Abstract

We investigate the cause of the insertion loss of our holographic switch by determining the relation between the diffraction efficiency and the hologram patterns generated by the control beams. According to the calculation the theoretical insertion loss is 7.4 dB with loss distribution of 0.03 dB under the conditions of a previous experiment. We find that incomplete storage of the interference pattern on the optically addressed spatial light modulator is the strongest factor determining the insertion loss.

© 1999 Optical Society of America

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References

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  1. J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.
  2. E. Marom, N. Konforti, “Dynamic optical interconnections,” Opt. Lett. 12, 539–541 (1987).
    [CrossRef] [PubMed]
  3. H. Yamazaki, M. Yamaguchi, “Experiments on a multichannel holographic optical switch with the use of a liquid-crystal display,” Opt. Lett. 17, 1228–1230 (1992).
    [CrossRef] [PubMed]
  4. D. C. O’Brien, R. J. Mears, T. D. Wilkinson, W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33, 2795–2803 (1994).
    [CrossRef] [PubMed]
  5. H. Yamazaki, S. Fukushima, “Holographic switch with a ferroelectric liquid-crystal spatial light modulator for a large-scale switch,” Appl. Opt. 34, 8137–8143 (1995).
    [CrossRef] [PubMed]
  6. H. Yamazaki, T. Matsunaga, S. Fukushima, “1 × 1104 holographic switching with a ferroelectric liquid crystal spatial light modulator,” Opt. Lett. 20, 1430–1431 (1995).
    [CrossRef] [PubMed]
  7. H. Yamazaki, T. Matsunaga, S. Fukushima, T. Kurokawa, “4 × 1204 holographic switching with an optically addressed spatial light modulator,” Appl. Opt. 36, 3063–3069 (1997).
    [CrossRef] [PubMed]
  8. S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
    [CrossRef]
  9. H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  10. S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, G. G. Yang, “Programmable binary phase-only optical device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28, 26–28 (1992).
    [CrossRef]

1997 (1)

1995 (2)

1994 (1)

1992 (2)

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

H. Yamazaki, M. Yamaguchi, “Experiments on a multichannel holographic optical switch with the use of a liquid-crystal display,” Opt. Lett. 17, 1228–1230 (1992).
[CrossRef] [PubMed]

1991 (1)

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

1987 (1)

1971 (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Broomfield, S. E.

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

Crossland, W. A.

Dammann, H.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Delboulbe, A.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

Fukushima, S.

Gortler, K.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Herriau, J. P.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

Huignard, J. P.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

Konforti, N.

Kurokawa, T.

H. Yamazaki, T. Matsunaga, S. Fukushima, T. Kurokawa, “4 × 1204 holographic switching with an optically addressed spatial light modulator,” Appl. Opt. 36, 3063–3069 (1997).
[CrossRef] [PubMed]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Marom, E.

Matsunaga, T.

Mears, R. J.

Neil, M. A. A.

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

O’Brien, D. C.

Ohno, M.

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Paige, E. G. S.

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

Pauliat, G.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

Roosen, G.

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

Wilkinson, T. D.

Yamaguchi, M.

Yamazaki, H.

Yang, G. G.

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

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Electron. Lett. (1)

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

Opt. Commun. (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Lett. (3)

Other (1)

J. P. Herriau, A. Delboulbe, J. P. Huignard, G. Roosen, G. Pauliat, “Optical beam steering for fiber array using dynamic holography,” in Digest of European Conference on Optical Communication (Convention of the National Societies of Electrical Engineers of Western Europe, Venice, Italy, 1985), Vol. 1, 419–422.

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Figures (8)

Fig. 1
Fig. 1

Structure of the proposed holographic switch.

Fig. 2
Fig. 2

Optical setup of the control system with three inputs for associating each input to a different control light source.

Fig. 3
Fig. 3

Interference pattern generated by two Gaussian beams and the binary hologram pattern recorded on the OASLM.

