Abstract

Although the technology of fixed optical interconnects has shown rapid progress, the programmability requirements remain a difficulty that has not yet been definitively solved. A new configuration of diffractive optical elements is presented that takes full advantage of the progress made in the field of fixed elements and also offers the possibility of programmability. The idea consists of serially combining a few elementary diffractive elements that might be spatially separated. One or some of these elements should be programmable. Configurations that make use of the assets of fixed elements are proposed that overcome the limitations, such as low resolution, that are associated with programmable elements. For illustration, an experiment is described.

© 1997 Optical Society of America

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References

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  1. H. Hamam, “Hartley holograms,” Appl. Opt. 35, 5286–5292 (1996).
    [CrossRef] [PubMed]
  2. S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
    [CrossRef]
  3. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Binary logic based purely on Fresnel diffraction,” Appl. Opt. 34, 5901–5906 (1995).
    [CrossRef] [PubMed]
  4. J. N. Mait, “Extension to Dammann’s method of binary phase grating design,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, ed., Proc. SPIE1052, 41–45 (1989).
    [CrossRef]
  5. F. Wyrowski, “Efficiency of quantized diffractive phase elements,” Opt. Commun. 29, 119–126 (1992).
    [CrossRef]
  6. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Diffraction efficiency of quantized phase elements: practical assessments,” Pure Appl. Opt. 5, 389–403 (1996).
    [CrossRef]
  7. J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
    [CrossRef]
  8. T. D. Wilkinson, R. J. Mears, “Breaking symmetry in the binary phase only matched filters,” Opt. Commun. 115, 26–28 (1995).
    [CrossRef]
  9. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).
    [CrossRef]
  10. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable joint fractional Talbot computer-generated holograms,” J. Opt. Soc. Am. A 12, 314–324 (1995).
    [CrossRef]
  11. J. E. Morris, M. R. Feldman, “Reconfigurable optical interconnects by a combined computer-generated hologram and spatial light modulator,” Appl. Opt. 33, 3683–3694 (1994).
    [CrossRef] [PubMed]
  12. H. Hamam, “Talbot array illuminators: a general approach,” Appl. Opt. 32, 2319–2327 (1997).
    [CrossRef]
  13. O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
    [CrossRef]

1997 (1)

H. Hamam, “Talbot array illuminators: a general approach,” Appl. Opt. 32, 2319–2327 (1997).
[CrossRef]

1996 (3)

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Diffraction efficiency of quantized phase elements: practical assessments,” Pure Appl. Opt. 5, 389–403 (1996).
[CrossRef]

H. Hamam, “Hartley holograms,” Appl. Opt. 35, 5286–5292 (1996).
[CrossRef] [PubMed]

1995 (4)

1994 (1)

1992 (2)

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

F. Wyrowski, “Efficiency of quantized diffractive phase elements,” Opt. Commun. 29, 119–126 (1992).
[CrossRef]

1970 (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Broomfield, S. E.

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Feldman, M. R.

Goodman, J. W.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Guyot, O.

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

Hamam, H.

Mait, J. N.

J. N. Mait, “Extension to Dammann’s method of binary phase grating design,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, ed., Proc. SPIE1052, 41–45 (1989).
[CrossRef]

Mears, R. J.

T. D. Wilkinson, R. J. Mears, “Breaking symmetry in the binary phase only matched filters,” Opt. Commun. 115, 26–28 (1995).
[CrossRef]

Morris, J. E.

Neil, M. A.

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

Paige, E. S.

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Wilkinson, T. D.

T. D. Wilkinson, R. J. Mears, “Breaking symmetry in the binary phase only matched filters,” Opt. Commun. 115, 26–28 (1995).
[CrossRef]

Wyrowski, F.

F. Wyrowski, “Efficiency of quantized diffractive phase elements,” Opt. Commun. 29, 119–126 (1992).
[CrossRef]

Yang, G. G.

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

Appl. Opt. (4)

Electron. Lett. (1)

S. E. Broomfield, M. A. Neil, E. S. Paige, G. G. Yang, “Programmable binary phase only optical device based on FLC SLM,” Electron. Lett. 28, 26–28 (1992).
[CrossRef]

IBM J. Res. Dev. (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

T. D. Wilkinson, R. J. Mears, “Breaking symmetry in the binary phase only matched filters,” Opt. Commun. 115, 26–28 (1995).
[CrossRef]

F. Wyrowski, “Efficiency of quantized diffractive phase elements,” Opt. Commun. 29, 119–126 (1992).
[CrossRef]

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

Pure Appl. Opt. (1)

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Diffraction efficiency of quantized phase elements: practical assessments,” Pure Appl. Opt. 5, 389–403 (1996).
[CrossRef]

Other (1)

J. N. Mait, “Extension to Dammann’s method of binary phase grating design,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, ed., Proc. SPIE1052, 41–45 (1989).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Fixed-programmable configuration: dynamic multifaceted architecture. The programmable element modulates the phases of the facets.

Fig. 2
Fig. 2

Fixed-programmable architecture: dynamic multifaceted architecture using the fractional Talbot effect. The programmable element is used to select the facets to be activated.

Fig. 3
Fig. 3

Programmable two-layer element used for selective illumination of the fixed DOE (1-to-4 decoder). When the value -1 moves according to the arrow, the nonzero element of h(x, y, z) moves in the opposite way.

Fig. 4
Fig. 4

Repeated hologram activated by the first DOE according to Fig. 2. The three remaining holograms are deactivated.

Fig. 5
Fig. 5

Optical reconstructions of four repeated holograms according to Fig. 2. The programmable element is used to select one fixed hologram, reconstructing one of patterns (a)–(d).

Tables (1)

Tables Icon

Table 1 Various Arrangements for the Fixed-Programmable Configuration and the Double-Programmable Configuration

Equations (5)

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r(x)=h(x)c(x),
h(x, z)=a=0q/2-1T(a, p, q)hx-d2+2adq, 0,
T(a, p, q)=2q b=0q/2-1 exp-iπ2 b2q p+b×expiπ 4baq,
h(x, y, z)=12 -ih(x, y, 0)+ihx-d2, y-d2+hx-d2, y+hx, y-d2.
h(x, y, 0)=h(x, y, 0)×f(x, y).

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