Energy density in continuous electromagnetic media

Tonning, A.

doi:10.1109/tap.1960.1144871

Cited by 21 publications

(10 citation statements)

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“…The damping factor can then be sent to zero when the calculation is finished. This procedure seems reasonable as discussed in [22] since the time-harmonic fields in the strictest sense never occur in physical experiments. Let  denote the small damping factor.…”

Section: Stored and Dissipated Field Energies In General Materialsmentioning

confidence: 92%

“…The (average) stored field energy densities and power loss density in the frequency domain can be found by taking the time averages of ( 19) to (22) over one period of the sinusoidal wave jt e  as follows…”

Section: Stored and Dissipated Field Energies In General Materialsmentioning

confidence: 99%

“…Ginzburg"s notes revealed a longstanding problem in fundamental electrodynamics. Formulating the energy densities for time-harmonic fields in complex media has been an active research area for many years and tremendous efforts have been devoted to solving this problem [1]- [22]. A common understanding is that there are no general formulations for field energy densities that are valid for an arbitrary medium.…”

Section: Introductionmentioning

confidence: 99%

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Stored electromagnetic field energies in general materials

Geyi¹

2019

J. Opt. Soc. Am. B

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The most general expressions of the stored energies for time-harmonic electromagnetic fields are derived from the time-domain Poynting theorem, and are valuable in characterizing the energy storage and transport properties of complex media. A new energy conservation law for the time-harmonic electromagnetic fields, which involves the derived general expressions of the stored energies, is introduced. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies; the imaginary part involves an equation related to the difference between the dissipated electric and magnetic field energies. In a lossless isotropic and homogeneous medium, the new energy conservation law has a clear physical implication: the stored electromagnetic field energy of a radiating system enclosed by a surface is equal to the total field energy inside the surface subtracted by the field energy flowing out of the surface.

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Section: Stored and Dissipated Field Energies In General Materialsmentioning

confidence: 92%

Section: Stored and Dissipated Field Energies In General Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stored electromagnetic field energies in general materials

Geyi¹

2019

J. Opt. Soc. Am. B

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“…A medium is said to be reciprocal if 7 is a symmetric matrix, i.e., if 7 = yT (19) where yT denotes the transpose of 7. In this case, and only in this case, will the dispersion relations (15) and (18) be identical.…”

Section: Jomentioning

confidence: 99%

“…One can derive (40) by a beat frequency approach [1], [18] or by a complex frequency (or damped harmonic frequency) approach [19]. We now sketch a variant of the latter approach for a general (Tellegen) medium.…”

Section: Jomentioning

confidence: 99%

Dispersion relations, stored energy and group velocity for anisotropic electromagnetic media

Kurss¹

1968

Quart. Appl. Math.

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Abstract.The Hermitian and skew-Hermitian components of the susceptibility matrix of a general linear electromagnetic medium are represented as Hilbert transforms of each other. These so-called dispersion relations lead to a priori inequalities which must be satisfied by the susceptibility of a passive medium in a frequency interval in which the medium is lossless. One such inequality states that the stored energy density for a given E(«) and H(ai) is always greater than in free space. This is also verified directly from the usual gyrotropic susceptibilities of ferrites and plasmas.The group velocity for an eigenwave or mode of a structure with one, two or three independent translational symmetry vectors is shown to be, in general, an average Poynting vector divided by an average stored energy density. This formula is then combined with the above inequality for the stored energy density to show that the magnitude of the group velocity is less than c, the velocity of light in free space.I. Introduction. A main point of the present paper is to extend some results, known for isotropic media [1], to the case of general anisotropic media. Moreover, some of the discussion, for example that relating to group velocity, is novel even when specialized to the isotropic case.For simplicity as well as for generality the discussion is phrased for a medium where As in the isotropic case, a consequence of causality and time invariance is that the susceptibility, 7(0>) -y0, satisfies an integral equation with (Cauchy) Kernel 1/(jV(x -«)), where the range of integration of x is from -co to + co. One can separate this integral equation into its real and imaginary components. The resulting equations [1], [5], called dispersion relations, state that the real and imaginary components of the susceptibility matrix, in their dependence upon frequency, are Hilbert transforms of each other. However, in the anisotropic case one has the additional possibility of separating the integral equation into its Hermitian and skew-Hermitian components. This leads to the new dispersion relations stated in Sec. III. These are particularly significant with regard

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2010

Foundations of Applied Electrodynamics

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Energy density in continuous electromagnetic media

Cited by 21 publications

References 2 publications

Stored electromagnetic field energies in general materials

Stored electromagnetic field energies in general materials

Dispersion relations, stored energy and group velocity for anisotropic electromagnetic media

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