Abstract

The fact that the formula used by Hannay in the preceding Comment [J. Opt. Soc. Am. A 25, 2165 (2008) ] is “from a standard text on electrodynamics” neither warrants that it is universally applicable nor that it is unequivocally correct. We have explicitly shown [J. Opt. Soc. Am. A 25, 543 (2008) ] that, since it does not include the boundary contribution toward the value of the field, the formula in question is not applicable when the source is extended and has a distribution pattern that rotates faster than light in vacuo. The neglected boundary term in the retarded solution to the wave equation governing the electromagnetic field forms the basis of diffraction theory. If this term were identically zero, for the reasons given by Hannay, the diffraction of electromagnetic waves through apertures on a surface enclosing a source would have been impossible.

© 2008 Optical Society of America

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References

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  1. J. H. Hannay, “Morphology of the nonspherically decaying radiation generated by a rotating superluminal source: comment,” J. Opt. Soc. Am. A 25, 2165-2166 (2008).
    [CrossRef]
  2. H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Fundamental role of the retarded potential in the electrodynamics of superluminal sources,” J. Opt. Soc. Am. A 25, 543-558 (2008).
    [CrossRef]
  3. A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
    [CrossRef]
  4. H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
    [CrossRef]
  5. H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns,” J. Opt. Soc. Am. A 21, 858-872 (2004).
    [CrossRef]
  6. H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source,” J. Opt. Soc. Am. A 24, 2443-2456 (2007).
    [CrossRef]
  7. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  8. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), Vol. 1.
  9. J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996).
    [CrossRef]
  10. J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation',” Phys. Rev. E 62, 3008-3009 (2000).
    [CrossRef]
  11. J. H. Hannay, “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves',” J. Math. Phys. 42, 3973-3974 (2001).
    [CrossRef]
  12. J. H. Hannay, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: comment,” J. Opt. Soc. Am. A 23, 1530-1534 (2006).
    [CrossRef]
  13. H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: reply to comment,” J. Opt. Soc. Am. A 23, 1535-1539 (2006).
    [CrossRef]

2008

2007

2006

2004

H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns,” J. Opt. Soc. Am. A 21, 858-872 (2004).
[CrossRef]

A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

2001

J. H. Hannay, “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves',” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

2000

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation',” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

1998

H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
[CrossRef]

1996

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996).
[CrossRef]

Ardavan, A.

Ardavan, H.

Fasel, J.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), Vol. 1.

Fopma, J.

A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

Halliday, D.

A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

Hannay, J. H.

J. H. Hannay, “Morphology of the nonspherically decaying radiation generated by a rotating superluminal source: comment,” J. Opt. Soc. Am. A 25, 2165-2166 (2008).
[CrossRef]

J. H. Hannay, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: comment,” J. Opt. Soc. Am. A 23, 1530-1534 (2006).
[CrossRef]

J. H. Hannay, “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves',” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation',” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996).
[CrossRef]

Hayes, W.

A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

Jackson, J. D.

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

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), Vol. 1.

Schmidt, A.

Singleton, J.

J. Appl. Phys.

A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, “Experimental observation of nonspherically-decaying radiation from a rotating superluminal source,” J. Appl. Phys. 96, 7760-7777(E) (2004). Corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

J. Math. Phys.

J. H. Hannay, “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves',” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. E

H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
[CrossRef]

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation',” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

Proc. R. Soc. London, Ser. A

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996).
[CrossRef]

Other

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

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953), Vol. 1.

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Equations (11)

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2 B 1 c 2 2 B t 2 = 4 π c × j .
B ( x P , t P ) = 1 c d 3 x [ × j ] x P x ,
E = P A 0 A ( c t P ) , B = P × A ,
2 A μ 1 c 2 2 A μ t 2 = 4 π c j μ , μ = 0 , , 3 ,
A μ ( x P , t P ) = 1 c 0 t P d t V d 3 x j μ G + 1 4 π 0 t P d t Σ d S ( G A μ A μ G ) 1 4 π c 2 V d 3 x ( A μ G t G A μ t ) t = 0 ,
A A + Λ , A 0 A 0 Λ t
G ( x , t ; x P , t P ) = δ ( t P t R c ) R ,
A μ ( x P , t P ) = c 1 d 3 x d t j μ ( x , t ) δ ( t P t R c ) R ,
B k ( x P , t P ) = 1 c 0 t P d t V d 3 x ( × j ) k G + 1 4 π 0 t P d t Σ d S ( G B k B k G ) 1 4 π c 2 V d 3 x ( B k G t G B k t ) t = 0 ,
B k ( x P , t P ) = 1 4 π 0 t P d t Σ d S ( G B k B k G ) ,
0 t P d t Σ d S ( G B k B k G ) = 0 t P d t ( Σ inner + Σ outer ) d S ( G B k B k G ) = 0

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