Abstract

The interference of two coherent images with a controlled phase difference between them is shown by using four-wave mixing in fluorescein-dye-doped boric acid glass and a liquid-crystal television spatial light modulator. We present results showing the digital optical exclusive or operation with milliwatt optical power and an output that is compatible with CCD camera sensitivities.

© 1992 Optical Society of America

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  1. C. P. Grover, R. Tremblay, “Real-time image subtraction using complementary photographic diffusers,” Appl. Opt. 21, 2666–2668 (1982).
  2. S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).
  3. A. E. Chiou, P. Yeh, “Parallel image subtraction using a phase-conjugate Michelson interferometer,” Opt. Lett. 11, 306–308 (1986).
  4. S. A. Boothroyd, J. Chrostowski, “Interferometer,” U.S. patent5,080,466 (14January1992).
  5. T. A. Shankoff, “Recording holograms in luminescent materials,” Appl. Opt. 8, 2282–2284 (1969).
  6. K. Nakagawa, H. Fujiwara, “Real-time and double-exposure phase conjugate interferometries using eosin-doped gelatin film,” Opt. Commun. 70, 73–76 (1989).
  7. H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).
  8. S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).
  9. M. A. Kramer, W. R. Tompkin, R. W. Boyd, “Nonlinear-optical interactions in fluorescein-doped boric acid glass,” Phys. Rev. A 34, 2026–2031 (1986).
  10. W. R. Tompkin, M. S. Malcuit, R. W. Boyd, J. E. Sipe, “Polarization properties of phase conjugation by degenerate four-wave mixing in a medium of rigidly held dye molecules,” J. Opt. Soc. Am. B 6, 757–760 (1989).
  11. M. S. O’Sullivan, P. Myslinski, “Joint transform correlator based on photo-induced anisotropy in fluorescein-doped boric acid glass,” in Spatial Light Modulators, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 43–46.
  12. W. R. Tompkin, M. S. Malcuit, R. W. Boyd, “Enhancement of the nonlinear optical properties of fluorescein doped boric-acid glass through cooling,” Appl. Opt. 29, 3921–3926 (1990).
  13. Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum. Electron. QE-17, 1967–1970 (1981).
  14. H. Fujiwara, K. Nakagawa, “Transient phase conjugation by degenerate four-wave mixing in saturable dyes,” J. Opt. Soc. Am. B 4, 121–128 (1987).
  15. M. Hercher, “An analysis of saturable absorbers,” Appl. Opt. 6, 947–954 (1967).
  16. S. A. Boothroyd, C. Grey Morgan, “Temporal development of phase conjugation in ruby by degenerate four-wave mixing,” J. Phys. D 16, L165–L168 (1983).
  17. R. L. Abrams, R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978); errata 3, 205 (1978).
  18. S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

1990 (2)

H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).

W. R. Tompkin, M. S. Malcuit, R. W. Boyd, “Enhancement of the nonlinear optical properties of fluorescein doped boric-acid glass through cooling,” Appl. Opt. 29, 3921–3926 (1990).

1989 (3)

S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).

K. Nakagawa, H. Fujiwara, “Real-time and double-exposure phase conjugate interferometries using eosin-doped gelatin film,” Opt. Commun. 70, 73–76 (1989).

W. R. Tompkin, M. S. Malcuit, R. W. Boyd, J. E. Sipe, “Polarization properties of phase conjugation by degenerate four-wave mixing in a medium of rigidly held dye molecules,” J. Opt. Soc. Am. B 6, 757–760 (1989).

1987 (1)

1986 (3)

S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).

A. E. Chiou, P. Yeh, “Parallel image subtraction using a phase-conjugate Michelson interferometer,” Opt. Lett. 11, 306–308 (1986).

M. A. Kramer, W. R. Tompkin, R. W. Boyd, “Nonlinear-optical interactions in fluorescein-doped boric acid glass,” Phys. Rev. A 34, 2026–2031 (1986).

1983 (1)

S. A. Boothroyd, C. Grey Morgan, “Temporal development of phase conjugation in ruby by degenerate four-wave mixing,” J. Phys. D 16, L165–L168 (1983).

