of moving dielectrics that restricts its applicability to a certain class of transformations. An alternative, completely covariant, approach is developed that is more generally applicable and provides a clearer picture of transformation optics.

physics.optics↗
arXiv2010

Transformation Optics in Nonvacuum Initial Dielectric Media

Previous formulations of transformation optics have generally been restricted to transformations from relatively simple initial media, such as the vacuum, because of limitations due to their non-covariance. I show that a completely covariant approach enables arbitrary transformations from arbitrarily complex initial linear dielectrics.

physics.optics↗
arXiv2009

DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions

Calculation of the vacuum polarization, $<ϕ^2(x)>$, and expectation value of the stress tensor, $ $, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to $d$ dimensions includes $d$-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for $<ϕ^2(x)>$ and $ $ calculations and a thorough introduction to the method of calculating $<ϕ^2(x)>$, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of $<ϕ^2(x)>$ and $ $ in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to $<ϕ^2(x)>$ for certain spacetimes is discussed, with application to four and five dimensions.

gr-qc↗