Abstract

The nonlinear interactions between gratings generated during multibeam photorefractive recording with one reference and N object beams have been investigated theoretically. It is shown that nonlinear cross talk between gratings, which is well known in three-beam recording, persists and even increases for the practical relevant case in which the number of object beams N is large. The magnitude of the cross talk depends on the particular grating, and it is significant for a range of intensities commonly used in many multibeam applications. Finally, it is shown that for large N (N>5) the nonlinear interactions strongly suppress most gratings, whereas specific gratings can be selectively amplified.

© 1999 Optical Society of America

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  1. P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
    [CrossRef]
  2. P. Ashtana, G. P. Nordin, A. R. Tanguay, Jr., and B. K. Jenkins, “Analysis of weighted fan-out/fan-in volume holographic optical interconnections,” Appl. Opt. 32, 1441–1469 (1993).
    [CrossRef]
  3. C. Gu, S. Campbell, and P. Yeh, “Matrix–matrix multiplication by using grating degeneracy in photorefractive media,” Opt. Lett. 18, 146–148 (1993).
    [CrossRef] [PubMed]
  4. C. Gu and P. Yeh, “Application of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
    [CrossRef]
  5. L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
    [CrossRef]
  6. F. Vachss and L. Hesselink, “Nonlinear photorefractive response at high modulation depth,” J. Opt. Soc. Am. A 5, 690–701 (1988).
    [CrossRef]
  7. L. B. Au and L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulations with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1562 (1990).
    [CrossRef]
  8. E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
    [CrossRef]
  9. R. Saxena and T. Y. Chang, “Perturbative analyses of higher-order photorefractive gratings,” J. Opt. Soc. Am. B 9, 1467–1472 (1992).
    [CrossRef]
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    [CrossRef]
  11. E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910–1912 (1995).
    [CrossRef] [PubMed]
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  13. P. E. Andersen, P. M. Petersen, and P. Buchhave, “Nonlinear combinations of gratings in drift dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
    [CrossRef]
  14. P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
    [CrossRef]
  15. L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
    [CrossRef]
  16. C. Gu, J. Hong, I. McMichael, R. Saxena, and F. Mok, “Cross-talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
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    [CrossRef]
  18. W. H. Press, S. A. Teukolsky, W. T. Weterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).
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    [CrossRef]
  20. L. Solymar, D. J. Webb, and A. Grunet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, Oxford, 1996).

1996

P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
[CrossRef]

1995

1994

P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
[CrossRef]

C. Gu and P. Yeh, “Application of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

L. Boutsikaris and F. Davidson, “Perturbative analyses of higher-order photorefractive gratings in InP:Fe,” Opt. Commun. 105, 411–420 (1994).
[CrossRef]

1993

1992

1990

L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
[CrossRef]

L. B. Au and L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulations with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1562 (1990).
[CrossRef]

1988

1979

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

1969

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

Agulló-López, F.

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910–1912 (1995).
[CrossRef] [PubMed]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

Andersen, P. E.

P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, “Nonlinear combinations of gratings in Bi12SiO20: theory and experiments,” J. Opt. Soc. Am. B 12, 1423–1435 (1995).

P. E. Andersen, P. M. Petersen, and P. Buchhave, “Nonlinear combinations of gratings in drift dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
[CrossRef]

Ashtana, P.

Au, L. B.

Bashaw, M. C.

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Boutsikaris, L.

L. Boutsikaris and F. Davidson, “Perturbative analyses of higher-order photorefractive gratings in InP:Fe,” Opt. Commun. 105, 411–420 (1994).
[CrossRef]

Buchhave, B.

P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
[CrossRef]

Buchhave, P.

P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
[CrossRef]

P. E. Andersen, P. M. Petersen, and P. Buchhave, “Nonlinear combinations of gratings in drift dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, “Nonlinear combinations of gratings in Bi12SiO20: theory and experiments,” J. Opt. Soc. Am. B 12, 1423–1435 (1995).

Campbell, S.

Carrascosa, M.

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910–1912 (1995).
[CrossRef] [PubMed]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

Chang, T. Y.

Davidson, F.

L. Boutsikaris and F. Davidson, “Perturbative analyses of higher-order photorefractive gratings in InP:Fe,” Opt. Commun. 105, 411–420 (1994).
[CrossRef]

Denz, C.

L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
[CrossRef]

Gu, C.

Hesselink, L.

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

F. Vachss and L. Hesselink, “Nonlinear photorefractive response at high modulation depth,” J. Opt. Soc. Am. A 5, 690–701 (1988).
[CrossRef]

Hong, J.

Jenkins, B. K.

Klees, L.

L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
[CrossRef]

Kogelnik, H.

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

Kukhtarev, N. V.

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

López, V.

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

Markov, V. B.

