Abstract

Nondiffracting beams are of interest for optical metrology applications because the size and shape of the beams do not change as the beams propagate. We have created a generating pattern consisting of a linear combination of two nondiffracting patterns. This pattern forms a nondiffracting interference pattern that appears as a circular array of nondiffracting spots. More complicated multiplexed arrays are also constructed that simultaneously yield two different nondiffracting patterns. We generate these Bessel function arrays with a programmable spatial light modulator. Such arrays would be useful for angular alignment and for optical interconnection applications.

© 1996 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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1996

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1989

1988

1987

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1984

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

1983

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Carcole, E.

Cottrell, D. M.

Davis, J. A.

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Friberg, A. T.

Guertin, J.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Piestun, R.

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Shamir, J.

Turunen, J.

Vasara, A.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Binary patterns written onto the SLM that form (a) the J 4 Bessel function beam where q = 6, (b) the J −4 Bessel function beam where q = 6, (c) linear combination of the J 4 and the J −4 Bessel function beams where q = 6.

Fig. 2
Fig. 2

Output intensities measured at a distance of 1.55 m from the MOSLM: (a) The intensity for the J 4 Bessel function beam where q = 6 is generated from Fig. 1(a) or 1(b). (b) The circular spot array for n = 4, q = 6 generated from Fig. 1(c). The output is an array of 2n = 8 spots. (c) The circular spot array for n = 4, q = 6 rotated by an angle of α = 22.5 deg. The output array is rotated accordingly.

Fig. 3
Fig. 3

Circular spot array for n = 6, q = 4. The output is an array of 2n = 12 spots. Intensities are measured at distances of (a) 0.9 m, (b) 1.55 m, (c) 2.20 m.

Fig. 4
Fig. 4

(a) Mask that simultaneously generates the J 1 beam (for q = 4) and the circular spot array for n = 16, q = 6. (b) The output intensity pattern with the pattern shown in (a).

Equations (7)

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T n ( r , θ ) = exp ( i n θ ) exp ( i 2 π r / r 0 ) ,
E ( ρ , ϕ ) J n ( 2 π ρ r 0 ) exp ( i n ϕ ) .
T n ( r , θ ) = { exp [ i ( n θ + α ) ] + exp [ i ( n θ α ) ] } × exp ( i 2 π r / r 0 ) ,
E ( ρ , ϕ ) J n ( 2 π ρ r 0 ) { exp [ i ( n ϕ + α ) ] + exp [ i ( n ϕ α ) ] } .
I ( ρ , ϕ ) J n 2 ( 2 π ρ r 0 ) cos 2 ( n θ + α ) .
T 1 ( r , r 0 A , θ ) + T n ( r , r 0 B , θ ) = χ exp ( i θ ) exp ( i 2 π r / r 0 A ) + η [ exp ( i n θ ) + exp ( i n θ ) ] exp ( i 2 π r / r 0 B ) ,
I ( ρ , ϕ ) χ 2 J 1 2 ( 2 π ρ r 0 A ) + η 2 J n 2 ( 2 π ρ r 0 B ) cos 2 ( n ϕ ) .

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