Abstract

We investigate the effects of inactive regions [dead zones (DZ’s)] in multiple-quantum-well binary-phase modulators used for free-space dynamic optical interconnection applications. Results, however, have implications for other types of pixelated spatial light modulators (SLM’s). To our knowledge, the effects of DZ’s in SLM’s have not before been thoroughly studied in a context other than optical correlation. We investigate the DZ’s (considered to be either opaque or transmissive) as a feature that may be exploited in system design, calculating light efficiency and fidelity as a function of DZ fractional width. It is shown that in particular cases an appropriate choice of DZ width would lead to an optical interconnection with substantially improved cross-talk performance.

© 1998 Optical Society of America

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  1. P. D. Gianino, C. L. Woods, “General treatment of spatial light modulator dead-zone effects on optical correlation. I. Computer simulations,” Appl. Opt. 32, 6527–6535 (1993).
    [CrossRef] [PubMed]
  2. J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. SPIE1296, 110–124 (1990).
    [CrossRef]
  3. M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
    [CrossRef]
  4. B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
    [CrossRef]
  5. P. D. Gianino, C. L. Woods, “Effects of spatial light modulator opaque dead zones on optical correlation,” Appl. Opt. 31, 4025–4033 (1992).
    [CrossRef] [PubMed]
  6. P. D. Gianino, C. L. Woods, “General treatment of spatial light modulator dead-zone effects on optical correlation. II. Mathematical analysis,” Appl. Opt. 32, 6536–6541 (1993).
    [CrossRef] [PubMed]
  7. J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
    [CrossRef]
  8. J. A. Trezza, J. S. Harris, “Creation and optimization of vertical cavity phase flip modulators,” J. Appl. Phys. 75, 4878–4884 (1994).
    [CrossRef]
  9. J. A. Trezza, J. S. Harris, “Two-state electrically controllable phase diffraction grating using arrays of vertical-cavity phase flip modulators,” IEEE Photonics Technol. Lett. 8, 1211–1213 (1996).
    [CrossRef]
  10. E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.
  11. L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.
  12. A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
    [CrossRef]
  13. N. McArdle, M. R. Taghizadeh, “Real-time reconfigurable interconnections for parallel optical processing,” Opt. Rev. 2, 189–193 (1995).
    [CrossRef]
  14. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  15. D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).
    [CrossRef]

1996

J. A. Trezza, J. S. Harris, “Two-state electrically controllable phase diffraction grating using arrays of vertical-cavity phase flip modulators,” IEEE Photonics Technol. Lett. 8, 1211–1213 (1996).
[CrossRef]

1995

N. McArdle, M. R. Taghizadeh, “Real-time reconfigurable interconnections for parallel optical processing,” Opt. Rev. 2, 189–193 (1995).
[CrossRef]

1994

D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).
[CrossRef]

J. A. Trezza, J. S. Harris, “Creation and optimization of vertical cavity phase flip modulators,” J. Appl. Phys. 75, 4878–4884 (1994).
[CrossRef]

1993

1992

P. D. Gianino, C. L. Woods, “Effects of spatial light modulator opaque dead zones on optical correlation,” Appl. Opt. 31, 4025–4033 (1992).
[CrossRef] [PubMed]

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

1990

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Bock, B. D.

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cottrell, D. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Cravatt, J. E.

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. SPIE1296, 110–124 (1990).
[CrossRef]

Crow, T. A.

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

Davis, J. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Desmulliez, M. P. Y.

L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

Gianino, P. D.

Giles, M. K.

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. SPIE1296, 110–124 (1990).
[CrossRef]

M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
[CrossRef]

Gioannini, B.

M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
[CrossRef]

Grann, E. B.

Grijalva, N.

M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
[CrossRef]

Harris, J. S.

J. A. Trezza, J. S. Harris, “Two-state electrically controllable phase diffraction grating using arrays of vertical-cavity phase flip modulators,” IEEE Photonics Technol. Lett. 8, 1211–1213 (1996).
[CrossRef]

J. A. Trezza, J. S. Harris, “Creation and optimization of vertical cavity phase flip modulators,” J. Appl. Phys. 75, 4878–4884 (1994).
[CrossRef]

Hegarty, J.

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

Horan, P.

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

Inbar, H.

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

Jennings, A.

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

Kelly, B.

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

McArdle, N.

N. McArdle, M. R. Taghizadeh, “Real-time reconfigurable interconnections for parallel optical processing,” Opt. Rev. 2, 189–193 (1995).
[CrossRef]

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Moharam, M. G.

Pommet, D. A.

Prince, S. M.

L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

Serrano, E.

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

Stanley, C. R.

L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.

Taghizadeh, M. R.

N. McArdle, M. R. Taghizadeh, “Real-time reconfigurable interconnections for parallel optical processing,” Opt. Rev. 2, 189–193 (1995).
[CrossRef]

Taylor, J.

M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
[CrossRef]

Trezza, J. A.

J. A. Trezza, J. S. Harris, “Two-state electrically controllable phase diffraction grating using arrays of vertical-cavity phase flip modulators,” IEEE Photonics Technol. Lett. 8, 1211–1213 (1996).
[CrossRef]

J. A. Trezza, J. S. Harris, “Creation and optimization of vertical cavity phase flip modulators,” J. Appl. Phys. 75, 4878–4884 (1994).
[CrossRef]

Wherrett, B. S.

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

Wilkinson, L. C.

L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.

Woods, C. L.

Appl. Opt.

IEEE Photonics Technol. Lett.

