Abstract

We report the writing of Fresnel phase-encoded lenses onto programmable spatial light modulators (SLM’s). When the product of the phase-encoded lens and the two-dimensional Fourier transform of a desired output spatial pattern is written onto the SLM, the desired spatial pattern is focused at programmable distances from the SLM. More importantly the inverted version of the desired pattern normally produced is encoded onto a diverging beam and is not imaged. Theoretical analysis and experimental results using the magneto-optic SLM are presented.

© 1989 Optical Society of America

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References

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  1. M. V. Klein, Optics (Wiley, New York, 1970), Chap. 8.
  2. M. R. Feldman, C. C. Guest, Appl. Opt. 26, 4377 (1987).
    [CrossRef] [PubMed]
  3. J. A. Davis, S. W. Connely, G. W. Bach, R. A. Lilly, D. M. Cottrell, Opt. Lett. 14, 102 (1989).
    [CrossRef] [PubMed]
  4. J. L. Horner, J. R. Leger, Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]
  5. W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).
  6. D. M. Cottrell, R. A. Lilly, J. A. Davis, T. Day, Appl. Opt. 26, 3755 (1987).
    [CrossRef] [PubMed]
  7. D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

1989 (1)

1987 (2)

1985 (1)

1984 (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

1983 (1)

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Bach, G. W.

Connely, S. W.

Cottrell, D. M.

Davis, J. A.

Day, T.

Feldman, M. R.

Guest, C. C.

Horner, J. L.

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 8.

Leger, J. R.

Lilly, R. A.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Appl. Opt. (3)

Opt. Eng. (2)

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Opt. Lett. (1)

Other (1)

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 8.

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Figures (3)

Fig. 1
Fig. 1

Diagram showing the input and output planes.

Fig. 2
Fig. 2

Photograph showing the output pattern distribution for a Fresnel zone plate that takes the input beam into 32 output spots at a focal length of 0.8 m. Note that only the +1 diffracted order is shown.

Fig. 3
Fig. 3

Photographs showing the output pattern distribution for a multiplexed filter that simultaneously forms (a) the letter R at a focal length of 1.5 m and (b) the letter S at a focal length of 2.0 m.

Equations (10)

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T ( x 1 , y 1 ) exp { i 2 π λ [ z 2 + ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 ] 1 / 2 } × d x 1 d y 1 .
exp [ i 2 π ( x 2 2 + y 2 2 ) 2 z λ ] T ( x 1 , y 1 ) exp [ i 2 π ( x 1 2 + y 1 2 ) 2 z λ ] × exp [ i 2 π ( x 1 x 2 + y 1 y 2 ) z λ ] d x 1 d y 1 .
Z 2 F ^ { Z 1 T } ,
T = Z 1 * F ^ - 1 { G Z 2 * } .
T = ½ [ Z 1 ( F ^ - 1 { G Z 2 * } ) * + Z 1 * F ^ - 1 { G Z 2 * } ] .
½ Z 2 F ^ { Z 1 Z 1 ( F ^ - 1 { G Z 2 * } ) * } + ½ Z 2 F ^ { F ^ - 1 { G Z 2 * } } .
z c = L 1 Δ 1 / λ = N 1 Δ 1 2 / λ .
Z 1 = exp [ i 2 π ( x 1 2 + y 1 2 ) 2 z λ ] .
Z 2 = exp [ i 2 π ( x 2 2 + y 2 2 ) 2 z λ ] = exp [ i 2 π m 2 ( x 1 2 + y 1 2 ) 2 z λ ] .
T = Z 1 A * F ^ * { G Z 2 A * } + Z 1 B * F ^ * { H Z 2 B * } .

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