1982 (1)

1981 (1)

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum. Electron. QE-17, 1967–1970 (1981).

1978 (1)

1969 (1)

1967 (1)

Abrams, R. L.

Bar-Joseph, I.

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum. Electron. QE-17, 1967–1970 (1981).

Beckwith, P. H.

S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

Boothroyd, S. A.

S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).

S. A. Boothroyd, C. Grey Morgan, “Temporal development of phase conjugation in ruby by degenerate four-wave mixing,” J. Phys. D 16, L165–L168 (1983).

S. A. Boothroyd, J. Chrostowski, “Interferometer,” U.S. patent5,080,466 (14January1992).

S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

Boyd, R. W.

Chan, L.

S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

Chiou, A. E.

Chrostowski, J.

S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).

S. A. Boothroyd, J. Chrostowski, “Interferometer,” U.S. patent5,080,466 (14January1992).

S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

Fujiwara, H.

H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).

K. Nakagawa, H. Fujiwara, “Real-time and double-exposure phase conjugate interferometries using eosin-doped gelatin film,” Opt. Commun. 70, 73–76 (1989).

H. Fujiwara, K. Nakagawa, “Transient phase conjugation by degenerate four-wave mixing in saturable dyes,” J. Opt. Soc. Am. B 4, 121–128 (1987).

Grey Morgan, C.

S. A. Boothroyd, C. Grey Morgan, “Temporal development of phase conjugation in ruby by degenerate four-wave mixing,” J. Phys. D 16, L165–L168 (1983).

Grover, C. P.

Hercher, M.

Kramer, M. A.

M. A. Kramer, W. R. Tompkin, R. W. Boyd, “Nonlinear-optical interactions in fluorescein-doped boric acid glass,” Phys. Rev. A 34, 2026–2031 (1986).

Kwong, S. K.

S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).

Lind, R. C.

Malcuit, M. S.

Myslinski, P.

M. S. O’Sullivan, P. Myslinski, “Joint transform correlator based on photo-induced anisotropy in fluorescein-doped boric acid glass,” in Spatial Light Modulators, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 43–46.

Nakagawa, K.

H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).

K. Nakagawa, H. Fujiwara, “Real-time and double-exposure phase conjugate interferometries using eosin-doped gelatin film,” Opt. Commun. 70, 73–76 (1989).

H. Fujiwara, K. Nakagawa, “Transient phase conjugation by degenerate four-wave mixing in saturable dyes,” J. Opt. Soc. Am. B 4, 121–128 (1987).

O’Sullivan, M. S.

S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).

M. S. O’Sullivan, P. Myslinski, “Joint transform correlator based on photo-induced anisotropy in fluorescein-doped boric acid glass,” in Spatial Light Modulators, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 43–46.

Rakuljic, G. A.

S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).

Shankoff, T. A.

Silberberg, Y.

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum. Electron. QE-17, 1967–1970 (1981).

Sipe, J. E.

Suzuki, T.

H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).

Tompkin, W. R.

Tremblay, R.

Yariv, A.

S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).

Yeh, P.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

S. K. Kwong, G. A. Rakuljic, A. Yariv, “Real time image subtraction and exclusive or operation using a self-pumped phase conjugate mirror,” Appl. Phys. Lett. 48, 201–203 (1986).

IEEE J. Quantum. Electron. (1)

Y. Silberberg, I. Bar-Joseph, “Transient effects in degenerate four-wave mixing in saturable absorbers,” IEEE J. Quantum. Electron. QE-17, 1967–1970 (1981).

J. Opt. Soc. Am. B (2)

J. Phys. D (1)

S. A. Boothroyd, C. Grey Morgan, “Temporal development of phase conjugation in ruby by degenerate four-wave mixing,” J. Phys. D 16, L165–L168 (1983).

Opt. Commun. (2)

K. Nakagawa, H. Fujiwara, “Real-time and double-exposure phase conjugate interferometries using eosin-doped gelatin film,” Opt. Commun. 70, 73–76 (1989).

H. Fujiwara, K. Nakagawa, T. Suzuki, “Real-time image subtraction and addition using two cross-polarized phase conjugate waves,” Opt. Commun. 79, 6–10 (1990).

