Abstract

We report on a new optical interconnect architecture for three-dimensional, multiple electro-optic gratings with LiNbO3 used in conjunction with substrate guided waves. First the operating mechanism of the system is studied in detail, and the momentum mismatch in the operating process of the system is also demonstrated. We then derive a new method for calculating coupling efficiency by introducing a compensation for the mismatch. This theoretical research allows the new optical interconnect architecture to provide a higher design accuracy and an optimized coupling efficiency, even though it is under the case of momentum mismatch. We achieve this result by introducing a substrate guided wave with 45° bouncing angle and 100-V applied voltage. The successful design and its theoretical analysis will be helpful for research on the grating coupler.

© 1997 Optical Society of America

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References

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  1. E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
    [CrossRef]
  2. D. G. Sun, L. M. He, N. X. Wang, Z. H. Weng, “Optoelectronic butterfly interconnection architecture of modified signed-digit arithmetic systems: fully parallel adder and subtracter,” Appl. Opt. 33, 6755–6761 (1994).
    [CrossRef] [PubMed]
  3. D. G. Sun, N. X. Wang, L. M. He, Z. W. Lu, Z. H. Weng, “Butterfly interconnection networks and their applications in digital computing and information processing: applications in FFT-based optical processing,” Appl. Opt. 32, 7184–7193 (1993).
    [CrossRef] [PubMed]
  4. A. Neyer, “Electro-optic X-switch using single mode Titanium Lithium Niobate channel waveguides,” Electron. Lett. 19, 553–554 (1993).
    [CrossRef]
  5. C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
    [CrossRef]
  6. R. V. Schmidt, P. S. Cross, “Efficient optical waveguide switch amplitude/modulator,” Opt. Lett. 2(2), 45–47 (1978).
    [CrossRef] [PubMed]
  7. O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
    [CrossRef]
  8. R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
    [CrossRef]
  9. R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
    [CrossRef]
  10. R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
    [CrossRef]
  11. R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
    [CrossRef]
  12. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  13. P. Moon, D. E. Spencer, Field Theory Handbook (Springer-Verlag, Berlin, 1971).
    [CrossRef]
  14. K. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Science Publishers, Tokyo, 1992), pp. 162–166.
  15. M. Li, S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245 (1994).
    [CrossRef]

1994 (2)

1993 (2)

1992 (2)

E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

1991 (1)

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

1990 (2)

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
[CrossRef]

1979 (1)

O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
[CrossRef]

1978 (2)

C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
[CrossRef]

R. V. Schmidt, P. S. Cross, “Efficient optical waveguide switch amplitude/modulator,” Opt. Lett. 2(2), 45–47 (1978).
[CrossRef] [PubMed]

Chen, R. T.

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
[CrossRef]

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

Cross, P. S.

El-Akkari, F. R.

C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
[CrossRef]

Gharavi, H.

E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
[CrossRef]

He, L. M.

Jannson, J.

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

Jannson, T.

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
[CrossRef]

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

Kawabe, M.

O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
[CrossRef]

Kim, S.

C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
[CrossRef]

Kitani, O. H.

O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
[CrossRef]

Koshiba, K.

K. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Science Publishers, Tokyo, 1992), pp. 162–166.

Li, M.

M. Li, S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245 (1994).
[CrossRef]

Liao, P. F.

E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
[CrossRef]

Lu, H.

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

Lu, Z. W.

Moon, P.

P. Moon, D. E. Spencer, Field Theory Handbook (Springer-Verlag, Berlin, 1971).
[CrossRef]

Namba, S.

O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
[CrossRef]

Neyer, A.

A. Neyer, “Electro-optic X-switch using single mode Titanium Lithium Niobate channel waveguides,” Electron. Lett. 19, 553–554 (1993).
[CrossRef]

Paek, E. G.

E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
[CrossRef]

Robinson, D.

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

Schmidt, R. V.

Sheard, S. J.

M. Li, S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245 (1994).
[CrossRef]

Sonek, G. J.

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

Spencer, D. E.

P. Moon, D. E. Spencer, Field Theory Handbook (Springer-Verlag, Berlin, 1971).
[CrossRef]

Sun, D. G.

Sun, Z.

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

Tsai, C. S.

C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
[CrossRef]

Wang, M. R.

R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
[CrossRef]

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

Wang, N. X.