Fig. 4
Fig. 4

Relation between the radius and the peak intensity of the control beams and the DE of the first-order light used as the output light. White point, radius and peak intensity of the control beams in the experiment. Curve, relation between radius and peak intensity of the control beams when the power of the control beams is fixed at the experimental value.

Fig. 5
Fig. 5

Examples of the binary hologram patterns recorded on the OASLM when the power of the control beams is constant and the radius and the peak intensity are varied. Circles, radius of the signal beam. (a) r c /r s is 2.40, and I A /T h is 0.36. The DE is 11%. (b) r c /r s is 1.65, and I A /T h is 0.76. The DE is 18%. (c) r c /r s is 1.00, and I A /T h is 2.07. The DE is 11%.

Fig. 6
Fig. 6

Relation between the DE and the ratio R of the light intensity of the two control beams. r c /r s of the two control beams is 1.65, and I A /T h of one of the control beams is 0.76. These are the experimental values. I A /T h of the other control beam is varied.

Fig. 7
Fig. 7

Examples of the binary hologram patterns recorded on the OASLM when the ratio R of the light intensity of the two control beams is varied. r c /r s of the two control beams is 1.65, and I A /T h of one of the control beams is 0.76. These are the experimental values. I A /T h of the other control beam is varied. Circles, radius of the signal beam. (a) R is 0.1, and the DE is 6%. (b) R is 1, and the DE is 18%. (c) R is 4, and the DE is 8%.

Fig. 8
Fig. 8

DE of the grating in the experiment.

Equations (26)

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Tr=0.5 sin22θ1-cos φ,
φ=2πdcellΔnλ,
Hu, v=-- hx, yexp-j2πxu+yvdxdy,  u=X/λf,  v=Y/λf,
Ec1x, y, t=A exp-x2+y2rc2+jωt-2πλ ax,
Ec2x, y, t=B exp-x2+y2rc2+jωt-2πλ bx,
Ecx, y, t=Ec1+Ec2=exp-x2+y2rc2+jωtA exp-j 2πλ ax+B exp-j 2πλ bx.
Icx, y=EcEc*=exp-2x2+y2rc2A2+B2+2AB cosπd1 x,
d1=λ2a-b.
IA=A2,
R=B2/A2.
Icx, y=IA exp-2x2+y2rc21+R+2R cosπd1 x.
Icx, y=m=-MMn=-NN IA exp-22md12+2nd22rc2×1+R+2R cosπd1 x×rectx-2md12d1recty-2nd22d2,
rectx=1,  |x|1/20,  |x|>1/2,
2m-1d1x2m+1d1,  2n-1d2y2n+1d2,
Th>IA exp-22md12+2nd22rc21+R2,  cm, n=0,  Th<IA exp-22md12+2nd22rc21-R2,  cm, n=1,  IA exp-22md12+2nd22rc21-R2Th  IA exp-22md12+2nd22rc21+R2,  cosπcm, n=Th2RIA×exp22md12+2nd22rc2-1+R2R.
gx, y=g0x, yexp-jϕ+1-g0x, y×exp-jϕ+π=2g0x, y-1exp-jϕ,
g0x, y=m=-MMn=-NN×rectx-2md12cm, nd1recty-2nd22d2,
sx, y=S0 exp-x2+y2rs2,
Pin=S02πrs22.
Ou, v=-- gx, ysx, yexp-j2πxu+yvdxdy.
sx, y=m=-MMn=-NN S0 exp-2md12+2nd22rs2×rectx-2md12d1recty-2nd22d2.
Ou, v=S0sin2πd2vπ2uv exp-jϕm=-MMn=-NN×2 sin2πcm, nd1u-sin2πd1u×exp-2md12+2nd22rs2-j4πmd1u+nd2v.
IOu, v=OO*,
12d1-2πrsu12d1+2πrs,  -2πrsv2πrs.
Pout=- 2πrs2πrs12d1 - 2πrs12d1 + 2πrs IOu, vdudv.
DE=PoutTrPin.

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