Abstract

It is shown that the approach proposed by Lax [Phys. Rev. A11, 1365 (1975)] for studying the propagation of an electromagnetic beam beyond the paraxial approximation can be efficiently employed even when the beam under consideration presents a very nonparaxial character. The method that we present consists of applying a nonlinear resummation scheme, the so-called δ transformation, to the divergent perturbative series arising from the Lax scheme. Numerical results pertinent to the evaluation of transverse and longitudinal components of the electric field are presented for the particular case of vectorial Gaussian beams, showing the effectiveness of the method.

© 2003 Optical Society of America

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  1. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  2. A. Wünsche, J. Opt. Soc. Am. A 9, 765 (1992).
    [CrossRef]
  3. S. R. Seshadri, J. Opt. Soc. Am. A 19, 2134 (2002).
    [CrossRef]
  4. G. A. Baker and P. R. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, Cambridge, 1996).
  5. P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
    [CrossRef]
  6. E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989).
    [CrossRef]
  7. U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
    [CrossRef] [PubMed]
  8. E. J. Weniger, Phys. Rev. A 56, 5165 (1997).
    [CrossRef]
  9. E. J. Weniger, Phys. Rev. Lett. 77, 2859 (1996).
    [CrossRef] [PubMed]
  10. R. Simon, E. C. G. Sudarshan, and N. Mukunda, J. Opt. Soc. Am. A 3, 536 (1986).
    [CrossRef]
  11. T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
    [CrossRef]
  12. R. Borghi, A. Ciattoni, and M. Santarsiero, J. Opt. Soc. Am. A 19, 1207 (2002).
    [CrossRef]

2002 (2)

2000 (2)

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
[CrossRef]

1997 (1)

E. J. Weniger, Phys. Rev. A 56, 5165 (1997).
[CrossRef]

1996 (1)

E. J. Weniger, Phys. Rev. Lett. 77, 2859 (1996).
[CrossRef] [PubMed]

1992 (1)

1989 (1)

E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989).
[CrossRef]

1986 (1)

1985 (1)

1975 (1)

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

Baker, G. A.

G. A. Baker and P. R. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, Cambridge, 1996).

Becher, J.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

Borghi, R.

Ciattoni, A.

Fukumitsu, O.

Graves-Morris, P. R.

P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
[CrossRef]

G. A. Baker and P. R. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, Cambridge, 1996).

Jentschura, U. D.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

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]

Mukunda, N.

Roberts, D. E.

P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
[CrossRef]

Salam, A.

P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
[CrossRef]

Santarsiero, M.

Seshadri, S. R.

Simon, R.

Soff, G.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

Sudarshan, E. C. G.

Takenaka, T.

Weniger, E. J.

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

E. J. Weniger, Phys. Rev. A 56, 5165 (1997).
[CrossRef]

E. J. Weniger, Phys. Rev. Lett. 77, 2859 (1996).
[CrossRef] [PubMed]

E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989).
[CrossRef]

Wünsche, A.

Yokota, M.

Comput. Phys. Rep. (1)

E. J. Weniger, Comput. Phys. Rep. 10, 189 (1989).
[CrossRef]

J. Comp. Appl. Math. (1)

P. R. Graves-Morris, D. E. Roberts, and A. Salam, J. Comp. Appl. Math. 122, 51 (2000).
[CrossRef]

J. Opt. Soc. Am. A (5)

Phys. Rev. A (2)

E. J. Weniger, Phys. Rev. A 56, 5165 (1997).
[CrossRef]

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

Phys. Rev. Lett. (2)

E. J. Weniger, Phys. Rev. Lett. 77, 2859 (1996).
[CrossRef] [PubMed]

U. D. Jentschura, J. Becher, E. J. Weniger, and G. Soff, Phys. Rev. Lett. 85, 2446 (2000).
[CrossRef] [PubMed]

Other (1)

G. A. Baker and P. R. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, Cambridge, 1996).

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