Abstract

The contrast ratio of an optically addressed spatial light modulator that uses electroabsorption in a GaAs single crystal is discussed experimentally and theoretically. The modulator has the same structure as a Pockels readout optical modulator. The contrast ratio depends strongly on the change in the absorption coefficient and on the thickness of the GaAs crystal. From the experimental results and from theoretical investigations of the Franz–Keldysh effect, the change in the absorption coefficient is estimated by use of the quadratic equation of an applied electric field that is not excessively strong. Under this condition, an optimum thickness of the GaAs crystal plate that will yield the maximum contrast ratio can be determined.

© 1998 Optical Society of America

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  1. J. Tanida, J. Nakagawa, E. Yagyu, M. Fukui, Y. Ichioka, “Experimental verification of parallel processing on a hybrid optical parallel array logic system,” Appl. Opt. 29, 2510–2521 (1990).
    [CrossRef] [PubMed]
  2. T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
    [CrossRef]
  3. T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
    [CrossRef]
  4. R. A. Sprague, P. Nisenson, “The PROM—a status report,” Opt. Eng. 17, 256–266 (1978).
    [CrossRef]
  5. Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).
  6. Y. Bitou, T. Minemoto, “Spatial light modulator using Franz–Keldysh effect of GaAs,” in 1997 Conference on Lasers and Electro-Optics (Pacific Rim) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997), p. 203.
  7. Y. Bitou, T. Minemoto, “High-speed and high-contrast spatial light modulator that uses electroabsorption in a GaAs single crystal,” Appl. Opt. 37, 1377–1385 (1998).
    [CrossRef]
  8. B. O. Seraphin, N. Bottka, “Franz–Keldysh effect of the refractive index in semiconductors,” Phys. Rev. 139, 560–565 (1965).
    [CrossRef]
  9. K. Tharmalingam, “Optical absorption in the presence of a uniform field,” Phys. Rev. 130, 2204–2207 (1963).
    [CrossRef]
  10. G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
    [CrossRef]
  11. R. H. Kingston, F. J. Leonberger, “Fourier transformation using an electroabsorptive CCD spatial light modulator,” IEEE J. Quantum. Electron. QE-19, 1443–1451 (1983).
    [CrossRef]
  12. T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
    [CrossRef]
  13. T. L. Worchesky, K. J. Ritter, R. Martin, B. Lane, “Large arrays of spatial light modulators hybridized to silicon integrated circuits,” Appl. Opt. 35, 1180–1185 (1996).
    [CrossRef] [PubMed]
  14. Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and electro-optic effects in a GaAs single crystal,” Appl. Opt. (to be published).
  15. Y. Bitou, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.
  16. T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
    [CrossRef]
  17. A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885–6898 (1991).
    [CrossRef]

1998 (1)

1996 (3)

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).

T. L. Worchesky, K. J. Ritter, R. Martin, B. Lane, “Large arrays of spatial light modulators hybridized to silicon integrated circuits,” Appl. Opt. 35, 1180–1185 (1996).
[CrossRef] [PubMed]

1995 (1)

T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
[CrossRef]

1991 (1)

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885–6898 (1991).
[CrossRef]

1990 (1)

1988 (1)

T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
[CrossRef]

1986 (1)

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

1983 (1)

R. H. Kingston, F. J. Leonberger, “Fourier transformation using an electroabsorptive CCD spatial light modulator,” IEEE J. Quantum. Electron. QE-19, 1443–1451 (1983).
[CrossRef]

1978 (1)

R. A. Sprague, P. Nisenson, “The PROM—a status report,” Opt. Eng. 17, 256–266 (1978).
[CrossRef]

1976 (1)

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

1965 (1)

B. O. Seraphin, N. Bottka, “Franz–Keldysh effect of the refractive index in semiconductors,” Phys. Rev. 139, 560–565 (1965).
[CrossRef]

1963 (1)

K. Tharmalingam, “Optical absorption in the presence of a uniform field,” Phys. Rev. 130, 2204–2207 (1963).
[CrossRef]

Bitou, Y.

