Abstract

A unified description of free-space cylindrical vector beams is presented that is an integral transformation solution to the vector Helmholtz equation and the transversality condition. In the paraxial condition, this solution not only includes the known J1 Bessel–Gaussian vector beam and the axisymmetric Laguerre–Gaussian vector beam that were obtained by solving the paraxial wave equations but also predicts two kinds of vector beam, called a modified Bessel–Gaussian vector beam.

© 2007 Optical Society of America

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2007 (2)

2006 (2)

2005 (1)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (2)

1998 (3)

1997 (1)

1996 (1)

1994 (2)

1981 (1)

1975 (1)

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

Ashkin, A.

A. Ashkin, IEEE J. Quantum Electron. 6, 841 (2000).
[CrossRef]

Bandres, M. A.

Biss, D. P.

Bosch, S.

Brown, T.

Brown, T. G.

Carnicer, A.

Chen, J.

Clark, G. H.

Davis, L. W.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Enderlein, J.

Greene, P. L.

Guo, H.

Gutiérrez-Vega, J. C.

Hall, D. G.

Jordan, R. H.

Lax, M.

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

Leger, J. R.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Li, C.-F.

C.-F. Li, Phys. Rev. A 76, 013811 (2007).
[CrossRef]

Louisell, W. H.

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

Martínez-Herrero, R.

McKnight, W. B.

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

Mejías, P. M.

Pampaloni, F.

Patsakos, G.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Ruschin, S.

Seshadri, S. R.

Tovar, A. A.

Youngworth, K.

Youngworth, K. S.

Zhan, Q.

Zhuang, S.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

A. Ashkin, IEEE J. Quantum Electron. 6, 841 (2000).
[CrossRef]

J. Opt. Soc. Am. A (8)

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (2)

C.-F. Li, Phys. Rev. A 76, 013811 (2007).
[CrossRef]

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

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

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Figures (1)

Fig. 1
Fig. 1

Dependence of normalized transverse intensity on the radial coordinate at the focal plane, where k w 0 = 1000 and r is in units of wavelength λ. Solid curve, β = 0.002 k ; dashed curve, β = 0.005 k .

Equations (26)

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2 E ( x ) + k 2 E ( x ) = 0 ,
E ( x ) = 0 .
E ( x ) = 1 2 π k 2 0 k k ρ d k ρ 0 2 π d φ A ( k ρ , φ ) exp ( i k x ) ,
A ( k ρ , φ ) = P A ̃ ( k ρ , φ )
P = ( s x p x s y p y s z p z ) ( s p )
s = e φ ,
p = k x k e ρ k ρ k e x .
A ̃ = ( l s l p ) A ( k ρ ) l ̃ A ( k ρ ) ,
exp ( i ρ cos ψ ) = m = i m J m ( ρ ) exp ( i m ψ ) ,
E ( x ) = i l s k 2 e ϕ 0 k A ( k ρ ) exp ( i x k x ) J 1 ( r k ρ ) k ρ d k ρ + i l p k 2 e r 0 k k x k A ( k ρ ) exp ( i x k x ) J 1 ( r k ρ ) k ρ d k ρ l p k 2 e x 0 k k ρ k A ( k ρ ) exp ( i x k x ) J 0 ( r k ρ ) k ρ d k ρ .
A ( k ρ ) = A 0 exp ( w 0 2 2 k ρ 2 ) A M ( k ρ ) ,
Δ θ = 1 k w 0 1 ,
E ( x ) = [ ( l s e ϕ + l p e r ) E T ( r , x ) l p e x E L ( r , x ) ] exp ( i k x ) ,
E T ( r , x ) = i k 2 0 A ( k ρ ) J 1 ( r k ρ ) k ρ d k ρ ,
E L ( r , x ) = 1 k 2 0 k ρ k A ( k ρ ) J 0 ( r k ρ ) k ρ d k ρ ,
A ( k ρ ) = A 0 exp ( w 2 2 k ρ 2 ) A M ( k ρ ) ,
w 2 = w 0 2 ( 1 + i x x R ) ,
A M = 1 ,
A ( k ρ ) = A 0 exp ( w 0 2 2 k ρ 2 ) .
E T ( r , x ) = i 2 π A 0 4 k 2 w 2 r w exp ( r 2 4 w 2 ) × [ I 0 ( r 2 4 w 2 ) I 1 ( r 2 4 w 2 ) ] ,
A M = exp ( w 0 2 2 β 2 ) J 1 ( β w 0 2 k ρ ) ,
E T ( r , x ) = i A 0 k 2 w 2 I 1 ( w 0 2 w 2 β r ) × exp [ 1 2 w 2 ( r 2 i β 2 w 0 4 x x R ) ] .
A M = exp ( w 0 2 2 β 2 ) I 1 ( β w 0 2 k ρ ) ,
E T ( r , x ) = i A 0 k 2 w 2 J 1 ( w 0 2 w 2 β r ) exp [ 1 2 w 2 ( r 2 + i β 2 w 0 2 x k ) ] .
A M = k ρ k L n 1 ( α 2 2 k ρ 2 ) ,
E T ( r , x ) = i A 0 k 3 w 3 ( 1 + α 2 w 2 ) n r w × exp ( r 2 2 w 2 ) L n 1 ( α 2 w 2 + α 2 r 2 2 w 2 ) .

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