J. A. Trezza, J. S. Harris, “Two-state electrically controllable phase diffraction grating using arrays of vertical-cavity phase flip modulators,” IEEE Photonics Technol. Lett. 8, 1211–1213 (1996).
[CrossRef]

A. Jennings, P. Horan, B. Kelly, J. Hegarty, “Asymmetric Fabry–Perot device arrays with low insertion loss and high uniformity,” IEEE Photonics Technol. Lett. 4, 858–860 (1992).
[CrossRef]

J. Appl. Phys.

J. A. Trezza, J. S. Harris, “Creation and optimization of vertical cavity phase flip modulators,” J. Appl. Phys. 75, 4878–4884 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, “Effects of sampling and binarization in the output of the joint Fourier transform correlator,” Opt. Eng. 29, 1094–1100 (1990).
[CrossRef]

Opt. Rev.

N. McArdle, M. R. Taghizadeh, “Real-time reconfigurable interconnections for parallel optical processing,” Opt. Rev. 2, 189–193 (1995).
[CrossRef]

Other

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

E. Serrano, M. P. Y. Desmulliez, S. M. Prince, H. Inbar, B. S. Wherrett, “Multiple-quantum-well binary-phase modulators: design and tolerance analysis,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 125–127.

L. C. Wilkinson, S. M. Prince, M. P. Y. Desmulliez, C. R. Stanley, “Fabrication and testing of a multiple quantum well binary phase modulator,” in Spatial Light Modulators, Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1997), pp. 114–116.

J. E. Cravatt, M. K. Giles, “An improved model of the TI deformable mirror device,” in Advances in Optical Information Processing IV, D. R. Pape, ed., Proc. SPIE1296, 110–124 (1990).
[CrossRef]

M. K. Giles, J. Taylor, N. Grijalva, B. Gioannini, “Optical image correlation using a deformable mirror device: a feasibility study,” in Acousto-Optic, Electro-Optic, and Magneto-Optic Devices and Applications, J. A. Lucero, ed., Proc. SPIE753, 72–81 (1987).
[CrossRef]

B. D. Bock, T. A. Crow, M. K. Giles, “Design considerations for miniature optical correlation systems that use pixelated input and filter transducers,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 297–309 (1990).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Geometry of 2 × 1 fan-out interconnections.

Fig. 2
Fig. 2

One-dimensional array of MQW binary-phase modulators: (a) Photograph. (b) Schematic drawing showing three pixels (fingers).

Fig. 3
Fig. 3

Amplitude transmittance of a binary-phase modulator array encoding a 2-finger/period modulation pattern: (a) Array with ODZ’s (f DZ = b/ a). (b) Array without DZ’s (f DZ = 0).

Fig. 4
Fig. 4

Two-finger/period modulation pattern with ODZ’s. The incident diffraction efficiency ηinc(f DZ) and the effective diffraction efficiency ηeff(f DZ) are shown.

Fig. 5
Fig. 5

Two-finger/period modulation pattern with ODZ’s. The intensity ratio of the first to the nth diffraction orders as a function of f DZ for (a) n = 3, (b) n = 5, (c) n = 7, and (d) n = 9.

Fig. 6
Fig. 6

Two-finger/period modulation pattern with ODZ’s. Shown is min{ I ratio 1 , n } as a function of f DZ (where {n = 3, 5, 7, … }); the nth diffraction order responsible for limiting the fidelity is indicated for each curve segment.

Fig. 7
Fig. 7

Two-finger/period modulation pattern with TDZ’s (A = 1). Shown are the intensity ratios of the first to the nth diffraction orders as functions of f DZ for (a) n = 0, (b) n = 2, (c) n = 4, (d) n = 6, and (e) n = 8.

Fig. 8
Fig. 8

Four-finger/period modulation pattern with ODZ’s. The incident diffraction efficiency ηinc(f DZ) and the effective diffraction efficiency ηeff(f DZ) are shown.

Fig. 9
Fig. 9

Four-finger/period modulation pattern with ODZ’s. Shown are the intensity ratios of the first to the nth diffraction orders as functions of f DZ for (a) n = 3, (b) n = 5, (c) n = 7, and (d) n = 9.

Fig. 10
Fig. 10

Four-finger/period modulation pattern with TDZ’s (A = 1). Shown are the intensity ratios of the first to the nth diffraction order as functions of f DZ for (a) n = 0, (b) n = 4, and (c) n = 8.

Fig. 11
Fig. 11

Schematic drawing of a three-node switching network. The dashed lines represent the bypass operation; the solid lines represent the exchange operation; Σ is the output plane.

Equations (11)

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G x ,   f DZ = b / a | T = 0 = 2 π n odd = 1 cos n π f DZ + 1 n sin n π   x a + sin n π f DZ n cos n π   x a ,
G x ,   f DZ = 0 = 4 π n odd = 1 1 n sin n π   x a .
η inc f DZ = 4 π 2 1 + cos π f DZ .
η eff f DZ = 4 π 2 1 + cos π f DZ 1 - f DZ .
I ratio 1 , n f DZ = n 2 1 + cos π f DZ 1 + cos n π f DZ ,
G x ,   f DZ = b / a | T = A exp i ϕ = G x ,   f DZ = b / a | T = 0 + A   exp i ϕ f DZ + 2 π   A   exp i ϕ × n even = 2 cos n π f DZ - 1 n sin n π   x a + sin n π f DZ n cos n π   x a .
I ratio 1,0 f DZ = 2 A 2 1 + cos π f DZ π f DZ 2 ,
I ratio 1 , n f DZ = n 2 A 2 1 + cos π f DZ 1 - cos n π f DZ .
I bypass 0 f DZ = 1 - f DZ 2 ,
I bypass n f DZ = 1 π 2 sin 2 n π f DZ n 2 .
I exchange n f DZ   =   2 π 2 1   +   cos n π f DZ n 2 ,

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