Abstract

Physically valid electromagnetic continuity equations can be generated from either the usual form of the Poynting vector E⃗×H⃗ or the alternative E⃗×B⃗ form. However, the continuity equations are not identical, which means that quantities following from E⃗×H⃗ cannot always be compared directly to those from E⃗×B⃗. In particular, the work done on the bound current densities are attributed differently in the two representations. We also comment on the negative refraction condition used.

©2009 Optical Society of America

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References

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  1. V. A. Markel, “Correct Definition of the Poynting Vector in Electrically and Magnetically Polarizable Medium Reveals that Negative Refraction is Impossible,” Opt. Express 16, 19,152 (2008).
    [Crossref]
  2. R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
    [Crossref]
  3. P. Kinsler, A. Favaro, and M. McCall, “Four Poynting theorems,” Eur. J. Phys., to appear.
  4. M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
    [Crossref]
  5. P. Kinsler and M. W. McCall, “Criteria for negative refraction in active and passive media,” Microwave Opt. Tech. Lett. 50, 1804 (2008).
    [Crossref]
  6. P. Kinsler and M. W. McCall, “Causality-based conditions for negative refraction must be used with care,” Phys. Rev. Lett. 101, 167,401 (2008).
    [Crossref]
  7. F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

2008 (4)

P. Kinsler and M. W. McCall, “Criteria for negative refraction in active and passive media,” Microwave Opt. Tech. Lett. 50, 1804 (2008).
[Crossref]

P. Kinsler and M. W. McCall, “Causality-based conditions for negative refraction must be used with care,” Phys. Rev. Lett. 101, 167,401 (2008).
[Crossref]

F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

V. A. Markel, “Correct Definition of the Poynting Vector in Electrically and Magnetically Polarizable Medium Reveals that Negative Refraction is Impossible,” Opt. Express 16, 19,152 (2008).
[Crossref]

2007 (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

2002 (1)

M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
[Crossref]

Favaro, A.

P. Kinsler, A. Favaro, and M. McCall, “Four Poynting theorems,” Eur. J. Phys., to appear.

Florian, M.

F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

Heckenberg, N. R.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

Henneberger, K.

F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

Kinsler, P.

P. Kinsler and M. W. McCall, “Causality-based conditions for negative refraction must be used with care,” Phys. Rev. Lett. 101, 167,401 (2008).
[Crossref]

P. Kinsler and M. W. McCall, “Criteria for negative refraction in active and passive media,” Microwave Opt. Tech. Lett. 50, 1804 (2008).
[Crossref]

P. Kinsler, A. Favaro, and M. McCall, “Four Poynting theorems,” Eur. J. Phys., to appear.

Lakhtakia, A.

M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
[Crossref]

Markel, V. A.

McCall, M.

M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
[Crossref]

P. Kinsler, A. Favaro, and M. McCall, “Four Poynting theorems,” Eur. J. Phys., to appear.

McCall, M. W.

P. Kinsler and M. W. McCall, “Causality-based conditions for negative refraction must be used with care,” Phys. Rev. Lett. 101, 167,401 (2008).
[Crossref]

P. Kinsler and M. W. McCall, “Criteria for negative refraction in active and passive media,” Microwave Opt. Tech. Lett. 50, 1804 (2008).
[Crossref]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

Richter, F.

F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

Weiglhofer, W. S.

M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
[Crossref]

Eur. J. Phys. (1)

M. McCall, A. Lakhtakia, and W. S. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353–359 (2002).
[Crossref]

Europhys. Lett. (1)

F. Richter, M. Florian, and K. Henneberger, “Poynting’s theorem and energy conservation in the propagation of light in bounded media,” Europhys. Lett. 13, 117–121 (2008).

Microwave Opt. Tech. Lett. (1)

P. Kinsler and M. W. McCall, “Criteria for negative refraction in active and passive media,” Microwave Opt. Tech. Lett. 50, 1804 (2008).
[Crossref]

Opt. Express (1)

Phys. Rev. Lett. (1)

P. Kinsler and M. W. McCall, “Causality-based conditions for negative refraction must be used with care,” Phys. Rev. Lett. 101, 167,401 (2008).
[Crossref]

Rev. Mod. Phys. (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197–1216 (2007).
[Crossref]

Other (1)

P. Kinsler, A. Favaro, and M. McCall, “Four Poynting theorems,” Eur. J. Phys., to appear.

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Equations (19)

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∇→ · E→=1ε0ρb,
∇→ · B→=0,
∇→ × E→=−∂tB→,
∇→ × B→=μ0J→b+μ0ε0∂tE→,
∂t12[ε0E→2+1μ0B→2]+1μ0∇→·(E→×B→)+E→·J→b=0 .
J→b=∂tP→+∇→×M→,
ρb=−∇→·P→ ,
D→=ε0E→+P→,
H→=1μ0B→−M→,
∇→ · D→=0 ,
∇→·B→=0 ,
∇→×E→=− ∂t B→ ,
∇→×H→=∂tD→.
E→·∂tD→+H→·∂tB→+∇→·(E→×H→)=0 .
−1μ0∇→·〈E→×B→〉=|〈E→·J→b〉,
−∇→·〈E→×H→〉=〈E→·∂tD→+H→·∂tB→〉,
〈E→·J→b〉=ω ∣E→0∣2 Im {μ(ω)ε(ω)}e−2k→″·r→,
〈E→·∂tD→+H→·∂tB→〉=ω [∣μ(ω)∣ε″(ω)+∣ε(ω)∣μ″(ω)]∣E→0∣∣μ(ω)∣e−2k→″·r→.
Im [μ(ω)ε(ω)]<0,

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