Abstract

The virtual source for generation of the fundamental scalar Bessel–Gauss wave is identified. An expression is derived for the Bessel–Gauss wave, which, in the appropriate limit, yields the paraxial approximation for the fundamental Bessel–Gauss beam. For the azimuthally symmetric beam, the first-order nonparaxial correction to the on-axis field is also determined. This nonparaxial correction reduces correctly to that of the fundamental Gaussian beam in the appropriate limit.

© 2002 Optical Society of America

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References

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  1. See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1967), Chap. 6.
  2. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  3. C. Altucci, R. Bruzzese, D. D'Antuoni, C. de Lisio, and S. Solimeno, J. Opt. Soc. Am. B 17, 34–42 (2000).
    [CrossRef]
  4. C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
    [CrossRef]
  5. F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
    [CrossRef]
  6. G. A. Deschamps, Electron. Lett. 7, 684–685 (1971).
    [CrossRef]
  7. L. B. Felsen, J. Opt. Soc. Am. 66, 751–760 (1976).
  8. E. Heyman and L. B. Felsen, J. Opt. Soc. Am. A 18, 1588–1611 (2001).
    [CrossRef]
  9. C. J. R. Sheppard, J. Opt. Soc. Am. A 18, 1579–1587 (2001).
    [CrossRef]
  10. M. Couture and P. A. Belanger, Phys. Rev. A 24, 355–359 (1981).
    [CrossRef]

2001

2000

1987

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1981

M. Couture and P. A. Belanger, Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

1978

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

1976

1971

G. A. Deschamps, Electron. Lett. 7, 684–685 (1971).
[CrossRef]

1967

See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1967), Chap. 6.

Altucci, C.

Belanger, P. A.

M. Couture and P. A. Belanger, Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Bruzzese, R.

Couture, M.

M. Couture and P. A. Belanger, Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

D'Antuoni, D.

de Lisio, C.

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Felsen, L. B.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Heyman, E.

Miceli, Jr., J. J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, J. Opt. Soc. Am. A 18, 1579–1587 (2001).
[CrossRef]

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

Solimeno, S.

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

Yariv, A.

See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1967), Chap. 6.

Electron. Lett.

G. A. Deschamps, Electron. Lett. 7, 684–685 (1971).
[CrossRef]

IEE J. Microwaves Opt. Acoust.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105–112 (1978).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491–495 (1987).
[CrossRef]

Phys. Rev. A

M. Couture and P. A. Belanger, Phys. Rev. A 24, 355–359 (1981).
[CrossRef]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Other

See, for example, A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1967), Chap. 6.

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Equations (22)

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Fρ,ϕ,z=Fmρ,zcos mϕ.
2ρ2+1ρρ-m2ρ2+2z2+k2Fmρ,z=-Sexδρ-ρexρδz-zex,
Fmρ,z=0dηηJmηρF¯mη,z,
F¯mη,z=0dρρJmηρFmρ,z,
Fmρ,z=0dηηJmηρJmηρex×Sexi2ζexpiζz-zex
ζ=k2-η21/2.
Fmρ,z=expikziSex2kexp-ikzex×0dηηJmηρJmηρexexp-iη22kz-zex.
Fmρ,z=expikziSex2kexp-ikzex×exp-32mπi-ikz-zexexpikρex22z-zex×expikρ22z-zexJm-kρexρz-zex.
Fm,pρ,0=expγexp-ρ2/w02Jmβρ,
γ=β2w02/4.
zex=i12kw02=ib.
ρex=βkzex=i12βw02=id.
Sex=-2ib exp-kbexp32mπi.
Fm,pρ,z=expikz1+iz/bexpγ1+iz/b×exp-ρ2w021+iz/bJmβρ1+iz/b,
Fmρ,z=b exp-kbexp32mπi×0dηηJmηρJmηidexpiζz-ibζ.
2x2+2y2+2z2+k2Gr,rex=-Sexδx-xexδy-yexδz-zex
Gr,rex=SexexpikR4πR,
R=x-xex2+y-yex2+z-zex21/2.
Fρ,ϕ,z=-ib2πexp-kbexp32mπi×02πdϕex cos mϕexexpikRR,
R=ρ2-d2-i2ρd cosϕex-ϕ+z-ib21/2.
F00,z=b exp-kb0dηηJ0ηidexpiζz-ibζ.
F00,z=expikz1+iz/bexpγ1+iz/b×1+1k2w0221+iz/b×L1-γ1+iz/b-L2-γ1+iz/b,

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