Y. Bitou, T. Minemoto, “High-speed and high-contrast spatial light modulator that uses electroabsorption in a GaAs single crystal,” Appl. Opt. 37, 1377–1385 (1998).
[CrossRef]

Y. Bitou, T. Minemoto, “Spatial light modulator using Franz–Keldysh effect of GaAs,” in 1997 Conference on Lasers and Electro-Optics (Pacific Rim) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997), p. 203.

Y. Bitou, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and electro-optic effects in a GaAs single crystal,” Appl. Opt. (to be published).

Bottka, N.

B. O. Seraphin, N. Bottka, “Franz–Keldysh effect of the refractive index in semiconductors,” Phys. Rev. 139, 560–565 (1965).
[CrossRef]

Bozler, C. O.

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

Chang, W. S. C.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

Efron, U.

T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
[CrossRef]

Fukui, M.

Garmire, E. M.

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885–6898 (1991).
[CrossRef]

Hiratsuka, H.

T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
[CrossRef]

Honda, A.

Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).

Hsu, T. Y.

T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
[CrossRef]

Ichioka, Y.

Ishikawa, J.

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

Kim, O.

T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
[CrossRef]

Kingston, R. H.

R. H. Kingston, F. J. Leonberger, “Fourier transformation using an electroabsorptive CCD spatial light modulator,” IEEE J. Quantum. Electron. QE-19, 1443–1451 (1983).
[CrossRef]

Lane, B.

Leonberger, F. J.

R. H. Kingston, F. J. Leonberger, “Fourier transformation using an electroabsorptive CCD spatial light modulator,” IEEE J. Quantum. Electron. QE-19, 1443–1451 (1983).
[CrossRef]

Martin, R.

Minemoto, T.

Y. Bitou, T. Minemoto, “High-speed and high-contrast spatial light modulator that uses electroabsorption in a GaAs single crystal,” Appl. Opt. 37, 1377–1385 (1998).
[CrossRef]

Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
[CrossRef]

Y. Bitou, T. Minemoto, “Spatial light modulator using Franz–Keldysh effect of GaAs,” in 1997 Conference on Lasers and Electro-Optics (Pacific Rim) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997), p. 203.

Y. Bitou, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and electro-optic effects in a GaAs single crystal,” Appl. Opt. (to be published).

Mizukawa, H.

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

Nakagawa, J.

Nisenson, P.

R. A. Sprague, P. Nisenson, “The PROM—a status report,” Opt. Eng. 17, 256–266 (1978).
[CrossRef]

Osugi, Y.

Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

Partovi, A.

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885–6898 (1991).
[CrossRef]

Ritter, K. J.

Rossi, J. A.

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

Seraphin, B. O.

B. O. Seraphin, N. Bottka, “Franz–Keldysh effect of the refractive index in semiconductors,” Phys. Rev. 139, 560–565 (1965).
[CrossRef]

Sprague, R. A.

R. A. Sprague, P. Nisenson, “The PROM—a status report,” Opt. Eng. 17, 256–266 (1978).
[CrossRef]

Stillman, G. E.

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

Tanida, J.

Tharmalingam, K.

K. Tharmalingam, “Optical absorption in the presence of a uniform field,” Phys. Rev. 130, 2204–2207 (1963).
[CrossRef]

Van Eck, T. E.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

Walpita, L. M.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

Wieder, H. H.

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

Wolte, C. M.

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

Worchesky, T. L.

Wu, W. Y.

T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
[CrossRef]

Yagyu, E.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

T. E. Van Eck, L. M. Walpita, W. S. C. Chang, H. H. Wieder, “Franz–Keldysh electrorefraction and electroabsorption in bulk InP and GaAs,” Appl. Phys. Lett. 48, 451–453 (1986).
[CrossRef]

G. E. Stillman, C. M. Wolte, C. O. Bozler, J. A. Rossi, “Electroabsorption in GaAs and its application to waveguide detectors and modulators,” Appl. Phys. Lett. 28, 544–546 (1976).
[CrossRef]

Electron. Lett. (1)

