Four Poynting theorems

Kinsler, Paul; Favaro, Alberto; McCall, Martin W.

doi:10.1088/0143-0807/30/5/007

Cited by 54 publications

(40 citation statements)

References 50 publications

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“…where ∆U DB is the total change in the independent field energy, and n is the outward unit vector normal to the surface S. There has been much discussion regarding the correct definition of the Poynting vector as the representation of electromagnetic flux (e.g., [30]). …”

Section: Susceptibility Tensorsmentioning

confidence: 99%

Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magnetoelectric medium

et al. 2013

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We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field operators in either a Green function or mode expansion representation. Here we present our results in the mode expansion picture with a view to applications in guided wave and cavity quantum optics.

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Section: Susceptibility Tensorsmentioning

confidence: 99%

Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magnetoelectric medium

et al. 2013

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“…Therefore, Equation (35) is valid regardless the optical properties of the material, simply because its derivation is independent of the particular structure of α (see Equations (30) and (34)). This means that in any material, …”

Section: Geometrical Optics and Light Beamsmentioning

confidence: 99%

“…We will rather concentrate only in two different proposals for the mathematical expression of the Poynting vector S , whose choice has created controversy even in recent years [22]- [30]. One given by = × S E H , which is the commonly used in literature and the one that appears in most textbooks and the other by…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic-Energy Flow in Anisotropic Metamaterials: The Proper Choice of Poynting’s Vector

Prieto-López¹,

Barrera²

2016

JMP

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We study the controversy about the proper determination of the electromagnetic energy-flux field in anisotropic materials, which has been revived due to the relatively recent experiments on negative refraction in metamaterials. Rather than analyzing energy-balance arguments, we use a pragmatic approach inspired by geometrical optics, and compare the predictions on angles of refraction at a flat interface of two possible choices on the energy flux: × E H and × E B 0 µ . We carry out this comparison for a monochromatic Gaussian beam propagating in an anisotropic nondissipative anisotropic metamaterial, in which the spatial localization of the electromagnetic field allows a more natural assignment of directions, in contrast to the usual study of plane waves. We compare our approach with the formalism of geometrical optics, which we generalize and analyze numerically the consequences of either choice.

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“…This vector points (has the orientation) in the propagation direction of an electromagnetic wave and has dimensions of power/area. According to [75], the choice of the theorem is not relevant for nondispersive (in theoretical physics terminology) or nondissipative (in mechanics terminology) linear materials. However, for dispersive/dissipative materials the choice of the flux vector j P may be decisive.…”

Section: Poynting Theoremsmentioning

confidence: 99%

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

Pérez-Aparicio

Palma

Taylor

2015

Arch Computat Methods Eng

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Combining several theories this paper presents a general multiphysics framework applied to the study of coupled and active materials, considering mechanical, electric, magnetic and thermal fields. The framework is based on thermodynamic equilibrium and nonequilibrium interactions, both linked by a two-temperature model.The multi-coupled governing equations are obtained from energy, momentum and entropy balances; the total energy is the sum of thermal, mechanical and electromagnetic parts. The momentum balance considers mechanical plus electromagnetic balances; for the latter the Abraham representation using the Maxwell stress tensor is formulated. This tensor is manipulated to automatically fulfill the angular momentum balance. The entropy balance is formulated using the classical Gibbs equation for equilibrium interactions and non-equilibrium thermodynamics. For the non-linear finite element formulations, this equation requires the transformation of thermoelectric coupling and conductivities into tensorial form.The two-way thermoelastic Biot term introduces damping: thermomechanical, pyromagnetic and pyroelectric converse electromagnetic dynamic interactions. Ponderomotrix and electromagnetic forces are also considered.The governing equations are converted into a variational formulation with the resulting four-field, multicoupled formalism implemented and validated with two custom-made finite elements in the research code FEAP. Standard first-order isoparametric eight-node elements with seven degrees of freedom (dof) per node (three displacements, voltage and magnetic scalar potentials plus two temperatures) are used. Non-linearities and dynamics are solved with Newton-Raphson and Newmark-β algorithms, respectively.Results of thermoelectric, thermoelastic, thermomagnetic, piezoelectric, piezomagnetic, pyroelectric, pyromagnetic and galvanomagnetic interactions are presented, including non-linear dependency on temperature and some second-order interactions.

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Four Poynting theorems

Cited by 54 publications

References 50 publications

Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magnetoelectric medium

Canonical quantization of macroscopic electrodynamics in a linear, inhomogeneous magnetoelectric medium

Electromagnetic-Energy Flow in Anisotropic Metamaterials: The Proper Choice of Poynting’s Vector

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

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