Abstract

The nonparaxial wave obtained by Seshadri [Appl. Opt. 45, 5335 (2006)] is correct. The difference in the input field distributions of the nonparaxial wave and the corresponding paraxial beam is correct and is not caused by any error in the treatment. As is to be expected, in the appropriate limit, the nonparaxial wave reduces to the paraxial beam for 0z including the secondary source plane and for z.

© 2008 Optical Society of America

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References

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  1. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
    [CrossRef]
  2. S. R. Seshadri, “Virtual sources for higher order Gaussian beams,” presented at the Progress in Electromagnetic Research Symposium, Cambridge, Massachusetts, 1-5 July 2002.
  3. S. R. Seshadri, “Electromagnetic Gaussian beam beyond the paraxial approximation,” presented at the 2004 USNC/URSI National Radio Science Meeting, Monterey, California, 20-25 June 2004.
  4. H. Kogelnik, Invited talk at the International Quantum Electronics Conference, Kyoto, 1970.
  5. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684-685 (1971).
    [CrossRef]
  6. G. P. Agrawal and D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575-578 (1979).
    [CrossRef]
  7. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177-1179 (1979).
    [CrossRef]
  8. M. Couture and P. A. Belanger, “From Gaussian beam to complex source point spherical wave,” Phys. Rev. A 24, 355-359 (1981).
    [CrossRef]
  9. S. R. Seshadri, “Independent waves in complex source point theory,” Opt. Lett. 32, 3218-3220 (2007).
    [CrossRef] [PubMed]

2007 (1)

1981 (1)

M. Couture and P. A. Belanger, “From Gaussian beam to complex source point spherical wave,” Phys. Rev. A 24, 355-359 (1981).
[CrossRef]

1979 (2)

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

1971 (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684-685 (1971).
[CrossRef]

Agrawal, G. P.

Belanger, P. A.

M. Couture and P. A. Belanger, “From Gaussian beam to complex source point spherical wave,” Phys. Rev. A 24, 355-359 (1981).
[CrossRef]

Couture, M.

M. Couture and P. A. Belanger, “From Gaussian beam to complex source point spherical wave,” Phys. Rev. A 24, 355-359 (1981).
[CrossRef]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177-1179 (1979).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684-685 (1971).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Invited talk at the International Quantum Electronics Conference, Kyoto, 1970.

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Pattanayak, D. N.

Seshadri, S. R.

S. R. Seshadri, “Independent waves in complex source point theory,” Opt. Lett. 32, 3218-3220 (2007).
[CrossRef] [PubMed]

S. R. Seshadri, “Virtual sources for higher order Gaussian beams,” presented at the Progress in Electromagnetic Research Symposium, Cambridge, Massachusetts, 1-5 July 2002.

S. R. Seshadri, “Electromagnetic Gaussian beam beyond the paraxial approximation,” presented at the 2004 USNC/URSI National Radio Science Meeting, Monterey, California, 20-25 June 2004.

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684-685 (1971).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Rev. A (3)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177-1179 (1979).
[CrossRef]

M. Couture and P. A. Belanger, “From Gaussian beam to complex source point spherical wave,” Phys. Rev. A 24, 355-359 (1981).
[CrossRef]

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Other (3)

S. R. Seshadri, “Virtual sources for higher order Gaussian beams,” presented at the Progress in Electromagnetic Research Symposium, Cambridge, Massachusetts, 1-5 July 2002.

S. R. Seshadri, “Electromagnetic Gaussian beam beyond the paraxial approximation,” presented at the 2004 USNC/URSI National Radio Science Meeting, Monterey, California, 20-25 June 2004.

H. Kogelnik, Invited talk at the International Quantum Electronics Conference, Kyoto, 1970.

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Equations (12)

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F p ( ρ , z ) = exp ( i k z ) f p ( ρ , z ) ,
F n p ( ρ , z ) = exp ( i k z ) f n p ( ρ , z ) ,
f p ( ρ , z ) = N ( i b z i b ) exp [ i k ρ 2 2 ( z i b ) ] .
f p ( ρ , z ) = N ( i b z ) exp ( i k ρ 2 2 z ) .
f n p ( ρ , z ) = m = 0 m = f 0 2 m f ( m ) ( ρ , z ) .
f n p ( ρ , z ) = N i b exp [ i k ( ρ 2 + z 2 ) 1 / 2 ] ( ρ 2 + z 2 ) 1 / 2 exp ( i k z ) .
F n p ( ρ , z ) = N i b exp [ i k ( ρ 2 + z 2 ) 1 / 2 ] ( ρ 2 + z 2 ) 1 / 2 .
F n p ( ρ , z ) = N b 0 d η η J 0 ( η ρ ) ζ 1 exp ( i ζ z ) ,
F n p ( ρ , z ) = N i b exp ( k b ) exp { i k [ ρ 2 + ( z i b ) 2 ] 1 / 2 } [ ρ 2 + ( z i b ) 2 ] 1 / 2 .
F n p ( ρ , z ) = N b exp ( k b ) 0 d η η J 0 ( η ρ ) ζ 1 exp [ i ζ ( z i b ) ] ,
F p ( ρ , 0 ) = N exp ( ρ 2 / w 0 2 ) ,
F n p ( ρ , 0 ) = N i b exp ( k b ) exp [ i k ( ρ 2 b 2 ) 1 / 2 ] ( ρ 2 b 2 ) 1 / 2 .

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