Abstract

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A 24, 2443 (2007) ] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (μ) that is by a factor of order μ23 slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density Sμα) whose index (α) is given by one of the values 23, 2, 83, or 4.

© 2008 Optical Society of America

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References

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  1. A. V. Bessarab, A. A. Gorbunov, S. P. Martynenko, and N. A. Prudkoy, “Faster-than-light EMP source initiated by short X-ray pulse of laser plasma,” IEEE Trans. Plasma Sci. 32, 1400-1403 (2004).
    [CrossRef]
  2. 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); A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, J. Appl. Phys. corrected version of 96(8), 4614-4631 (2004).
    [CrossRef]
  3. A. V. Bessarab, S. P. Martynenko, N. A. Prudkoi, A. V. Soldatov, and V. A. Terekhin, “Experimental study of electromagnetic radiation from a faster-than-light vacuum macroscopic source,” Radiat. Phys. Chem. 75, 825-831 (2006).
    [CrossRef]
  4. B. M. Bolotovskii and A. V. Serov, “Radiation of superluminal sources in vacuum,” Radiat. Phys. Chem. 75, 813-824 (2006).
    [CrossRef]
  5. B. M. Bolotovskii and V. P. Bykov, “Radiation by charges moving faster than light,” Sov. Phys. Usp. 33, 477-487 (1990).
    [CrossRef]
  6. H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
    [CrossRef]
  7. 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]
  8. 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]
  9. V. A. Borovikov, Uniform Stationary Phase Method (Institution of Electrical Engineers, 1994).
  10. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  11. S. Sallmen, D. C. Backer, T. H. Hankins, D. Moffett, and S. Lundgren, “Simultaneous dual-frequency observations of giant pulses from the Crab pulsar,” Astrophys. J. 517, 460-471 (1999).
    [CrossRef]
  12. A. Kinkhabwala and S. E. Thorsett, “Multifrequency observation of giant radio pulses from the millisecond pulsar B1937+21,” Astrophys. J. 535, 365-372 (2000).
    [CrossRef]
  13. A. V. Popov, A. D. Kuz'min, O. M. Ul'yanov, A. A. Deshpande, A. A. Ershov, V. V. Zakharenko, V. I. Kondrat'ev, S. V. Kostyuk, B. Y. Losovskii, and V. A. Soglansnov, “Instantaneous radio spectra of giant pulses from the Crab pulsar from decimeter to decameter wavelengths,” Astron. Rep. 50, 562-568 (2006).
    [CrossRef]
  14. 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]
  15. D. Lorimer and M. Kramer, Handbook of Pulsar Astronomy (Cambridge U. Press, 2005).

2007 (1)

2006 (3)

A. V. Bessarab, S. P. Martynenko, N. A. Prudkoi, A. V. Soldatov, and V. A. Terekhin, “Experimental study of electromagnetic radiation from a faster-than-light vacuum macroscopic source,” Radiat. Phys. Chem. 75, 825-831 (2006).
[CrossRef]

B. M. Bolotovskii and A. V. Serov, “Radiation of superluminal sources in vacuum,” Radiat. Phys. Chem. 75, 813-824 (2006).
[CrossRef]

A. V. Popov, A. D. Kuz'min, O. M. Ul'yanov, A. A. Deshpande, A. A. Ershov, V. V. Zakharenko, V. I. Kondrat'ev, S. V. Kostyuk, B. Y. Losovskii, and V. A. Soglansnov, “Instantaneous radio spectra of giant pulses from the Crab pulsar from decimeter to decameter wavelengths,” Astron. Rep. 50, 562-568 (2006).
[CrossRef]

2004 (3)

A. V. Bessarab, A. A. Gorbunov, S. P. Martynenko, and N. A. Prudkoy, “Faster-than-light EMP source initiated by short X-ray pulse of laser plasma,” IEEE Trans. Plasma Sci. 32, 1400-1403 (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); A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, J. Appl. Phys. corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

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]

2003 (1)

2000 (1)

A. Kinkhabwala and S. E. Thorsett, “Multifrequency observation of giant radio pulses from the millisecond pulsar B1937+21,” Astrophys. J. 535, 365-372 (2000).
[CrossRef]

1999 (1)