T. Y. Hsu, W. Y. Wu, U. Efron, “Amplitude and phase modulation in a 4 μm-thick GaAs/AlGaAs multiple quantum well modulator,” Electron. Lett. 24, 603–605 (1988).
[CrossRef]

IEEE J. Quantum. Electron. (1)

R. H. Kingston, F. J. Leonberger, “Fourier transformation using an electroabsorptive CCD spatial light modulator,” IEEE J. Quantum. Electron. QE-19, 1443–1451 (1983).
[CrossRef]

J. Appl. Phys. (1)

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885–6898 (1991).
[CrossRef]

Opt. Eng. (1)

R. A. Sprague, P. Nisenson, “The PROM—a status report,” Opt. Eng. 17, 256–266 (1978).
[CrossRef]

Opt. Rev. (2)

T. Minemoto, Y. Osugi, H. Mizukawa, J. Ishikawa, “Effect of dynamic range input image on performance of binary subtracted joint transform correlator,” Opt. Rev. 3, 505–511 (1996).
[CrossRef]

T. Minemoto, O. Kim, H. Hiratsuka, “Parallel image processing algorithms based on mathematical morphology using a multiple-imaging system,” Opt. Rev. 2, 352–361 (1995).
[CrossRef]

Optics (1)

Y. Osugi, A. Honda, T. Minemoto, “A Bi12SiO20 spatial light modulator for coherent light,” Optics 25, 48–54 (1996) (in Japanese).

Phys. Rev. (2)

B. O. Seraphin, N. Bottka, “Franz–Keldysh effect of the refractive index in semiconductors,” Phys. Rev. 139, 560–565 (1965).
[CrossRef]

K. Tharmalingam, “Optical absorption in the presence of a uniform field,” Phys. Rev. 130, 2204–2207 (1963).
[CrossRef]

Other (3)

Y. Bitou, T. Minemoto, “Spatial light modulator using Franz–Keldysh effect of GaAs,” in 1997 Conference on Lasers and Electro-Optics (Pacific Rim) (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1997), p. 203.

Y. Bitou, T. Minemoto, “High-contrast spatial light modulator by use of the electroabsorption and electro-optic effects in a GaAs single crystal,” Appl. Opt. (to be published).

Y. Bitou, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

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Figures (6)

Fig. 1
Fig. 1

(a) Structure and (b) equivalent circuit of a device. C G , C I , and C B , capacitances of the GaAs crystal plate, the mica insulator, and the lens-bond layers, respectively; R G , resistance of the GaAs crystal plate.

Fig. 2
Fig. 2

Dependence of Δα on the applied electric-field strength E. The experimental data are shown by filled (wavelength, λ = 900 nm) and open (λ = 890 nm) circles. The solid and the dashed curves show the fitting curves of the quadratic equation at the wavelengths given.

Fig. 3
Fig. 3

Dependence of the optical transmission ratio T for λ = 900 nm and the electric-field strength E on the thickness of GaAs. These results were calculated from Eqs. (4), (7), and (8).

Fig. 4
Fig. 4

Changes in the absorption coefficient Δα of GaAs (solid curves) and the differentials of Δα (dashed curves) as functions of the electric-field strength E. These results were calculated from Eq. (11) with (a) λ = 890 nm and (b) λ = 900 nm.

Fig. 5
Fig. 5

Sensitivity curves of the optical transmission ratio T versus the writing light intensity. The results were taken at f = 500 Hz and V a = 4 kV with λ = 900 nm and I r = 1.9 mW/cm2.

Fig. 6
Fig. 6

Examples of images: (a) the input (writing) image and (b) the readout image.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

T = I O E / I O 0 = exp - Δ α E L G ,
Δ α E = α E - α 0 ,
E = V a L G + 2   G I   L I + 4   G B   L B ,
Δ α E ,   λ = α 1 λ | E | + α 2 λ E 2 .
L GO = 2 rL I   V a + 2 RrL I V a - 2 RrL I ,
L GO 2 rL I ,
Δ α ω ,   E = C ω   θ 1 / 2 dAi β d β 2 - β | Ai β | ,

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