Abstract

We studied the two-wave mixing anisotropic diffraction process in GaAs for demodulation of static and dynamic phase encoded signals. The static results quantitatively agreed with a previous theoretical model for cubic crystals. This model has been described explicitly for all beam polarizations and crystal rotation angles with respect to the plane of incidence. Dynamic phase modulation, in which the signal beam was phase modulated at frequency f s and the reference beam at f r = f s + Δf, produced a signal at Δf that was proportional to the difference between the static beam intensities with and without two-wave mixing under all conditions of polarization and crystal orientation studied. A significant dynamic output signal was produced even when only a shift in polarization but no energy transfer occurred as a result of the anisotropic two-wave mixing process. Therefore not only is the two-wave mixing gain important when the photorefractive effect is used for dynamic phase demodulation, but so are the polarization shifts occurring from the mixing process.

© 2000 Optical Society of America

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References

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  1. P. Günter, ed., Electro-optic and Photorefractive Materials (Springer-Verlag, New York, 1987).
    [CrossRef]
  2. S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.
  3. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  4. F. M. Davidson, ed., Photorefractive Materials Vol. MS 86 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994).
  5. M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
    [CrossRef]
  6. J. P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
    [CrossRef]
  7. J. W. Wagner, “Optical detection of ultrasound,” in Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Vol. 19, Chap. 5.
  8. G. Hamel de Monchenault, J. P. Huignard, “Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection,” J. Appl. Phys. 63, 624–627 (1988).
    [CrossRef]
  9. R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
    [CrossRef]
  10. J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
    [CrossRef] [PubMed]
  11. F. Davidson, L. Boutsikaris, “Coherent optical detection through two-wave mixing in photorefractive materials,” Opt. Lett. 13, 506–508 (1988).
    [CrossRef] [PubMed]
  12. H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
    [CrossRef]
  13. T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
    [CrossRef]
  14. T. C. Hale, K. Telschow, V. A. Deason, “Photorefractive optical lock-in vibration spectral measurement,” Appl. Opt. 36, 8248–8258 (1997).
    [CrossRef]
  15. K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
    [CrossRef]
  16. R. C. Troth, J. C. Dainty, “Holographic interferometry using anisotropic self-diffraction in Bi12SiO20,” Opt. Lett. 16, 53–55 (1991).
    [CrossRef] [PubMed]
  17. P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am B 4, 1382–1386 (1987).
    [CrossRef]
  18. The GaAs crystal was obtained from Atomergic Chemetals Corporation, 71 Carolyn Blvd., Farmingdale, N.Y. 11735; (631) 694-9000; info@atomergic.com.
  19. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  20. N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
    [CrossRef]
  21. matlab version 5.2.0, The Mathworks Inc., Natick, Mass. 01760-2098.
  22. Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
    [CrossRef]

1999 (1)

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

1997 (3)

M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
[CrossRef]

N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

T. C. Hale, K. Telschow, V. A. Deason, “Photorefractive optical lock-in vibration spectral measurement,” Appl. Opt. 36, 8248–8258 (1997).
[CrossRef]

1996 (1)

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

1995 (1)

Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

1994 (1)

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
[CrossRef]

1991 (2)

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

R. C. Troth, J. C. Dainty, “Holographic interferometry using anisotropic self-diffraction in Bi12SiO20,” Opt. Lett. 16, 53–55 (1991).
[CrossRef] [PubMed]

1988 (2)

F. Davidson, L. Boutsikaris, “Coherent optical detection through two-wave mixing in photorefractive materials,” Opt. Lett. 13, 506–508 (1988).
[CrossRef] [PubMed]

G. Hamel de Monchenault, J. P. Huignard, “Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection,” J. Appl. Phys. 63, 624–627 (1988).
[CrossRef]

1987 (1)

P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am B 4, 1382–1386 (1987).
[CrossRef]

1981 (2)

J. P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Boutsikaris, L.

Buchhave, P.

M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
[CrossRef]

N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

Dainty, J. C.

Davidson, F.

de Montmorillon, L. A.

Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Deason, V. A.

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

T. C. Hale, K. Telschow, V. A. Deason, “Photorefractive optical lock-in vibration spectral measurement,” Appl. Opt. 36, 8248–8258 (1997).
[CrossRef]

Delaye, Ph.

Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Hale, T. C.

T. C. Hale, K. Telschow, V. A. Deason, “Photorefractive optical lock-in vibration spectral measurement,” Appl. Opt. 36, 8248–8258 (1997).
[CrossRef]

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

Hamel de Monchenault, G.

G. Hamel de Monchenault, J. P. Huignard, “Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection,” J. Appl. Phys. 63, 624–627 (1988).
[CrossRef]

Huignard, J. P.

G. Hamel de Monchenault, J. P. Huignard, “Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection,” J. Appl. Phys. 63, 624–627 (1988).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

J. P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Ing, R. K.

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Kukhtarev, N.

N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Lyuksyutov, S.

M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
[CrossRef]

Lyuksyutov, S. F.

N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Marrakchi, A.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibration analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

J. P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Monchalin, J.-P.

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Petersen, P. M.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
[CrossRef]

Rohleder, H.

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
[CrossRef]

Roosen, G.

Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

Schley, R. S.

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.

Telschow, K.

T. C. Hale, K. Telschow, V. A. Deason, “Photorefractive optical lock-in vibration spectral measurement,” Appl. Opt. 36, 8248–8258 (1997).
[CrossRef]

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

Telschow, K. L.

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

Troth, R. C.

