Ponderable Media Research Articles

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.

Casimir effect between ponderable media as modeled by the standard model extension

The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form $- \frac{1}{4} (k _{F}) _{\alpha \beta \mu \nu} F ^{\alpha \beta} F ^{\mu \nu}$, where the Lorentz-violating (LV) background tensor $(k _{F}) _{\alpha \beta \mu \nu}$ possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.

Revisiting the Balazs thought experiment in the case of a left-handed material: electromagnetic-pulse-induced displacement of a dispersive, dissipative negative-index slab

We propose a set of postulates to describe the mechanical interaction between a plane-wave electromagnetic pulse and a dispersive, dissipative slab having a refractive index of arbitrary sign. The postulates include the Abraham electromagnetic momentum density, a generalized Lorentz force law, and a model for absorption-driven mass transfer from the pulse to the medium. These opto-mechanical mechanisms are incorporated into a one-dimensional finite-difference time-domain algorithm that solves Maxwell's equations and calculates the instantaneous force densities exerted by the pulse onto the slab, the momentum-per-unit-area of the pulse and slab, and the trajectories of the slab and system center-of-mass. We show that the postulates are consistent with conservation of global energy, momentum, and center-of-mass velocity at all times, even for cases in which the refractive index of the slab is negative or zero. Consistency between the set of postulates and well-established conservation laws reinforces the Abraham momentum density as the one true electromagnetic momentum density and enables, for the first time, identification of the correct form of the electromagnetic mass density distribution and development of an explicit model for mass transfer due to absorption, for the most general case of a ponderable medium that is both dispersive and dissipative.

Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p EM = S ( r , t) / c 2. Here S ( r , t) = E ( r , t) × H ( r , t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n 2 + i κ 2, submerged in a transparent dielectric of refractive index n 1, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n 1, n 2, κ 2, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n 1 is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.

Electromagnetic force and torque in ponderable media

Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with conservation laws of energy, momentum, and angular momentum. We demonstrate consistency with the conservation laws by showing that, when a beam of light enters a magnetic dielectric, a fraction of the incident linear (or angular) momentum pours into the medium at a rate determined by the Abraham momentum density, E x H/c(2), and the group velocity V(g) of the electromagnetic field. The balance of the incident, reflected, and transmitted momenta is subsequently transferred to the medium as force (or torque) at the leading edge of the beam, which propagates through the medium with velocity V(g). Our analysis does not require "hidden" momenta to comply with the conservation laws, nor does it dissolve into ambiguities with regard to the nature of electromagnetic momentum in ponderable media. The linear and angular momenta of the electromagnetic field are clearly associated with the Abraham momentum, and the phase and group refractive indices (n(p) and n(g)) play distinct yet definitive roles in the expressions of force, torque, and momentum densities.

Statistical foundation of the Minkowski tensor for ponderable media.

The Minkowski stress tensor is statistically derived from the Maxwell-Lorentz field equations and the Liouville equation for a system of composite particles subject to an electromagnetic field. The derivation is subject to the condition that the fluctuations of field vectors are not statistically correlated. It is also shown by deriving the electromagnetic-field-momentum balance equation and the mechanical-momentum balance equation that the electromagnetic field momentum may be taken with ${c}^{\mathrm{\ensuremath{-}}1}$D\ifmmode\times\else\texttimes\fi{}B instead of ${c}^{\mathrm{\ensuremath{-}}1}$E\ifmmode\times\else\texttimes\fi{}H. The pressure in ponderable media is shown to contain an electromagnetic contribution: p=${p}_{0}$+(D\ensuremath{\cdot}E+B\ensuremath{\cdot}H)/2, where ${p}_{0}$ is the pressure in the case of no field. The electromagnetic contribution does not contain an adjustable, or undetermined, parameter unlike that in the existing theories.

IV.The equations of electrodynamics for moving ponderable media and the principle of relativity

IV.<i>The equations of electrodynamics for moving ponderable media and the principle of relativity</i>