Abstract

Using coupled wave theory and the law of refraction, diffraction properties of volume holograms are discussed. Reconfigurable interconnections by either wavelength tuning or spatial division techniques are proposed. Reflection type volume holograms can be used for a large number of reconfigurable interconnections in terms of finite wavelength tunability. Transmission volume holograms encoded in pinhole holograms can be easily reconfigured by spatial light modulator. Experimental demonstrations obtained by using these methods are presented.

© 1990 Optical Society of America

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References

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  1. J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
    [CrossRef]
  2. A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–149 (1986).
  3. P. A. Yeh, A. E. T. Chiou, J. Hong, “Optical Interconnection Using Photorefractive Dynamic Holograms,” Appl. Opt. 27, 2093–2096 (1988).
    [CrossRef] [PubMed]
  4. F. Lin, “Optical Holographic Interconnection Networks for Parallel and Distributed Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989).
  5. E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
    [CrossRef]
  6. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Grating,” Bell Syst. Tech. J 48, 2902–2947 (1969).
  7. A. C. Strasser, E. S. Maniloff, K. M. Johnson, S. D. D. Goggin, “Procedure for Recording Multiple-Exposure Holograms with Equal Diffraction Efficiency in Photorefractive Media,” Opt. Lett. 14, 6–8 (1989).
    [CrossRef] [PubMed]
  8. L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
    [CrossRef]
  9. S. Xu, G. Mendes, S. Hart, J. C. Dainty, “Pinhole Hologram and its Applications,” Opt. Lett. 14, 107–109 (1989).
    [CrossRef] [PubMed]
  10. L. Solyman, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).
  11. J. K. Yamamoto, A. S. Bhalla, “Growth of SrxBa1−xNb2O6 Single Crystal Fibers,” Mater. Res. Bull. 24, 761–765 (1989).
    [CrossRef]
  12. L. Hesselink, S. Redfield, “Photorefractive Holographic Recording in Strontium Barium Niobate Fibers,” Opt. Lett. 13, 877–879 (1988).
    [CrossRef] [PubMed]
  13. S. Gray, “A New Breed of Photonic Polymers,” Photon. Spectra 23, 9 (1989).

1989 (5)

E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
[CrossRef]

J. K. Yamamoto, A. S. Bhalla, “Growth of SrxBa1−xNb2O6 Single Crystal Fibers,” Mater. Res. Bull. 24, 761–765 (1989).
[CrossRef]

S. Gray, “A New Breed of Photonic Polymers,” Photon. Spectra 23, 9 (1989).

A. C. Strasser, E. S. Maniloff, K. M. Johnson, S. D. D. Goggin, “Procedure for Recording Multiple-Exposure Holograms with Equal Diffraction Efficiency in Photorefractive Media,” Opt. Lett. 14, 6–8 (1989).
[CrossRef] [PubMed]

S. Xu, G. Mendes, S. Hart, J. C. Dainty, “Pinhole Hologram and its Applications,” Opt. Lett. 14, 107–109 (1989).
[CrossRef] [PubMed]

1988 (2)

1986 (1)

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–149 (1986).

1984 (1)

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

1975 (1)

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Grating,” Bell Syst. Tech. J 48, 2902–2947 (1969).

Amodei, J. J.

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

Athale, R.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

Bhalla, A. S.

J. K. Yamamoto, A. S. Bhalla, “Growth of SrxBa1−xNb2O6 Single Crystal Fibers,” Mater. Res. Bull. 24, 761–765 (1989).
[CrossRef]

Bradley, E.

E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
[CrossRef]

Burke, W. J.

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

Chiou, A. E. T.

Cooke, D. J.

L. Solyman, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

Dainty, J. C.

Goggin, S. D. D.

Goodman, J. W.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

Gray, S.

S. Gray, “A New Breed of Photonic Polymers,” Photon. Spectra 23, 9 (1989).

Hart, S.

Hesselink, L.

Hong, J.

Jenkins, B. K.

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–149 (1986).

Johnson, K. M.

Jonston, A. R.

E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Grating,” Bell Syst. Tech. J 48, 2902–2947 (1969).

Kung, S. Y.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

Leonberger, F.

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

Lin, F.

F. Lin, “Optical Holographic Interconnection Networks for Parallel and Distributed Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989).

Maniloff, E. S.

Mendes, G.

Phillips, W.

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

Redfield, S.

Sawchuk, A. A.

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–149 (1986).

Solyman, L.

L. Solyman, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

Staeble, L.

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

Strasser, A. C.

Xu, S.

Yamamoto, J. K.

J. K. Yamamoto, A. S. Bhalla, “Growth of SrxBa1−xNb2O6 Single Crystal Fibers,” Mater. Res. Bull. 24, 761–765 (1989).
[CrossRef]

Yeh, P. A.

Yu, P. K. L.

E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Staeble, W. J. Burke, W. Phillips, J. J. Amodei, “Multiple Storage and Erasure of Fixed Holograms in Fe-Doped LiNbO3,” Appl. Phys. Lett. 26, 182–186 (1975).
[CrossRef]

Bell Syst. Tech. J (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Grating,” Bell Syst. Tech. J 48, 2902–2947 (1969).

Mater. Res. Bull. (1)

J. K. Yamamoto, A. S. Bhalla, “Growth of SrxBa1−xNb2O6 Single Crystal Fibers,” Mater. Res. Bull. 24, 761–765 (1989).
[CrossRef]

Opt. Eng. (1)

E. Bradley, P. K. L. Yu, A. R. Jonston, “System Issues Relating to Diode Requirements for VLSI Holographic Optical Interconnections,” Opt. Eng. 28, 201–211 (1989).
[CrossRef]

Opt. Lett. (3)

Photon. Spectra (1)

S. Gray, “A New Breed of Photonic Polymers,” Photon. Spectra 23, 9 (1989).

Proc IEEE (1)

J. W. Goodman, F. Leonberger, S. Y. Kung, R. Athale, “Optical Interconnections for VLSI Systems,” Proc IEEE 72, 850–866 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. A. Sawchuk, B. K. Jenkins, “Dynamic Optical Interconnections for Parallel Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 143–149 (1986).