S. Sallmen, D. C. Backer, T. H. Hankins, D. Moffett, and S. Lundgren, “Simultaneous dual-frequency observations of giant pulses from the Crab pulsar,” Astrophys. J. 517, 460-471 (1999).
[CrossRef]

1998 (1)

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

1990 (1)

B. M. Bolotovskii and V. P. Bykov, “Radiation by charges moving faster than light,” Sov. Phys. Usp. 33, 477-487 (1990).
[CrossRef]

Astron. Rep. (1)

A. V. Popov, A. D. Kuz'min, O. M. Ul'yanov, A. A. Deshpande, A. A. Ershov, V. V. Zakharenko, V. I. Kondrat'ev, S. V. Kostyuk, B. Y. Losovskii, and V. A. Soglansnov, “Instantaneous radio spectra of giant pulses from the Crab pulsar from decimeter to decameter wavelengths,” Astron. Rep. 50, 562-568 (2006).
[CrossRef]

Astrophys. J. (2)

S. Sallmen, D. C. Backer, T. H. Hankins, D. Moffett, and S. Lundgren, “Simultaneous dual-frequency observations of giant pulses from the Crab pulsar,” Astrophys. J. 517, 460-471 (1999).
[CrossRef]

A. Kinkhabwala and S. E. Thorsett, “Multifrequency observation of giant radio pulses from the millisecond pulsar B1937+21,” Astrophys. J. 535, 365-372 (2000).
[CrossRef]

IEEE Trans. Plasma Sci. (1)

A. V. Bessarab, A. A. Gorbunov, S. P. Martynenko, and N. A. Prudkoy, “Faster-than-light EMP source initiated by short X-ray pulse of laser plasma,” IEEE Trans. Plasma Sci. 32, 1400-1403 (2004).
[CrossRef]

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, 7760-7777(E) (2004); A. Ardavan, W. Hayes, J. Singleton, H. Ardavan, J. Fopma, and D. Halliday, J. Appl. Phys. corrected version of 96(8), 4614-4631 (2004).
[CrossRef]

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

Phys. Rev. E (1)

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

Radiat. Phys. Chem. (2)

A. V. Bessarab, S. P. Martynenko, N. A. Prudkoi, A. V. Soldatov, and V. A. Terekhin, “Experimental study of electromagnetic radiation from a faster-than-light vacuum macroscopic source,” Radiat. Phys. Chem. 75, 825-831 (2006).
[CrossRef]

B. M. Bolotovskii and A. V. Serov, “Radiation of superluminal sources in vacuum,” Radiat. Phys. Chem. 75, 813-824 (2006).
[CrossRef]

Sov. Phys. Usp. (1)

B. M. Bolotovskii and V. P. Bykov, “Radiation by charges moving faster than light,” Sov. Phys. Usp. 33, 477-487 (1990).
[CrossRef]

Other (3)

V. A. Borovikov, Uniform Stationary Phase Method (Institution of Electrical Engineers, 1994).

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

D. Lorimer and M. Kramer, Handbook of Pulsar Astronomy (Cambridge U. Press, 2005).

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Equations (37)

