Abstract

Hannay’s comment [J. Opt. Soc. Am. A 23, 1530 (2006) ; this issue] is based on an argument that is mathematically inconsistent when applied to superluminal sources. Moreover, it ignores our published experimental data [e.g., J. Appl. Phys. 96, 7760(E) (2004) ] that completely support the conclusions of our theoretical paper.

© 2006 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. R. F. Hoskins, Generalised Functions (Horwood, 1979), Chap. 7.
  4. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale U. Press, 1923), Dover reprint (1952).
  5. 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, 4614-4631 (2004); 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)
    [CrossRef]
  6. J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).
  7. B. M. Bolotovskii and A. V. Serov, "Radiation of superluminal sources in vacuum," Usp. Fiz. Nauk 175, 943-955 (2005).
    [CrossRef]
  8. H. Ardavan, A. Ardavan, and J. Singleton, "Frequency spectrum of focused broadband pulses of electromagnetic radiation generated by polarization currents with superluminally rotating distribution patterns," J. Opt. Soc. Am. A 20, 2137-2155 (2003).
    [CrossRef]
  9. H. Ardavan, "Reply to Comments on 'Generation of focused, nonspherically decaying pulses of the electromagnetic radiation'," Phys. Rev. E 62, 3010-3013 (2000).
    [CrossRef]
  10. H. Ardavan, "Method of handling the divergences in the radiation theory of sources that move faster than their waves," J. Math. Phys. 40, 4331-4336 (1999).
    [CrossRef]
  11. H. Ardavan, "Generation of focused, nonspherically decaying pulses of the electromagnetic radiation," Phys. Rev. E 58, 6659-6684 (1998).
    [CrossRef]
  12. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2 (Interscience, 1966).

2006 (1)

2005 (1)

B. M. Bolotovskii and A. V. Serov, "Radiation of superluminal sources in vacuum," Usp. Fiz. Nauk 175, 943-955 (2005).
[CrossRef]

2004 (3)

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

2003 (1)

2000 (1)

H. Ardavan, "Reply to Comments on 'Generation of focused, nonspherically decaying pulses of the electromagnetic radiation'," Phys. Rev. E 62, 3010-3013 (2000).
[CrossRef]

1999 (1)

H. Ardavan, "Method of handling the divergences in the radiation theory of sources that move faster than their waves," J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

1998 (1)

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

Ardavan, A.

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (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]

H. Ardavan, A. Ardavan, and J. Singleton, "Frequency spectrum of focused broadband pulses of electromagnetic radiation generated by polarization currents with superluminally rotating distribution patterns," J. Opt. Soc. Am. A 20, 2137-2155 (2003).
[CrossRef]

Ardavan, H.

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]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

H. Ardavan, A. Ardavan, and J. Singleton, "Frequency spectrum of focused broadband pulses of electromagnetic radiation generated by polarization currents with superluminally rotating distribution patterns," J. Opt. Soc. Am. A 20, 2137-2155 (2003).
[CrossRef]

H. Ardavan, "Reply to Comments on 'Generation of focused, nonspherically decaying pulses of the electromagnetic radiation'," Phys. Rev. E 62, 3010-3013 (2000).
[CrossRef]

H. Ardavan, "Method of handling the divergences in the radiation theory of sources that move faster than their waves," J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

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

Bolotovskii, B. M.

B. M. Bolotovskii and A. V. Serov, "Radiation of superluminal sources in vacuum," Usp. Fiz. Nauk 175, 943-955 (2005).
[CrossRef]

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2 (Interscience, 1966).

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

Hadamard, J.

J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale U. Press, 1923), Dover reprint (1952).

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, 4614-4631 (2004); 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)
[CrossRef]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

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, 4614-4631 (2004); 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)
[CrossRef]

Hannay, J. H.

Hayes, W.

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2 (Interscience, 1966).

Hoskins, R. F.

R. F. Hoskins, Generalised Functions (Horwood, 1979), Chap. 7.

Serov, A. V.

B. M. Bolotovskii and A. V. Serov, "Radiation of superluminal sources in vacuum," Usp. Fiz. Nauk 175, 943-955 (2005).
[CrossRef]

Singleton, J.

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, 4614-4631 (2004); 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)
[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, 4614-4631 (2004); 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)
[CrossRef]

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

H. Ardavan, A. Ardavan, and J. Singleton, "Frequency spectrum of focused broadband pulses of electromagnetic radiation generated by polarization currents with superluminally rotating distribution patterns," J. Opt. Soc. Am. A 20, 2137-2155 (2003).
[CrossRef]

IEEE Conference Digest (1)

J. Singleton, A. Ardavan, H. Ardavan, J. Fopma, D. Halliday, and W. Hayes, "Experimental demonstration of emission from a superluminal polarization current—a new class of solid-state source for MHz-THz and beyond," IEEE Conference Digest 04EX857, 591-592 (2004).

J. Appl. Phys. (1)

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, 4614-4631 (2004); 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)
[CrossRef]

J. Math. Phys. (1)

H. Ardavan, "Method of handling the divergences in the radiation theory of sources that move faster than their waves," J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

J. Opt. Soc. Am. A (3)

Phys. Rev. E (2)

H. Ardavan, "Reply to Comments on 'Generation of focused, nonspherically decaying pulses of the electromagnetic radiation'," Phys. Rev. E 62, 3010-3013 (2000).
[CrossRef]

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

Usp. Fiz. Nauk (1)

B. M. Bolotovskii and A. V. Serov, "Radiation of superluminal sources in vacuum," Usp. Fiz. Nauk 175, 943-955 (2005).
[CrossRef]

Other (3)

R. F. Hoskins, Generalised Functions (Horwood, 1979), Chap. 7.

J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale U. Press, 1923), Dover reprint (1952).

R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2 (Interscience, 1966).

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Equations (15)

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2 A 1 c 2 2 A t 2 = 4 π c j ,
j r , φ , z ( r , φ , z , t ) = j r , φ , z ( r , φ ̂ , z ) ,
φ ̂ φ ω t
2 G z 1 c 2 2 G z t 2 = 4 π c r δ ( r r ) δ ( φ ω t φ ̂ ) δ ( z z )
A z ( r P , φ ̂ P , z P ) = c 1 j z ( r , φ ̂ , z ) G z ( r , φ ̂ , z ; r P , φ ̂ P , z P ) r d r d φ ̂ d z ,
G z = φ = φ j 1 R ( φ ) r r P sin ( φ P φ ) ,
R ( φ ) = [ ( z P z ) 2 + r P 2 + r 2 2 r P r cos ( φ P φ ) ] 1 2
B = P × ( A z e ̂ z ) = e ̂ z × P A z = c 1 e ̂ z × j z P G z r d r d φ ̂ d z ,
2 B 1 c 2 2 B t 2 = 4 π c × j ,
B = c 1 e ̂ z × j z G z r d r d φ ̂ d z .
B = c 1 e ̂ z × j z ret R ( φ ) r d r d φ d z ,
φ ̂ ret = φ ω [ t P R ( φ ) c ]
V j = V 0 cos [ m ω ( j Δ t t ) ] cos ( Ω t ) ,
P cusp P sub = C R μ ,
J ( β 3 ) d β = J ( α ) δ ( α β 3 ) d α d β = 2 9 J ( α ) α 5 3 d α ,

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