Abstract

Fields of a linearly polarized fundamental Gaussian beam are derived exactly using the propagation characteristics of a complex-source-point spherical wave diverging from the origin. Intensity distributions are calculated and compared with their counterparts in a truncated series. It is found that utility of the exact fields is limited by a discontinuity inherent in the vector potential from which they have been obtained.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  11. G. Z. Wang and J. F. Webb, Phys. Rev. E 72, 046501 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. S. Yan and B. Yao, Phys. Rev. A 77, 023827 (2008).
    [CrossRef]

2008 (1)

S. Yan and B. Yao, Phys. Rev. A 77, 023827 (2008).
[CrossRef]

2007 (2)

2005 (1)

G. Z. Wang and J. F. Webb, Phys. Rev. E 72, 046501 (2005).
[CrossRef]

2004 (1)

2003 (1)

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. E 67, 016501 (2003).
[CrossRef]

2002 (2)

Y. I. Salamin and C. H. Keitel, Phys. Rev. Lett. 88, 095005 (2002).
[CrossRef] [PubMed]

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. ST Accel. Beams 5, 101301 (2002).
[CrossRef]

2001 (1)

1992 (1)

1989 (1)

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

1985 (1)

1981 (1)

M. Couture and Pierre-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

1979 (1)

L. W. Davis, Phys. Rev. A 19, 1177 (1979).
[CrossRef]

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Alexander, D. R.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Barton, J. P.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Belanger, Pierre-A.

M. Couture and Pierre-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

Chan, C. T.

Couture, M.

M. Couture and Pierre-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

Davis, L. W.

L. W. Davis, Phys. Rev. A 19, 1177 (1979).
[CrossRef]

Fukumitsu, O.

Keitel, C. H.

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. E 67, 016501 (2003).
[CrossRef]

Y. I. Salamin and C. H. Keitel, Phys. Rev. Lett. 88, 095005 (2002).
[CrossRef] [PubMed]

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. ST Accel. Beams 5, 101301 (2002).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Lin, Z.

Liu, S.

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Luo, H.

McDonald, K. T.

K. T. McDonald, hep.princeton.edu/~mcdonald/accel/gaussian.ps.

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Mitsuhiro, Y.

Mocken, G. R.

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. E 67, 016501 (2003).
[CrossRef]

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. ST Accel. Beams 5, 101301 (2002).
[CrossRef]

Petrov, N. I.

Salamin, Y. I.

Y. I. Salamin, Appl. Phys. B. 86, 319 (2007).
[CrossRef]

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. E 67, 016501 (2003).
[CrossRef]

Y. I. Salamin and C. H. Keitel, Phys. Rev. Lett. 88, 095005 (2002).
[CrossRef] [PubMed]

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. ST Accel. Beams 5, 101301 (2002).
[CrossRef]

Takenaka, T.

Wang, G. Z.

G. Z. Wang and J. F. Webb, Phys. Rev. E 72, 046501 (2005).
[CrossRef]

Webb, J. F.

G. Z. Wang and J. F. Webb, Phys. Rev. E 72, 046501 (2005).
[CrossRef]

Wünsche, A.

Yan, S.

S. Yan and B. Yao, Phys. Rev. A 77, 023827 (2008).
[CrossRef]

Yao, B.

S. Yan and B. Yao, Phys. Rev. A 77, 023827 (2008).
[CrossRef]

Zhan, Q.

Appl. Phys. B. (1)

Y. I. Salamin, Appl. Phys. B. 86, 319 (2007).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (4)

M. Couture and Pierre-A. Belanger, Phys. Rev. A 24, 355 (1981).
[CrossRef]

S. Yan and B. Yao, Phys. Rev. A 77, 023827 (2008).
[CrossRef]

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

L. W. Davis, Phys. Rev. A 19, 1177 (1979).
[CrossRef]

Phys. Rev. E (2)

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. E 67, 016501 (2003).
[CrossRef]

G. Z. Wang and J. F. Webb, Phys. Rev. E 72, 046501 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

Y. I. Salamin and C. H. Keitel, Phys. Rev. Lett. 88, 095005 (2002).
[CrossRef] [PubMed]

Phys. Rev. ST Accel. Beams (1)

Y. I. Salamin, G. R. Mocken, and C. H. Keitel, Phys. Rev. ST Accel. Beams 5, 101301 (2002).
[CrossRef]

Other (1)

K. T. McDonald, hep.princeton.edu/~mcdonald/accel/gaussian.ps.

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Figures (3)

Fig. 1
Fig. 1

Normalized field intensities in the plane z = 0 (and along the line y = 0 ) for two values of the waist radius at focus w 0 .

Fig. 2
Fig. 2

Normalized field intensities in the plane z = 0 (and along the line y = 0 ) for four values of w 0 . Evolution of the field intensities of the LS and CSPSW representations with increased focusing are shown here separately.

Fig. 3
Fig. 3

Normalized field intensities in the plane z = 0 (and along the line y = 0 ) for focusing down to w 0 = 0.4 λ . The CSPSW representation becomes entirely of no use as ξ ξ c = 0.4 π 1.257 .

Equations (21)

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2 A + k 2 A = 0 .
A = x ̂ A 0 exp ( i k z ) Ψ ( x , y , z ) ,
E = i ω k 2 ( A ) i ω A , B = × A .
Ψ = n = 0 ε 2 n Ψ 2 n ,
E x = i E 0 f exp ( f ρ 2 i k z ) n = 0 6 ε 2 n E 2 n x ( f , ρ ) ,
E y = i E 0 f exp ( f ρ 2 i k z ) ξ υ n = 1 6 ε 2 n E 2 n y ( f , ρ ) ,
E z = E 0 f exp ( f ρ 2 i k z ) ξ n = 0 6 ε 2 n + 1 E 2 n + 1 z ( f , ρ ) ,
B y = i E 0 c f exp ( f ρ 2 i k z ) n = 0 6 ε 2 n B 2 n y ( f , ρ ) ,
B z = E 0 c f exp ( f ρ 2 i k z ) υ n = 0 5 ε 2 n + 1 B 2 n + 1 z ( f , ρ ) ,
E x = i E 0 f exp ( i k z f ρ 2 ) ,
E z = E 0 f 2 ε ξ exp ( i k z f ρ 2 ) ,
B y = i E 0 c f exp ( i k z f ρ 2 ) ,
B z = E 0 c f 2 ε υ exp ( i k z f ρ 2 ) .
A = x ̂ A 0 exp ( i k R c ) R c , R c = r 2 + ( z + i z r ) 2 .
E x = i ω A 0 exp ( i k R c ) R c + i ω A 0 k 2 exp ( i k R c ) { i k R c 2 + 1 + k 2 x 2 R c 3 3 i k x 2 R c 4 3 x 2 R c 5 } ,
E y = i ω A 0 k 2 x y exp ( i k R c ) { k 2 R c 3 3 i k R c 4 3 R c 5 } ,
E z = i ω A 0 k 2 x ( z + i z r ) exp ( i k R c ) { k 2 R c 3 3 k R c 4 3 R c 5 } ,
B y = A 0 ( z + i z r ) exp ( i k R c ) { i k R c 2 + 1 R c 3 } ,
B z = A 0 y exp ( i k R c ) { i k R c 2 + 1 R c 3 } .
exp ( i k R c ) exp ( k z r ) exp ( i k z ) exp ( f ρ 2 ) .
1 R c n = ( f i z r ) n [ 1 ( ε f ρ ) 2 ] n 2 ; n = 1 , 2 , , 5 .

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