Abstract

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.

© 1996 Optical Society of America

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References

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1995

1993

1992

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).

Andres, P.

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.

Heckenberg, N. R.

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

S. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
[CrossRef] [PubMed]

Kolodziejczyk, A.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

S. B. Vinas, Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, “Zone plates with black focal spots,” Appl. Opt. 31, 192–198 (1992).
[CrossRef] [PubMed]

Martinez-Corral, M.

McDuff, R.

Miceli, J. J.

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

Ojeda-Castaneda, J.

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).

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).

Ramirez, G.

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).

Smith, C. P.

Sypek, M.

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).

Vinas, S. B.

White, A. G.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Opt. Eng.

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).

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 (6)

Fig. 1
Fig. 1

Patterns written onto the MOSLM that form (a) the J 0 Bessel function beam, (b) the J 1 Bessel function beam, and (c) J 2 Bessel function beam.

Fig. 2
Fig. 2

Output intensities measured at a distance of 1.55 m from the MOSLM showing (a) the J 0 Bessel function beam, (b) the J 1 Bessel function beam, and (c) the J 2 Bessel function beam.

Fig. 3
Fig. 3

Output intensity forthe J 1 Bessel function beam at distances of (a) 0.9 m, (b) 1.55 m, (c) 2.20 m.

Fig. 4
Fig. 4

Interference patterns formed between the dc beam and the J 1 Bessel function beam at distances of (a) 1.128 m, (b) 1.199 m, (c) 1.270 m.

Fig. 5
Fig. 5

Formation of higher-order Bessel function beams by the binary patterns shown in Fig. 1.

Fig. 6
Fig. 6

Interference patterns formed between p = 1 and p = 3 harmonics of the binarized pattern for the J 0 Bessel function beam at distances of (a) 0.6045 m, (b) 0.6222 m, (c) 0.6400 m.

Equations (18)

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T n ( r , θ ) = exp ( i n θ ) exp ( i 2 π r / r 0 ) ,
E ( ρ , ϕ , z ) = exp ( ikz ) ikz exp ( i k ρ 2 2 z ) 0 R 0 2 π T n ( r , θ ) × exp ( i k r 2 2 z ) exp [ ikr ρ cos ( θ ϕ ) z ] 2 π r d r d θ .
E ( ρ , ϕ , z ) = exp ( ikz ) ikz exp ( i k ρ 2 2 z ) exp [ i n ( ϕ π 2 ) ] × 0 R exp ( i k r 2 2 z ) exp ( i 2 π r r 0 ) J n ( k r ρ z ) r d r .
E ( ρ , ϕ , z ) = C ( r 0 ) z J n ( 2 π ρ r 0 ) exp ( i γ n ) .
γ n = k z + n ( ϕ π 2 ) ] + π λ z r 0 2 + k ρ 2 2 z .
L = q N Δ 2 2 λ .
W 0 = 0.766 q Δ .
E dc exp ( ikz ) .
I ( z ) = E dc 2 + E J n 2 ( ρ ) + 2 E dc E J n ( ρ ) × cos [ n ( ϕ π 2 ) π λ z r 0 2 + k ρ 2 2 z ] ,
E J n ( ρ ) = C ( r 0 ) z J n ( 2 π ρ r 0 ) .
D = 2 r 0 2 λ .
p = a p T n p ( r , θ ) = p = a p exp ( inp θ ) exp ( i 2 π p r / r 0 ) ,
a 0 = 0 , a ± 1 = 2 / π , a ± 2 = 0 , a ± 3 = 2 / 3 π .
p = a p C ( r 0 / p ) z exp ( i γ n p ) J n p ( 2 π p ρ r 0 ) = K p = z exp ( i γ n p ) J n ( 2 π p ρ r 0 ) .
γ n p ( ρ , z , ϕ , r 0 ) = n p ( ϕ π 2 ) π λ p 2 z r 0 2 .
I ( z ) = ( a 0 E J 01 ) 2 + ( a 3 E J 03 ) 2 + 2 a 0 a 3 E J 01 E J 03 cos ( 8 π λ z r 0 2 ) .
D = 4 r 0 2 λ .
p = a p A p ( r , θ ) T n p ( r , θ ) .

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