Opt. Lett. (3)

S. A. Boothroyd, J. Chrostowski, M. S. O’Sullivan, “Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,” Opt. Lett. 14, 948–950 (1989).

A. E. Chiou, P. Yeh, “Parallel image subtraction using a phase-conjugate Michelson interferometer,” Opt. Lett. 11, 306–308 (1986).

R. L. Abrams, R. C. Lind, “Degenerate four-wave mixing in absorbing media,” Opt. Lett. 2, 94–96 (1978); errata 3, 205 (1978).

Phys. Rev. A (1)

M. A. Kramer, W. R. Tompkin, R. W. Boyd, “Nonlinear-optical interactions in fluorescein-doped boric acid glass,” Phys. Rev. A 34, 2026–2031 (1986).

Other (3)

S. A. Boothroyd, J. Chrostowski, “Interferometer,” U.S. patent5,080,466 (14January1992).

S. A. Boothroyd, P. H. Beckwith, L. Chan, J. Chrostowski, “Multiple grating optical processing in barium titanate,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of OSA 1991 Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 423–426; “Optical processing in photorefractive media,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (Canadian Society for Electrical and Computer Engineering, Montréal, 1991), pp. 52.5.1–52.5.4.

M. S. O’Sullivan, P. Myslinski, “Joint transform correlator based on photo-induced anisotropy in fluorescein-doped boric acid glass,” in Spatial Light Modulators, Vol. 14 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 43–46.

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Figures (7)

Fig. 1
Fig. 1

Ground-state absorption coefficient measured for a 60-μm-thick sample of fluorescein-doped boric acid glass.

Fig. 2
Fig. 2

Intensity-dependent transmission of fluorescein-doped boric acid glass. ▲, ■, and ◆ are the measured data points at 457.9, 465.8, and 476.5 nm, respectively.

Fig. 3
Fig. 3

Experimental arrangement: PZT; piezoelectric mirror; PC, personal computer.

Fig. 4
Fig. 4

Liquid-crystal television pixel scale and arrangement: R, red filter; G, green filter; B, blue filter.

Fig. 5
Fig. 5

Synchronization of the alternating television signal representing patterns A and B with the stepping of the piezoelectric mirror. NTSC, National Television Systems Committee.

Fig. 6
Fig. 6

Timing of laser light transmission through the SLM and polarizer with the stepping of the piezoelectric mirror. (a) The alternation of patterns A and B was synchronized with the mirror displacement, case 1 in Fig. 5; (b) the mirror stepping was out of phase with the changing pattern, case 2 in Fig. 5. The top group of traces in both (a) and (b) shows the light signal detected through a region of pixels that were transmitting in pattern A and opaque in pattern B. The middle group shows the light signal detected through a region of pixels that were blocking in pattern A and transmitting in pattern B. The dashed curves denote a region of pixels at the start of the television scan, the dotted curves denote a region in the middle of the television screen, and the solid curves denote a region of pixels at the end of the television scan. The bottom trace in each figure represents the voltage signal to the piezomirror.

Fig. 7
Fig. 7

Phase-conjugate image recorded by the CCD camera shown in Fig. 3. (a) Phase-conjugate output when pattern A is displayed on the SLM, (b) output for pattern B, (c) phase-conjugate output that results when both A and B are alternated on the SLM at video rate, (d) patterns A and B are alternating on the SLM and have a π phase shift between them.

Equations (4)

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E A = T A exp i ( ϕ SLM - k A · r ) , E B = T B exp i ( ϕ SLM + ϕ - k B · r ) ,
E A * = r A T A exp i ( - ϕ SLM + k A · r ) , E B * = r B T B exp i ( - ϕ SLM - ϕ + k B · r ) ,
I = E A * + E B * 2 = r A 2 T A 2 + r B 2 T B 2 + 2 r A r B T A T B cos ( ϕ ) .
R A = r A 2 = | E A * ( 0 ) E A ( 0 ) | 2 , R B = r B 2 = | E B * ( 0 ) E B ( 0 ) | 2 .

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