Other (2)

F. Lin, “Optical Holographic Interconnection Networks for Parallel and Distributed Processing,” in Technical Digest, Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1989).

L. Solyman, D. J. Cooke, Volume Holography and Volume Gratings (Academic, New York, 1981).

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Figures (12)

Fig. 1
Fig. 1

Writing angle inside and outside the recording media: (a) transmission hologram; (b) reflection hologram.

Fig. 2
Fig. 2

Dispersion (1/λ) (dλ/) as a function of half-writing angle α, n = 2.28: a, transmission hologram; b, reflection hologram.

Fig. 3
Fig. 3

Angular selectivity of volume holograms normalized by λ/d, n = 2.28: a, transmission hologram; b, reflection hologram.

Fig. 4
Fig. 4

Wavelength selectivity of volume holograms normalized by λ/d, n = 2.28: a, transmission hologram (the scale on right); b, reflection hologram (the scale on the left).

Fig. 5
Fig. 5

Diffracted wave vectors derived according to momentum conservation (the horizontal components of the dephasing vector should always be zero): (a) transmission hologram with incident angular deviation; (b) reflection hologram with incident angular deviation; (c) transmission hologram with reading wavelength deviation; (d) reflection holoram with reading wavelength deviation.

Fig. 6
Fig. 6

Principle of reconfigurable optical interconnects with volume holograms. OA and OB are two grating vectors with the same magnitude and an angular separation ΔΘ. CE and DF are the perpendicular bisectors of OA and OB.

Fig. 7
Fig. 7

Reconfigurable optical crossbar: C, z-cut LiNbO3 crystal; L1, L2, collimating and focusing lens; P1, P2, input and output planes; LA, DA, laser diode array and line detector array on the planes P1 and P2.

Fig. 8
Fig. 8

Geometry for reconfigurable interconnections with spatial division: (a) recording setup; (b) reading setup. L1, condensing lens; L2, collimating lens; SLM, spatial light modulator; C, recording media; P, page plane; Q, laser diode plane.

Fig. 9
Fig. 9

Experimental setup: C, y-cut LiNbO3; PBS, polarizing beam splitter; λ/2, halfwave plate; M, mirror; L, focusing lens; P, output plane.

Fig. 10
Fig. 10

Readout light spots with eight different wavelengths.

Fig. 11
Fig. 11

Reconstruction wavelength as a function of the deflected angle.

Fig. 12
Fig. 12

Reconfigurable interconnections with spatial division: (a) reconstructed patterns on the page plane by three different reading directions with the same pinhole position; (b) reconstructed six focal spots on the SLM plane by one reading beam.

Equations (35)

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k = 2 n sin Θ λ ,
Δ λ λ = cot ( Θ ) Δ Θ - 1 2 Δ Θ 2 ,
Δ Θ = cos α n 2 - sin 2 α Δ α ,
{ Δ λ λ } = cot ( α ) Δ α - 1 2 cos 2 α n 2 - sin 2 α ( Δ α ) 2 .
Δ Θ = sin α n 2 - cos 2 α Δ α ,
{ Δ λ λ } = sin α cos α n 2 - cos 2 α Δ α - 1 2 sin 2 α n 2 - cos 2 α ( Δ α ) 2 ,
( i . e . , 1 λ d λ d α )
η = sin 2 ( ν 2 + ζ 2 ) 1 / 2 ( 1 + ξ 2 / ν 2 ) ,
ζ = 2 π n d sin θ λ Δ Θ = - 2 π n d λ sin 2 Θ cos Θ Δ λ λ
η = ν 2 sinc 2 ζ .
{ Δ Θ } t = λ n d sin Θ ,
{ Δ λ λ } t = λ cos Θ n d sin 2 Θ ,
{ Δ α } t n 2 - sin 2 α sin α cos α λ d ,
{ Δ λ λ } t = n 2 - sin 2 α sin 2 α λ d .
η = 1 [ 1 + { 1 - ζ 2 ν 2 } / sh ( ν 2 - ζ 2 ) 1 / 2 ] ,
ν = j π n 1 d / λ sin Θ , ζ = 2 π n d cos Θ λ Δ Θ = - 2 π n d sin Θ λ Δ λ λ .
η = ν 2 sinc 2 ζ .
{ Δ α } r = n 2 - cos 2 α sin α cos α λ d ,
{ Δ λ λ } r = 1 n 2 - cos 2 α λ d ,
( α t ) opt = arcsin n ( n - n 2 - 1 ) ,
( α r ) opt = arccos n ( n - n 2 - 1 ) ,
{ Δ λ λ } t and { Δ λ λ } r
Δ k = k 1 - k 2 - k 3 + k 4 ,
( Δ k ) x = ( Δ k ) y = 0.
ζ = ( Δ k ) z · d .
Δ Θ = 2 tan Θ Δ λ λ .
[ Δ λ λ ]
{ Δ λ λ } = λ Δ f c ,
d λ n 2 - cos 2 α 1 { Δ λ λ } s = d max .
{ Δ λ λ } c
n l L = λ 2 { Δ λ λ } c ,
{ Δ λ λ } s = 2.4 × 10 - 5 ,
{ Δ λ λ } c = 6.7 × 10 - 5 ,
0.1 { Δ λ λ } s
M = π η 1 / 2 n 1 n d λ .

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