Vasnetsov, M.

M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Wagner, J. W.

J. W. Wagner, “Optical detection of ultrasound,” in Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Vol. 19, Chap. 5.

Watson, S. M.

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

Yeh, P.

P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am B 4, 1382–1386 (1987).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

R. K. Ing, J.-P. Monchalin, “Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal,” Appl. Phys. Lett. 59, 3233–3235 (1991).
[CrossRef]

T. C. Hale, K. Telschow, “Optical lock-in vibration detection using photorefractive frequency domain processing,” Appl. Phys. Lett. 69, 2632–2634 (1996).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

J. Acoust. Soc. Am. (1)

K. L. Telschow, V. A. Deason, R. S. Schley, S. M. Watson, “Direct imaging of Lamb waves in plates using photorefractive dynamic holography,” J. Acoust. Soc. Am. 106, 2578–2587 (1999).
[CrossRef]

J. Appl. Phys. (2)

H. Rohleder, P. M. Petersen, A. Marrakchi, “Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: a comparison with electronic speckle pattern interferometry,” J. Appl. Phys. 76(1), 81–84 (1994).
[CrossRef]

G. Hamel de Monchenault, J. P. Huignard, “Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection,” J. Appl. Phys. 63, 624–627 (1988).
[CrossRef]

J. Opt. Soc. Am B (1)

P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am B 4, 1382–1386 (1987).
[CrossRef]

Opt. Commun. (3)

Ph. Delaye, L. A. de Montmorillon, G. Roosen, “Transmission of time modulated optical signals through an absorbing photorefractive crystal,” Opt. Commun. 118, 154–164 (1995).
[CrossRef]

M. Vasnetsov, P. Buchhave, S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

N. Kukhtarev, P. Buchhave, S. F. Lyuksyutov, “Optical and electric properties of dynamic holographic gratings with arbitrary contrast,” Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

Other (7)

matlab version 5.2.0, The Mathworks Inc., Natick, Mass. 01760-2098.

The GaAs crystal was obtained from Atomergic Chemetals Corporation, 71 Carolyn Blvd., Farmingdale, N.Y. 11735; (631) 694-9000; info@atomergic.com.

J. W. Wagner, “Optical detection of ultrasound,” in Physical Acoustics, R. N. Thurston, A. D. Pierce, eds. (Academic, New York, 1990), Vol. 19, Chap. 5.

P. Günter, ed., Electro-optic and Photorefractive Materials (Springer-Verlag, New York, 1987).
[CrossRef]

S. I. Stepanov, International Trends in Optics (Academic, New York, 1991), Chap. 9.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

F. M. Davidson, ed., Photorefractive Materials Vol. MS 86 of SPIE Milestone Series (SPIE, Bellingham, Wash., 1994).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for the anisotropic diffraction two-wave mixing measurements. OD, optical density.

Fig. 2
Fig. 2

Geometric orientation of the crystal and input optical beams.

Fig. 3
Fig. 3

Output beam intensities measured as a function of the analyzing polarizer angle for the (a) static and (b) dynamic modulation signals.

Fig. 4
Fig. 4

(a) Static and (b) dynamic measurement results for the 0° orientation with an input signal beam polarization of 45° and a reference beam polarization of 45°.

Fig. 5
Fig. 5

(a) Static and (b) dynamic measurement results for the 0° orientation with an input signal beam polarization of 0° and a reference beam polarization of 0°.

Fig. 6
Fig. 6

(a) Static and (b) dynamic measurement results for the 0° orientation with an input signal beam polarization of 0° and a reference beam polarization of 90°.

Fig. 7
Fig. 7

(a) Static and (b) dynamic measurement results for the 0° orientation with an input signal beam polarization of 45° and a reference beam polarization of 0°.

Equations (10)

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xˆyˆzˆ=RΨaˆbˆcˆ, RΨ=12cosΨcosΨ2 sinΨ-sinΨ-sinΨ2 cosΨ1-10,
MrAs*Bs+Ap*Bp cos2θexp-iK · r+c.c.I0,
I0As2+Ap2+Bs2+Bp2, K=k2-k1=2πλ2 sinθxˆ,
Esc=MrEd, Ed=|Ed|expiϕKˆ, Kˆ=K|K|//xˆ,
ddz As=i2βexpiϕΓss · Bs+Γsp2 · Bp · M*rC, ddz Bs=i2βexp-iϕΓss · As+Γsp1 · Ap · MrC, ddz Ap=i2βexpiϕΓp1s · Bs+Γp1p2 · Bp · M*rC, ddz Bp=i2βexp-iϕΓp2s · As+Γp2p1 · Ap · MrC,
ε0=ε0n2100010001, Δεr=-ε02n4r410Esc·cˆEsc·bˆEsc·cˆ0Esc·aˆEsc·bˆEsc·aˆ0,
Esc=|Esc|2cosΨaˆ+cosΨbˆ+2 sinΨcˆ
Δεrˆ=Δεmrˆ1202 sinΨcosΨ2 sinΨ0cosΨcosΨcosΨ0,
Γss=sˆΔεrsˆ=Δεmr-sinΨ3 cos2Ψ-1, Γp1p2=Γp2p1=ΔεmrsinΨ×3 cos2θcos2Ψ+sin2θ, Γsp1=Γp1s=Γsp2=Γp2s=Δεmr×cosθcosΨ3 cos2Ψ-2,
IBoutmixing-IBoutno mixingIBoutno mixing=m[1-exp-ΓL1+m exp-ΓLΓL1m1+mΓL,

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