Abstract

A virtual source that generates a cylindrically symmetric Laguerre–Gauss wave of radial mode number n is introduced. An expression is derived for this Laguerre–Gauss wave that in the appropriate limit yields the corresponding Laguerre–Gauss beam. From the spectral representation of the Laguerre–Gauss wave, the first three orders of nonparaxial corrections for the paraxial Laguerre–Gauss beam are determined. On the beam axis, the number of orders of nonvanishing nonparaxial corrections is found to be equal to n.

© 2002 Optical Society of America

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References

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  1. C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
    [CrossRef]
  2. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. C. Altucci, R. Bruzzese, D. D’Antuoni, C. de Lisio, and S. Solimeno, J. Opt. Soc. Am. B 17, 34 (2000).
    [CrossRef]
  5. M. Couture and P. A. Belanger, Phys. Rev. A 24, 355 (1981).
    [CrossRef]
  6. T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
    [CrossRef]
  7. E. Heyman and L. B. Felsen, J. Opt. Soc. Am. A 18, 1588 (2001), Refs. 20 and 32.
    [CrossRef]
  8. S. R. Seshadri, Opt. Lett. 27, 998 (2002).
    [CrossRef]
  9. G. P. Agrawal and D. N. Pattanayak, J. Opt. Soc. Am. 69, 575 (1979).
    [CrossRef]
  10. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), p. 847, formula 7.421.2.

2002 (1)

2001 (1)

2000 (1)

1987 (2)

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

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1985 (1)

1981 (1)

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

1979 (1)

1978 (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Agrawal, G. P.

Altucci, C.

Belanger, P. A.

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

Bruzzese, R.

Couture, M.

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

D’Antuoni, D.

de Lisio, C.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Felsen, L. B.

Fukumitsu, O.

Gori, F.

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

Gradshteyn, S.

S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), p. 847, formula 7.421.2.

Guattari, G.

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

Heyman, E.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Padovani, C.

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

Pattanayak, D. N.

Ryzhik, I. M.

S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), p. 847, formula 7.421.2.

Seshadri, S. R.

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Solimeno, S.

Takenaka, T.

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Yokota, M.

IEE J. Microwaves Opt. Acoust. (1)

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

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

Opt. Lett. (1)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other (1)

S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), p. 847, formula 7.421.2.

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Equations (32)

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t2+2/z2+k2Fnρ,z=-Sext2nδρ/ρδz-zex,
t2=2ρ2+1ρρ,
Fnρ,z=0dηηJ0ηρF¯nη,z,
F¯nη,z=0dρρJ0ηρFnρ,z,
Fnρ,z=0dηηJ0ηρ-η2n×iSex2ζexpiζz-zex
ζ=k2-η21/2.
Fnρ,z=expikziSex2kexp-ikzex×0dηηJ0ηρ-η2nexp-iη22kz-zex.
0dηηJ0ηρη2n exp-p2η2=n!2p-2n+1 exp-ρ24p2Lnρ24ρ2,
Fnρ,z=expikziSex2kexp-ikzex-1nn!2×iz-zex2k-n+1 expikρ22z-zexLn-ikρ22z-zex.
Fn,pρ,0=-1n22nn!Lnρ2/w02exp-ρ2/w02.
zex=i12kw02=ib,
Sex=-2ibw02nexp-kb.
Fn,pρ,z=expikzqz2n+1-1n22nn!×Lnvexp-v,
q2z=1+iz/b-1,
v=q2zρ2w0-2.
Fnρ,z=b exp-kbw02n×0dηηJ0ρη-η2nζ-1expiζz-ib.
t2+2/z2+k2Gρ,z=-δρ2πρδz-ib
Gρ,z=expikR/4πR,
R=ρ2+z-ib21/2.
Fnρ,z=-ib exp-kbw02nt2nexpikRR.
Fnρ,z=expikzw022w02n0dηηJ0ηρ-η2n×exp-iη22kz-ibG¯η,z,
G¯η,z=1+kw0-2G¯2η,z+kw0-4G¯4η,z+kw0-6G¯6η,z,
G¯2η,z=w02η22-w04η416q2z,
G¯4η,z=3w04η48-w06η616q2z+w08η8512q4z,
G¯6η,z=5w06η616-15w08η8256q2z+3w010η101024q4z-w012η126×4096q6z.
Fnρ,z=expikzqz2n+1-1n22n×exp-vn!Lnv+kw0-2q2zfn,2ρ,z+kw0-4q4zfn,4ρ,z+kw0-6q6zfn,6ρ,z,
fn,2ρ,z=2n+1!Ln+1v-n+2!Ln+2v,
fn,4ρ,z=6n+2!Ln+2v-4n+3!Ln+3v+12n+4!Ln+4v,
fn,6ρ,z=20n+3!Ln+3v-15n+4!Ln+4v+3n+5!Ln+5v-16n+6!Ln+6v.
fn,20,z=n!-n+1n,
fn,40,z=n!12n+2n+1nn-1,
fn,60,z=n!-16n+3n+2n+1×nn-1n-2.

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