Shrinking cloaks in expanding space-times: The role of coordinates and the meaning of transformations in transformation optics

Thompson, Robert T.; Fathi, Mohsen

doi:10.1103/physreva.92.013834

Cited by 17 publications

(22 citation statements)

References 21 publications

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“…The advent of structured composite metamaterials that possess some of the unnatural properties required to actually realize these unusual devices [9][10][11] provides an exciting demonstration that the geometrical, space-time manifold aspects of electrodynamics and light propagation are not just an academic abstraction, but can have real applications in engineering. Progress understanding and developing this new theoretical technology relies on the type of covariant formulation of electrodynamics in media studied here [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Covariant electrodynamics in linear media: Optical metric

Thompson

2018

Phys. Rev. D

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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 timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian 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. * robert@cosmos.phy.tufts.edu

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Section: Introductionmentioning

confidence: 99%

Covariant electrodynamics in linear media: Optical metric

Thompson

2018

Phys. Rev. D

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“…Transformation design-the use of the mathematical transformation of reference materials into those interesting 'device' properties is an area of active research interest-all the way from the most abstract theory and conceptualising [1][2][3][4][5], through to concrete theoretical proposals [6][7][8][9] and technological implementations [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…When we map the manifolds onto charts with coordinate systems (see figure 2), we are using an 'active transformation', not a passive 'coordinate transformation'. It is important to appreciate that the physics of Transformation Optics is independent of this coordinate representation, a point discussed further in [4]. One other crucial point is that on both manifolds, the underlying spacetime metric is taken to be Minkowski with Lorentzian signature (−, +, +, +).…”

Section: Introductionmentioning

confidence: 99%

On spacetime transformation optics: temporal and spatial dispersion

et al. 2016

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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.

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“…It is worth investigating how such techniques are implemented under our new CMCR scheme. In transformation optics it is the optical metric where the cloaking or other transformation design is implemented; and it is important to note that that optical metric is distinct from the background physical (spacetime) metric [52][53][54].…”

Section: B Transformation Electromagneticsmentioning

confidence: 99%

Electromagnetism, axions, and topology: A first-order operator approach to constitutive responses provides greater freedom

2020

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We show how the standard constitutive assumptions for the macroscopic Maxwell equations can be relaxed. This is done by arguing that the Maxwellian excitation fields (D, H) should be dispensed with, on the grounds that they (a) cannot be measured, and (b) act solely as gauge potentials for the charge and current. In the resulting theory, it is only the links between the fields (E, B) and the charge and current (ρ, J ) that matter; and so we introduce appropriate linear operator equations that combine the Gauss and Maxwell-Ampère equations with the constitutive relations, eliminating (D, H). The result is that we can admit more types of electromagnetic media -notably, the new relations can allow coupling in the bulk to a homogeneous axionic material; in contrast to standard EM where any homogeneous axion-like field is completely decoupled in the bulk, and only accessible at boundaries. We also consider a wider context, including the role of topology, extended non-axionic constitutive parameters, and treatment of Ohmic currents. A range of examples including an axionic response material is presented, including static electromagnetic scenarios, a possible metamaterial implementation, and how the transformation optics paradigm would be modified. Notably, these examples include one where topological considerations make it impossible to model using (D, H).

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Shrinking cloaks in expanding space-times: The role of coordinates and the meaning of transformations in transformation optics

Cited by 17 publications

References 21 publications

Covariant electrodynamics in linear media: Optical metric

Covariant electrodynamics in linear media: Optical metric

On spacetime transformation optics: temporal and spatial dispersion

Electromagnetism, axions, and topology: A first-order operator approach to constitutive responses provides greater freedom

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