Weng, Z. H.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Appl. Opt. (2)

Appl. Phys. Lett. (3)

R. T. Chen, M. R. Wang, T. Jannson, “Intraplane guided wave massive fanout optical interconnections,” Appl. Phys. Lett. 57, 2071–2073 (1990).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, Z. Sun, J. Jannson, “60 GHz board-to-board interconnection using polymer optical buses in conjunction with microprizm couplers,” Appl. Phys. Lett. 60, 536–538 (1992).
[CrossRef]

R. T. Chen, H. Lu, D. Robinson, T. Jannson, “Highly multiplexed graded-index polymer waveguide hologram for near-infrared eight-channel wavelength division demultiplexing,” Appl. Phys. Lett. 59, 1144–1146 (1991).
[CrossRef]

Electron. Lett. (1)

A. Neyer, “Electro-optic X-switch using single mode Titanium Lithium Niobate channel waveguides,” Electron. Lett. 19, 553–554 (1993).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. S. Tsai, S. Kim, F. R. El-Akkari, “Optical channel waveguide switch and coupler using total internal reflection,” IEEE J. Quantum Electron. QE-14, 513–517 (1978).
[CrossRef]

O. H. Kitani, S. Namba, M. Kawabe, “Electro-optic Bragg deflection modulators in corrugated waveguides,” IEEE J. Quantum Electron. QE-15(5), 270–272 (1979).
[CrossRef]

Opt. Commun. (1)

M. Li, S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109, 239–245 (1994).
[CrossRef]

Opt. Eng. (2)

E. G. Paek, P. F. Liao, H. Gharavi, “Derivation of neural network models and their computational circuits for associative memory,” Opt. Eng. 31, 986–994 (1992).
[CrossRef]

R. T. Chen, M. R. Wang, G. J. Sonek, T. Jannson, “Optical interconnection using polymer microstructure waveguides,” Opt. Eng. 30, 622–628 (1990).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

P. Moon, D. E. Spencer, Field Theory Handbook (Springer-Verlag, Berlin, 1971).
[CrossRef]

K. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Science Publishers, Tokyo, 1992), pp. 162–166.

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Figures (8)

Fig. 1
Fig. 1

Construction of LiNbO3-based EO diffraction grating.

Fig. 2
Fig. 2

Relationships among the unmodulated LiNbO3 sublayer 1, the modulated layer 2, and the photopolymer memory layer 3.

Fig. 3
Fig. 3

Distribution curve of index modulation as a function of x.

Fig. 4
Fig. 4

Wave vectors and modulation scheme of an x-cut LiNbO3 crystal.

Fig. 5
Fig. 5

Relationship between grating period and diffraction angle.

Fig. 6
Fig. 6

Relationship between Δαλ/2π and diffraction angle.

Fig. 7
Fig. 7

Frequency spectrum of interaction depth of grating: (a) diffraction theorem; (b) spatial frequency spectrum.

Fig. 8
Fig. 8

Coupling efficiency as a function of grating period.

Equations (38)

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1ne2θ=sin2θno2+cos2 θne2,
θc=arcsinnpneθ1,
2Vz2+2Vx2=0,
εz2Vz2+εx2Vx2=0,
x=εz/εxx.
2Vz2+2Vx2=0.
z=a cosh u cos v,
x=a sin u sin v,
Ez=-Uaπcosh u sin vcosh2 u-cos2 v,
Ex=-Uaπsinh u cos vcosh2-cos2 vεz/εx.
Δneθ1=ne3 sin2 θ1Δno+no3 cos2 θ1Δneno2 cos2 θ1+ne2 sin2 θ13/2,
Δne=-12ne3γ33Ez,
Δno=-12no3γ13Ez,
β1=2πλneθ1sin θ1,
β2=2πλneθ2sin θ2,
kg=2πΛ.
α1=2πλneθ1cos θ1,
α2=2πλneθ2cos θ2,
Δβ=β1-β2-mkg,
Δα=α2-α1.
Λ=λneθ1sin θ1-neθ2sinθ2.
dA1xdx=-ik12A2xexpiΔαx,
dA2xdx=-ik12*A1xexp-Δαx,
k12=ω2μ2 α1α2P1·ΔεP2,
Δε=2εononeno3 cos3 θ1Δne+ne3 sin3 θ1Δnone2 sin2 θ1+no2 cos2 θ12.
ddxA12+A22=0.
A2x=m=-exp-iΔαx fm2z,
fm2z=hm2z/Dm2,
Dm2=0Λhm2z2dz,
hm2z=Δneθ1,xexp-iβ2z.
A2Δr=-Le/2Le/2 fm2zexp-iΔrxdx,
τΔr=sinLeΔrLeΔr2.
dA1xdx=-ik12A2x,
dA2xdx=-ik12*A1x.
η=sinLeΔαLeΔα2 sin2k12Le.
k12=4π2noneλ2α1α2no3 cos3θ1Δne+ne3 sin3θ1Δnone2 sin2θ1+no2 cos2θ12×cosθ1-θ2,
k12Le=-Le0k12dx,
-Le0 k12dx=4π2no4ne4 cosθ1-θ2λ2ne2 sin2θ1+no2 cos2θ12α1α2×r33 cos3θ1+r13 sin3θ1-Le0 Ezdx.

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