Abstract

We demonstrate the existence of vector Helmholtz–Gauss (vHzG) and vector Laplace–Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel–Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz–Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu–Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.

© 2005 Optical Society of America

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  1. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004).
    [CrossRef] [PubMed]
  2. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
    [CrossRef]
  3. A. P. Kiselev, Opt. Spectrosc. 96, 479 (2004).
    [CrossRef]
  4. J. C. Gutiérrez-Vega and M. A. Bandres, J. Opt. Soc. Am. A 22, 289 (2005).
    [CrossRef]
  5. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  6. L. W. Davis and G. Patsakos, Opt. Lett. 6, 22 (1981).
    [CrossRef] [PubMed]
  7. Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
    [CrossRef]
  8. D. G. Hall, Opt. Lett. 21, 9 (1996).
    [CrossRef] [PubMed]
  9. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  10. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).
  11. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
    [CrossRef]
  12. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, Opt. Lett. 29, 44 (2004).
    [CrossRef] [PubMed]

2005

2004

2000

1996

1995

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

1987

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

1981

1975

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

Bandres, M. A.

Bouchal, Z.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Chávez-Cerda, S.

Davis, L. W.

Feshbach, H.

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

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Gutierrez-Vega, J. C.

Gutiérrez-Vega, J. C.

Hall, D. G.

Iturbe-Castillo, M. D.

Kiselev, A. P.

A. P. Kiselev, Opt. Spectrosc. 96, 479 (2004).
[CrossRef]

Lax, M.

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

Louisell, W. H.

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

McKnight, W. B.

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

Morse, P.

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

Olivík, M.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Patsakos, G.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

J. Mod. Opt.

Z. Bouchal and M. Olivík, J. Mod. Opt. 42, 1555 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

A. P. Kiselev, Opt. Spectrosc. 96, 479 (2004).
[CrossRef]

Phys. Rev. A

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

Other

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

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

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Equations (25)

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[ t 2 + 2 i k z ] { E t , H t } = 0 ,
{ E z , H z } = ( i k ) t { E t , H t } .
H t = ( ϵ 0 μ 0 ) 1 2 z ̂ × E t .
E t ( r ) = U ( X , Y , ζ ) G ( r ) ,
G ( r ) = ζ 1 exp ( r 2 w 0 2 ζ )
T 2 U ( 4 ζ 2 w 0 2 ) U ζ = 0 ,
Z ( ζ ) = exp [ k t 2 w 0 2 ( ζ 1 1 ) 4 ] ,
T 2 Ψ + k t 2 Ψ = 0 .
Ψ ( 1 ) = T W ( X , Y ) , Ψ ( 2 ) = z ̂ × Ψ ( 1 ) ,
E t ( 1 ) = Z ( ζ ) G ( r ) T W ,
E z ( 1 ) = i Z ( ζ ) G ( r ) ζ ( k t 2 k W + 2 k w 0 T W r t w 0 ) ,
H t ( 1 ) = ϵ 0 μ 0 Z ( ζ ) G ( r ) ( z ̂ × T W ) ,
H z ( 1 ) = ϵ 0 μ 0 2 i k w 0 Z ( ζ ) G ( r ) ζ ( z ̂ × T W ) r t w 0 .
E t ( 2 ) = Z ( ζ ) G ( r ) ( z ̂ × T W ) ,
E z ( 2 ) = 2 i k w 0 Z ( ζ ) G ( r ) ζ ( z ̂ × T W ) r t w 0 ,
H t ( 2 ) = ϵ 0 μ 0 Z ( ζ ) G ( r ) T W ,
H z ( 2 ) = ϵ 0 μ 0 i Z ( ζ ) G ( r ) ζ ( k t 2 k W + 2 k w 0 T W r t w 0 ) .
E TM = exp ( i k z z ) ( t W z ̂ i k t 2 k W ) ,
H TM = ϵ 0 μ 0 exp ( i k z z ) ( z ̂ × t W ) ,
E TE = exp ( i k z z ) ( z ̂ × t W ) ,
H TE = ϵ 0 μ 0 exp ( i k z z ) ( t W z ̂ i k t 2 k W ) ,
E t ( 1 ) = G ( r ) T W ¯ ,
E z ( 1 ) = 2 i k w 0 G ( r ) ζ ( T W ¯ r t w 0 ) ,
H t ( 1 ) = ϵ 0 μ 0 G ( r ) ( z ̂ × T W ¯ ) ,
H z ( 1 ) = ϵ 0 μ 0 2 i k w 0 G ( r ) ζ ( z ̂ × T W ¯ ) r t w 0 .

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