Abstract

The characteristic dimensions of Bessel beams are fully determined by the corresponding Bessel functions. We consider a way of obtaining a narrower diameter of the central core of a diffractive pattern generated by the Bessel beams. The method relies on superposition of two or more Bessel beams with appropriately chosen amplitudes and widths. The disturbing influence of the aperture’s edges can be eliminated by addition of the proper amplitude filter.

© 1996 Optical Society of America

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References

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  1. A. C. S. van Heel, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1963), Vol.1, pp. 289–329.
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  3. V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, Appl. Opt. 34, 5761 (1995).
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  4. J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  5. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
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  6. A. Vasara, J. Turunen, A. T. Friberg, J. Opt. Soc. Am. A 6, 1748 (1989).
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  7. G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
    [CrossRef]
  8. F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
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  9. W. D. Montgomery, J. Opt. Soc. Am. 57, 772 (1967).
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  11. S. De Nicola, Opt. Commun. 80, 299 (1991).
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  12. P. L. Overfelt, C. S. Kenney, J. Opt. Soc. Am. A 8, 732 (1991).
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  14. Z. Jaroszewicz, J. Sochacki, A. Kolodziejczyk, L. R. Staronski, Opt. Lett. 18, 1893 (1993).
    [CrossRef] [PubMed]

1995 (1)

1993 (2)

1992 (1)

1991 (2)

1990 (1)

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

1989 (1)

1987 (2)

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

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

1983 (1)

A. W. Lohmann, J. Ojeda-Castaňeda, N. Streibl, Opt. Acta 30, 1259 (1983).
[CrossRef]

1967 (1)

1952 (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Bloisi, F.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

Cavaliere, P.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

Christensen, D. A.

Churin, E. G.

Cox, A. J.

D’Anna, J.

De Nicola, S.

S. De Nicola, Opt. Commun. 80, 299 (1991).
[CrossRef]

Durnin, J.

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

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

Eberly, J. H.

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

Friberg, A. T.

Gwynn, R. B.

Jaroszewicz, Z.

Kenney, C. S.

Kolodziejczyk, A.

Koronkevich, V. P.

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castaňeda, N. Streibl, Opt. Acta 30, 1259 (1983).
[CrossRef]

Martelucci, S.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

Miceli, J. J.

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

Mikhaltsova, I. A.

Montgomery, W. D.

Ojeda-Castaneda, J.

A. W. Lohmann, J. Ojeda-Castaňeda, N. Streibl, Opt. Acta 30, 1259 (1983).
[CrossRef]

Overfelt, P. L.

Sochacki, J.

Staronski, L. R.

Streibl, N.

A. W. Lohmann, J. Ojeda-Castaňeda, N. Streibl, Opt. Acta 30, 1259 (1983).
[CrossRef]

Toraldo di Francia, G.

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Turunen, J.

van Heel, A. C. S.

A. C. S. van Heel, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1963), Vol.1, pp. 289–329.
[CrossRef]

Vasara, A.

Vicari, L.

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

Yurlov, Yu. I.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nuovo Cimento D (1)

F. Bloisi, L. Vicari, P. Cavaliere, S. Martelucci, Nuovo Cimento D 12, 757 (1990).
[CrossRef]

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Opt. Acta (1)

A. W. Lohmann, J. Ojeda-Castaňeda, N. Streibl, Opt. Acta 30, 1259 (1983).
[CrossRef]

Opt. Commun. (1)

S. De Nicola, Opt. Commun. 80, 299 (1991).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

Other (1)

A. C. S. van Heel, in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1963), Vol.1, pp. 289–329.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Solid curve, value of the central peak of the intensity for the interference of the J0 beam with a plane wave in the function of first zero position normalized to the position of the first zero of the J0 beam, i.e., snorm = s0/s00, where s00 = 0.7655π. Dotted curve, approximate relation given by Eq. (4b).

Fig. 2
Fig. 2

On-axis intensity for the interference of the J0 beam with the plane wave. (a) Infinite aperture; the distribution is calculated with the help of relation (5) for a = 0.65 and α1 = 4.5 × 10−3 rad. (b) Finite aperture; the distribution is calculated with the help of Eq. (6) for R = 4.5 mm; other parameters as in the previous case. (c) Apodized finite aperture; the distribution is calculated with the help of Eq. (6), where the integrand is additionally multiplied by the function A(r) given by Eq. (7). ΔR = 0.25R; other parameters as in the previous case.

Fig. 3
Fig. 3

Transversal intensity distribution in the minimum plane z8 = 531.25 mm (eighth self-image plane). (a) Infinite aperture; the distribution is calculated with the help of relation (8) for a = 0.65 and α1 = 4.5 × 10−3 rad (the J02 distribution is shown for comparison). (b) Apodized finite aperture; the distribution is calculated with the help of Eq. (6), where the integrand is additionally multiplied by the function A(r) given by Eq. (7). R = 4.5 mm, ΔR = 0.25R, other parameters as in the previous case. The lower curve in both figures represents the modulus of the difference between the two distributions, multiplied by a factor of 10.

Equations (9)

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I ( ρ , z ) | exp ( i k γ 1 z ) J 0 ( k α 1 ρ ) + a exp ( i k γ 2 z ) J 0 ( k α 2 ρ ) | 2 ,
z m = ( m + 1 / 2 ) λ γ 2 γ 1 , m = 0 , 1 , .
I ( s , z m ) [ J 0 ( s ) a J 0 ( c s ) ] 2 ,
s 0 = 2 [ ( 1 a ) / ( 1 a c 2 ) ] 1 / 2 ,
I ( 0 ) / I 0 = δ s 0 4 , δ = ( 1 a c 2 ) 2 / 16 .
I ( z ) 1 + a 2 + 2 a cos ( k α 1 2 z / 2 ) ,
I ( s , z ) = ( k / z ) 2 × | 0 R exp ( i k r 2 / 2 z ) J 0 ( k r ρ / z ) [ J 0 ( k α 1 r ) + a ] r d r | 2
A ( r ) = cos 2 [ π ( r R + Δ R ) / 2 Δ R ] , r R Δ R , R , A ( r ) = 1 elsewhere ,
I ( s ) [ J 0 ( s ) a ] 2 .

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