Abstract

A new nonspreading beam is proposed for the case in which diffraction occurs only in one transverse coordinate. The beam has the shape of a pulse in one dimension and is constant in the other (slitlike shape). The intensity of the pulse’s peak remains almost constant along a finite interval on the propagation axis. The proposed beam is analyzed and demonstrated experimentally. The analogy between this beam and the temporal pulse in a dispersive medium is discussed.

© 1995 Optical Society of America

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References

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  1. E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
    [CrossRef]
  2. B. H. Kolner, M. Nazarathy, Opt. Lett. 14, 630 (1989).
    [CrossRef] [PubMed]
  3. A. W. Lohmann, D. Mendlovic, Appl. Opt. 31, 6212 (1992).
    [CrossRef] [PubMed]
  4. M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
    [CrossRef]
  5. J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  6. J. Rosen, A. Yariv, Opt. Lett. 19, 843 (1994).
    [CrossRef] [PubMed]
  7. A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7, p. 222.
  8. J. Rosen, Opt. Lett. 19, 369 (1994).
    [CrossRef] [PubMed]
  9. R. Piestun, J. Shamir, Opt. Lett. 19, 771 (1994).
    [CrossRef] [PubMed]

1994 (4)

1992 (1)

1989 (1)

1987 (1)

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

1969 (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Godil, A. A.

M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Kauffman, M. T.

M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

Kolner, B. H.

Lohmann, A. W.

Mendlovic, D.

Miceli, J. J.

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

Nazarathy, M.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7, p. 222.

Piestun, R.

Rosen, J.

Shamir, J.

Treacy, E. B.

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. T. Kauffman, W. C. Banyai, A. A. Godil, D. M. Bloom, Appl. Phys. Lett. 64, 270 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. B. Treacy, IEEE J. Quantum Electron. QE-5, 454 (1969).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

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

Other (1)

A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7, p. 222.

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Figures (3)

Fig. 1
Fig. 1

Schematic system used to obtain the PND beam.

Fig. 2
Fig. 2

Computer-simulated axial intensity distribution of the PND beam (solid curve) and the ordinary focused beam (dashed curve). The insets show the transverse cross section of the PND beam (solid curves) and the ordinary focused beam (dashed curves) at some points along the axis.

Fig. 3
Fig. 3

Holograms that produce (a) the PND beam and (b) the ordinary focused beam. The 2-D intensity distribution of (c) the PND and (d) the ordinary focused beam.

Equations (11)

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u ( x , z ) = exp [ j k ( z + 2 f ) ] j λ f × - g ( x i ) exp [ - j k f ( z x i 2 2 f + x x i ) ] d x i ,
u ( 0 , z ) = exp [ j k ( z + 2 f ) ] j λ f × - g ( x i ) exp ( - j k z x i 2 2 f 2 ) d x i .
g ( x i ) = exp { - j 2 π [ | x i b | p - ( x i a ) 2 ] } ,             p > 2 ,
u ( 0 , z ) { B exp ( j k z ) 2 ( ζ - 1 / a 2 ) ζ < - α Λ + 1 a 2 exp ( j k z ) [ C + D ( ζ - 1 a 2 ) ] - α Λ + 1 a 2 < ζ < Λ + 1 a 2 B exp ( j k z ) 2 ( ζ - 1 / a 2 ) ( 1 2 exp { - j 2 π [ ( ζ - 1 a 2 ) ( 2 b 2 p ) ] p / ( p - 2 ) ( 1 + p ) } + 1 ) Λ + 1 a 2 < ζ ,
u ( x , z 0 ) = 2 exp [ j k ( z 0 + 2 f ) ] j λ f × - cos { 2 π [ ( x i b ) p - ( x i a ) 2 ] } × exp ( - j k f x x i ) d x i .
u ( x , z 0 ) x 2 - p / 2 ( p - 1 ) cos [ 2 π ( 1 - p ) ( b x p λ f ) p / ( p - 1 ) ] .
t ( x L ) = [ g * L ( f ) ] L ( - f ) , L ( f ) = exp ( j k x 2 f ) .
s ( x L ) = 1 + 1 2 t ( x L ) + 1 2 t * ( x L ) .
u ( t , z ) = exp ( j β 0 z ) - U ( ω ) exp ( - j β 2 z 2 ω 2 ) × exp [ j ω ( t - β 1 z ) ] d ω .
u ( ŧ , z ) = exp ( j β 0 z ) 2 j π β 2 z - u ( t ) exp [ j ( ŧ - t ) 2 2 β 2 z ] d t ,
u ( ŧ , z ) = exp [ j β 0 ( z + 2 f ) ] 2 j π β 2 f × - u ( t ) exp [ - j β 2 f ( t z 2 f - ŧ t ) ] d t ,

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