Covariant electrodynamics in linear media: Optical metric

Abstract

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

Bespoke analogue space-times: meta-material mimics

“…Ideas along these lines (sometimes only partially implemented) date back, at the very least, to Gordon [2], and to Landau and Lifshitz [3]. There have also been significant related efforts from both the general relativity [4,5,6,7,8,9] and the optics communities [10,11,12]. These electromagnetic analogue spacetimes complement the acoustic analogue spacetimes of [13,14,15,16,17,18].…”

Remarks on the Abraham-Minkowski problem, from the formal and from the experimental side

“…We have shed light on the Abraham-Minkowski problem from two quite different perspectives. Our formal approach was related to the Gordon metric g G which is also a Finslerian metric [39], defined in classical relativistic electrodynamics [40]. If the medium is isotropic and at rest, the Fermat and Gordon metrics are related through the conformal transformation, g = n 2 g G .…”

Backgrounds in gravitational effective field theory

“…With the latter quantities identified as explicit background fields, Finsler geometry has been conjectured as a possible route to escape the no-go constraints in Riemann geometry [2]. Investigating this conjecture in detail is hampered by the lack of a satisfactory definition for Lorentz-Finsler geometry, which is currently the subject of active research [103][104][105][106][107][108][109][110][111][112][113][114][115][116]. Support for the conjecture includes the demonstration that the trajectory of a fermion or scalar particle in the present of explicit backgrounds corresponds to a geodesic in a Riemann-Finsler space [103,104,[117][118][119][120].…”