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

McMichael, I.

Mok, F.

Nordin, G. P.

Odulov, S. G.

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

Petersen, P. M.

P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
[CrossRef]

P. E. Andersen, P. M. Petersen, and P. Buchhave, “Nonlinear combinations of gratings in drift dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, “Nonlinear combinations of gratings in Bi12SiO20: theory and experiments,” J. Opt. Soc. Am. B 12, 1423–1435 (1995).

P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
[CrossRef]

Saxena, R.

Serrano, E.

E. Serrano, M. Carrascosa, and F. Agulló-López, “Nonperturbative analytical solution for steady-state photorefractive recording,” Opt. Lett. 20, 1910–1912 (1995).
[CrossRef] [PubMed]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

Solymar, L.

Soskin, M. S.

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

Tanguay , Jr., A. R.

Tschudi, T.

L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
[CrossRef]

Vachss, F.

Vasnetsov, M. V.

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, “Nonlinear combinations of gratings in Bi12SiO20: theory and experiments,” J. Opt. Soc. Am. B 12, 1423–1435 (1995).

Vinetskii, V. L.

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

Yeh, P.

C. Gu and P. Yeh, “Application of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

C. Gu, S. Campbell, and P. Yeh, “Matrix–matrix multiplication by using grating degeneracy in photorefractive media,” Opt. Lett. 18, 146–148 (1993).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

P. E. Andersen, P. M. Petersen, and B. Buchhave, “Cross-talk in dynamic optical interconnects in photorefractive crystals,” Appl. Phys. Lett. 65, 271–273 (1994).
[CrossRef]

Bell Syst. Tech. J.

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

Ferroelectrics

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

IEEE J. Quantum Electron.

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady-state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30, 875–880 (1994).
[CrossRef]

Int. J. Nonlinear Opt. Phys.

C. Gu and P. Yeh, “Application of photorefractive volume holography in optical computing,” Int. J. Nonlinear Opt. Phys. 3, 317–337 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

L. Boutsikaris and F. Davidson, “Perturbative analyses of higher-order photorefractive gratings in InP:Fe,” Opt. Commun. 105, 411–420 (1994).
[CrossRef]

P. E. Andersen, P. Buchhave, and P. M. Petersen, “Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20,” Opt. Commun. 128, 185–192 (1996).
[CrossRef]

L. Klees, C. Denz, and T. Tschudi, “Intensity crosstalk and angular selectivity of multibeam coupling in photorefractive BaTiO3,” Opt. Commun. 77, 65–70 (1990).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Other

W. H. Press, S. A. Teukolsky, W. T. Weterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

L. Solymar, D. J. Webb, and A. Grunet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, Oxford, 1996).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental configuration for multibeam recording.

Fig. 2
Fig. 2

Semilogarithmic plot of nonlinear coupling parameter Δη versus intensity ratio β=IR/I0 for (a) grating 1, (b) grating, 2, and (c) grating 5. The curves correspond to various numbers N of object beams.

Fig. 3
Fig. 3

Dependence of nonlinear coupling parameter Δη on the order number n of the grating for (filled triangles) two, (filled squares) five, and (filled circles) eight object beams. Two intensity ratios are considered: (a) β=IR/I0=10-2 and (b) β=1.

Fig. 4
Fig. 4

Diffraction efficiency η as a function of the order number of the primary gratings for two intensity ratios: (a) β=IR/I0=10-2 and (b) β=1. Different numbers of object beams were considered: (filled triangles) N=2, (filled squares) N=5, and (filled circles) N=8. In each case the values of the diffraction efficiency in the linear approximation have been included for comparison (dotted lines).

Fig. 5
Fig. 5

Grating diffraction efficiencies versus the number of object beams N for (a) β=IR/I0=10-2 and (b) β=IR/I0=1. Squares, outer grating G1; circles, inner grating (see text). The dotted curves show the diffraction efficiency calculated in the linear (noncoupled gratings) approximation.

Equations (10)

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An=½[A0 exp(ikn·r+ϕn)+c.c.],
AR=½[AR exp(ik·r)+c.c.],
I(x)=IT1+n=1Nm cos(Knx)+n=1Nl=1,l>nNM cos[(l-n)ΔKx],
ESC=-kBTe1n(x)nx=-n=1NEDnm sin(Knx)+l=1l>nNEDnlM sin[(l-n)ΔKx]1+n=1Nm cos(Knx)+l=1l>nNM cos[(l-n)ΔKx],
ESC=-l=1El sin(lΔKx),
Δn=-(½reffn03)n=1EKn sin(Knx)=n=1Δnn sin(Knx),
ηn=sin2Δnn πLλ sin θ,
Δηn=ηn-ηnηn,
ηnΔnn2πLλ sin θ2.
ΔηnEn2-En2En2.

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