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P r , φ , z ( r , φ , z , t ) = s r , φ , z ( r , z ) cos ( m φ ̂ ) cos ( Ω t ) ,
π < φ ̂ π ,
φ ̂ φ ω t ,
E = P A 0 A ( c t P ) , B = P × A
A μ ( x P , t P ) = c 1 d 3 x d t j μ ( x , t ) δ ( t P t R c ) R ,
μ = 0 , , 3 .
B ns 4 3 i exp [ i ( Ω ω ) ( φ P + 3 π 2 ) ] μ = μ ± μ exp ( i μ φ ̂ P ) × j = 1 3 q ¯ j Δ 0 r ̂ d r ̂ d z ̂ Δ 1 2 u j exp ( i μ ϕ ) ,
q ¯ j ( 1 i Ω ω i Ω ω ) ,
u 1 s r cos θ P e ̂ + s φ e ̂ ,
u 2 s φ cos θ P e ̂ + s r e ̂ , u 3 s z sin θ P e ̂ ,
Δ ( r ̂ P 2 1 ) ( r ̂ 2 1 ) ( z ̂ z ̂ P ) 2 ,
ϕ ± R ̂ ± + φ ± φ P ,
φ ± = φ P + 2 π arccos [ ( 1 Δ 1 2 ) ( r ̂ r ̂ P ) ] ,
R ̂ ± [ ( z ̂ z ̂ P ) 2 + r ̂ 2 + r ̂ P 2 2 ( 1 Δ 1 2 ) ] 1 2 ,
I Δ 0 r ̂ d r ̂ d z ̂ Δ 1 2 u j exp ( i μ ϕ )
r ̂ = ( 1 + ρ 2 cosh 2 σ ) 1 2 ,
z ̂ = z ̂ P + ( r ̂ P 2 1 ) 1 2 ρ sinh σ .
ϕ ( ρ , σ ) = [ r ̂ P 2 1 2 ( r ̂ P 2 1 ) 1 2 ρ + ( r ̂ P 2 sinh 2 σ + 1 ) ρ 2 ] 1 2 + 2 π arccos { r ̂ P 1 ( 1 + ρ 2 cosh 2 σ ) 1 2 [ 1 + ( r ̂ P 2 1 ) 1 2 ρ ] } ,
ϕ = ϕ σ = 0 + 1 2 b ζ 2 ,
b 2 ϕ σ 2 σ = 0 = ρ 2 [ r ̂ P 2 1 ( r ̂ P 2 1 ) 1 2 ρ + r ̂ P 2 ρ 2 ] ( 1 + ρ 2 ) [ ( r ̂ P 2 1 ) 1 2 ρ ] .
ϕ σ σ ζ = b ζ ,
ϕ σ 2 σ ζ 2 + 2 ϕ σ 2 ( σ ζ ) 2 = b ,
I = d ρ d ζ Q ( ρ , ζ ) exp ( i β ζ 2 ) ,
Q ( ρ , ζ ) = ρ cosh σ u j exp ( i μ ϕ σ = 0 ) σ ζ ,
σ ζ = b ζ R ̂ ( 1 + ρ 2 cosh 2 σ ) ρ 2 sinh σ cosh σ [ r ̂ P 2 1 ( r ̂ P 2 1 ) 1 2 ρ + r ̂ P 2 ρ 2 cosh 2 σ ] 1 ,
b ρ 2 r ̂ P , R ̂ P 1 ,
I ( 2 π μ ) 1 2 d ρ ρ u j σ = 0 b 1 2 exp [ i ( μ ϕ σ = 0 + π 4 ) ] ( σ ζ ) σ = 0 ( 2 π μ ) 1 2 r ̂ P 1 2 exp { i [ μ ( r ̂ P + 3 π 2 ) + π 4 ] } × d ρ u j r ̂ = ( 1 + ρ 2 ) 1 2 , z ̂ = z ̂ P exp [ i μ ( arctan ρ ρ ) ] ,
R ̂ P 1 ,
I ( 2 π μ ) 1 2 r ̂ P 1 2 u j r ̂ = 1 , z ̂ = z ̂ P exp { i [ μ ( r ̂ P + 3 π 2 ) + π 4 ] } × 0 ( r ̂ > 2 1 ) 1 2 d ρ exp [ i μ ( arctan ρ ρ ) ] ,
I = 3 2 3 Γ ( 1 3 ) ( 2 π ) 1 2 μ 5 6 u j r ̂ = 1 , z ̂ = z ̂ P exp { i [ μ ( r ̂ P + 3 π 2 ) + π 12 ] } r ̂ P 1 2
B 4 3 i ( 2 π ) 1 2 r ̂ P 1 2 exp [ i ( Ω ω ) ( φ P + 3 π 2 ) ] μ = μ ± μ 1 2 sgn ( μ ) exp { i [ μ ( φ ̂ P + r ̂ P + 3 π 2 ) + π 4 sgn ( μ ) ] } j = 1 3 q ¯ j u j r ̂ = 1 , z ̂ = z ̂ P J ,
J 0 ( r ̂ > 2 1 ) 1 2 d ρ exp [ i μ ( arctan ρ ρ ) ] ,
J 3 2 3 Γ ( 1 3 ) exp ( i π 6 ) μ 1 3
S μ 2 3 , θ P = π 2 , Ω ω μ ;
S μ 2 , θ P π 2 , Ω ω μ ;
S μ 8 3 , θ P = π 2 ; Ω ω μ or j = 1 ,
S μ 4 , θ P π 2 ; Ω ω μ or j = 1.

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