Abstract

The dynamic range, defined as the range of intensity ratios for which two writing beams can induce a detectable photorefractive grating, is measured for ferroelectric crystals BaTiO3, KNbO3, SrxBa1−xNbO6, BaxSr2−xK1−yNayNb5O15. Our results show a large dynamic range in all these crystals, 70–100 dB, which should prove these crystals useful for signal processing and computing applications. The observed limit on the dynamic range was due predominantly to the detector noise and therefore was not the fundamental limit imposed by the underlying physics of photorefractive noise. The calculations of noise based on limited photon density flux (shot noise) and thermally induced grating fluctuations (thermal noise) show the dynamic range to be 4–5 orders of magnitude higher than that observed experimentally.

© 1992 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
    [CrossRef]
  5. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  33. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4.

1991 (4)

1990 (3)

1989 (2)

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

1988 (3)

1987 (3)

1986 (3)

1985 (2)

D. Psaltis, J. Yu, J. Hong, “Bias-free time-integrating optical correlator using a photorefractive crystal,” Appl. Opt. 24, 3860–3865 (1985).
[CrossRef] [PubMed]

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1981 (1)

1980 (2)

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

1979 (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).
[CrossRef]

Anderson, D. Z.

Beckwith, P. H.

Brady, D.

Campbell, S.

Chang, T.

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

Chang, T. Y.

Chiou, A. E.

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

Clark, W. W.

Cory, W. K.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Dunning, G. J.

Ewbank, M. D.

R. A. Vazquez, M. D. Ewbank, R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[CrossRef]

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Fainman, Y.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-beam coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Feinberg, J.

J. Feinberg, “Photorefractive nonlinear optics,” Phys. Today 41(10), 46–52 (1988).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Gu, C.

Hall, W. F.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hong, J.

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

D. Psaltis, J. Yu, J. Hong, “Bias-free time-integrating optical correlator using a photorefractive crystal,” Appl. Opt. 24, 3860–3865 (1985).
[CrossRef] [PubMed]

F. Vachss, J. Hong, “Intensity noise limits in photorefractive holograms,” submitted to J. Appl. Phys.

Hong, J. H.

Hong, Y H.

Huignard, J.-P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

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

Khoshnevisan, M.

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-beam coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Klein, M. B.

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 195–236.
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).
[CrossRef]

Kukhtarev, N. V.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Kwong, S.

Lee, S. H.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-beam coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Lininger, D. M.

Marom, E.

Marrakchi, A.

McGraw, R.

R. McGraw, “Light-scattering and nonlinear optical response near a critical point,” Phys. Rev. A 42, 2235–2247 (1990).
[CrossRef] [PubMed]

R. McGraw, “Light-scattering fluctuations and thermal noise in photorefractive media,” Phys. Rev. A (to be published).

Miller, M. J.

Mok, F. H.

Neurgaonkar, R. N.

Neurgaonkar, R. R.

R. A. Vazquez, M. D. Ewbank, R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[CrossRef]

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Oliver, J. R.

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Owechko, Y.

Psaltis, D.

Rajbenbach, H.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Refregier, P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Rodriguez, J.

Salamo, G.

Saxena, R.

Sharp, E. J.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4.

Siahmakoun, A.

Soffer, B. H.

Solymar, L.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Stoll, H. M.

Tackitt, M. C.

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Vachss, F.

F. Vachss, J. Hong, “Intensity noise limits in photorefractive holograms,” submitted to J. Appl. Phys.

Vazquez, R. A.

R. A. Vazquez, M. D. Ewbank, R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[CrossRef]

Vinetskii, V. L.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Wagner, K.

White, J. O.

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Wood, G. L.

Yariv, A.

A. Yariv, S. Kwong, “Associative memories based on message-bearing optical modes in phase conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef]

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

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

Yeh, P.

Yu, J.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. O. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2945 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Appl. Phys. (2)

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Opt. Commun. (1)

R. A. Vazquez, M. D. Ewbank, R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[CrossRef]

Opt. Eng. (3)

R. R. Neurgaonkar, W. K. Cory, J. R. Oliver, M. D. Ewbank, W. F. Hall, “Development and modification of photorefractive properties in the tungsten bronze family crystals,” Opt. Eng. 26, 392–405 (1987).
[CrossRef]

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal coherent image amplification by two-beam coupling in photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

P. Yeh, A. E. Chiou, J. Hong, T. Chang, M. Khoshnevisan, “Photorefractive nonlinear optics and optical computing,” Opt. Eng. 28, 328–342 (1989).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. A (1)

R. McGraw, “Light-scattering and nonlinear optical response near a critical point,” Phys. Rev. A 42, 2235–2247 (1990).
[CrossRef] [PubMed]

Phys. Today (1)

J. Feinberg, “Photorefractive nonlinear optics,” Phys. Today 41(10), 46–52 (1988).
[CrossRef]

Sov. Phys. Usp. (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, “Dynamic self-diffraction of coherent light beams,” Sov. Phys. Usp. 22, 742–756 (1979).
[CrossRef]

Other (8)

P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1988).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 4.

