Abstract

It is shown that, when all macroscopic currents associated with the electric and magnetic polarizability are properly accounted for, the standard expression for the Poynting vector and the average work exerted by the electric field on the electric charges provide exactly the same value for the heating rate. Therefore, there is no contradiction between negative refraction and thermodynamics.

© 2009 Optical Society of America

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References

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  1. V. A. Markel "Correct denition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible." Opt. Express. 16, 19152-19168 (2008).
    [CrossRef]
  2. J. D. Jackson, Classical Electrodynamics, 3rd ed., (Wiley, 1999).
  3. In some textbooks (e.g. [4]) this equation is formulated only for the entire body, and the surface integral is taken in free space, outide the body. In this case the surface integral formally disappear (however its contribution is still present, due to the infinite derivatives of M just on the surface of the body). However, when the surface integral is placed inside the body (or just on the surface of the body), this contribution is necessary in order to recover the magnetization.
  4. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamisc of Continuous Media, (Pergamon, 1984).

2008

V. A. Markel "Correct denition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible." Opt. Express. 16, 19152-19168 (2008).
[CrossRef]

Markel, V. A.

V. A. Markel "Correct denition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible." Opt. Express. 16, 19152-19168 (2008).
[CrossRef]

Opt. Express.

V. A. Markel "Correct denition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible." Opt. Express. 16, 19152-19168 (2008).
[CrossRef]

Other

J. D. Jackson, Classical Electrodynamics, 3rd ed., (Wiley, 1999).

In some textbooks (e.g. [4]) this equation is formulated only for the entire body, and the surface integral is taken in free space, outide the body. In this case the surface integral formally disappear (however its contribution is still present, due to the infinite derivatives of M just on the surface of the body). However, when the surface integral is placed inside the body (or just on the surface of the body), this contribution is necessary in order to recover the magnetization.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamisc of Continuous Media, (Pergamon, 1984).

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

q = 1 4 π D t + H · B t
q = J · E .
q = E · P t + c M · × E .
qdv = ( P t + c × M ) dv + c ( M × n ) ds
J v = P t + c × M
J s = c M × n .
δ m δV M dv = 1 2 δV r × ( × M ) dv + 1 2 δ∑ r × ( M × n ) ds

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