F. Vachss, J. Hong, “Intensity noise limits in photorefractive holograms,” submitted to J. Appl. Phys.

R. McGraw, “Light-scattering fluctuations and thermal noise in photorefractive media,” Phys. Rev. A (to be published).

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

Sanders Associates, Nashua, N.H. 03061.

CSK Co., Culver City, Calif. 90230.

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 195–236.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Generic holographic arrangement used to explain the dynamic range of photorefractive gratings. The dynamic range is defined as the range of writing-beam intensity ratio I2/I1 that can induce a detectable photorefractive grating. The detection is done by a Bragg-matched nondestructive readout beam Iread and a sensitive detector that detects Idiff.

Fig. 2
Fig. 2

Schematic of the experimental arrangement used to measure the dynamic range of gratings in various photorefractive crystals: M’s, mirrors; S’s, shutters; F, color filter; B, light baffle.

Fig. 3
Fig. 3

Timing sequence for turning on and off the writing and the reading beams. This particular timing sequence was chosen to minimize the reading beam’s interacting with the diffracted beam. The bottom trace shows the expected diffracted signal beam; the fuzz (δV) in the trace is caused by noise that ultimately limits the detectability of the signal (ΔV) or the dynamic range. δV′ shows (electronic) noise in the detection system, since it is present when there is no light. When δV = ΔV, or when the signal-to-noise ratio is 1, we define the corresponding writing-beam ratio to be the minimum value.

Fig. 4
Fig. 4

Typical oscilloscope traces of experimentally detected signal beam (a) near the minimum writing-beam ratio and (b) at a somewhat higher beam ratio (10−7–10−5). The slight overshoot in the trace in (b) indicates that there is some interaction between the reading and the diffracted beams. However, the uncertainty in the diffracted signal was incorporated into our data with appropriate error bars and did not affect the result significantly. The exponential rise and decay times in the traces are caused by a capacitor that was used to integrate the signal with the RC time constant of 0.5 s.

Fig. 5
Fig. 5

Experimental results: log-log plots of grating diffraction efficiency versus writing beam ratio for (a) BaTiCO3, (b) Rh:BSKNN-II, (c) Fe:KNbO3, and (d) Rh:SBN:60. The dots are the experimental data, and the solid curves are the fits to Kogelnik’s theory, given in Eq. (1). As is discussed in the text, the observed dynamic range (up to 100 dB) was limited mainly by the detector noise.

Tables (3)

Tables Icon

Table 1 Physical Parameters of the Photorefractive Crystals Used in the Dynamic Range Experiments

Tables Icon

Table 2 Maximum Index Change Δn in the Photorefractive Gratinga

Tables Icon

Table 3 Calculated Fundamental Limit on the Dynamic Range Due to Each Noise Source

Equations (21)

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

η = c sin 2 ( 2 π Δ n m l λ r cos θ r β 1 + β ) ,
SNR ϕ = β N ϕ ( 0.075 + 0.44 β N ϕ ) 1 / 2
β ϕ , min = 0.58 N ϕ = 0.58 h ν P τ pr ,
SNR pr = 2 β N eff V E D E q + E D ,
E D = k B T k g e , E q = e N eff k g ,
β pr , min = 1 2 N eff V E D + E q E D E D E q 1 N eff V .
k D = ( e 2 N eff k B T ) 1 / 2 .
SNR Kerr = β n 7 r eff 2 N eff V 2 r n 2 [ E q E D ( E q + E D ) 2 ] ,
β Kerr , min = α β pr , min ,
α = 4 r n 2 n 7 r eff 2 ( E q + E D E q ) .
U sc = 2 V E sc 2 ( x ) d x ,
U sc = 2 V E sc 2 ( x ) d x = V 2 | δ E sc | 2 = k B T / 2 .
| δ E sc | 2 diffusion limit = k B T / ( V ) ,
| δ E sc ( k g ) | 2 = k B T V [ 1 + k g 2 k D 2 ] 1 ,
δ = ( 2 ) δ E sc ,
( 2 ) = n 4 r .
| δ ( q ) | 2 pr = k B T V ( 1 + k g 2 k D 2 ) 1 [ ( 2 ) ] 2 .
I ( x ) = I 0 [ 1 + m cos ( k g x ) ] ,
E sc eq ( x ) = k B T k g e ( 1 + k g 2 k D 2 ) 1 m sin ( k g x ) .
| Δ ( k g ) | 2 = 1 2 ( k B T k g e ) 2 ( 1 + k g 2 k D 2 ) 2 [ ( 2 ) ] 2 m 2 .
SNR pr = | Δ ( k g ) | 2 | δ ( k g ) | 2 pr = k B T k g 2 V m 2 2 e 2 ( 1 + k g 2 k D 2 ) 1 = N eff V 2 ( 1 + k D 2 k g 2 ) 1 m 2 ,

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