Abstract

Higher-order combinational gratings play an important role in explaining so-called nonlinear cross talk between index gratings in photorefractive media. We present what are to our knowledge the first experimental results showing the existence of a new, strong combinational index grating in a three-wave mixing experiment. We investigate the kinetics of the first harmonic, the second harmonic, and the new combinational index gratings. As a novel result, we demonstrate that the rise time of the new grating is strongly dependent on the intensity ratio of the incident recording beams. For low values of the intensity ratio the rise time is more than twice the value of the ordinary second-harmonic grating. Furthermore, it is shown that the steady-state strength of the new grating can be more than five times greater than that of ordinary second-harmonic gratings and can lead to substantial nonlinear cross talk on the first- and second-harmonic gratings.

© 1998 Optical Society of America

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References

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  1. J.-P. Huignard and B. Ledu, “Collinear Bragg diffraction in photorefractive Bi12SiO20,” Opt. Lett. 7, 310–312 (1982).
    [Crossref] [PubMed]
  2. S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
    [Crossref]
  3. 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, 1422–1433 (1995).
    [Crossref]
  4. H. C. Pedersen, P. E. Andersen, P. M. Petersen, and P. M. Johansen, “Theory of nonlinear multiple-grating interaction in diffusion-dominated photorefractive media,” J. Opt. Soc. Am. B 13, 2569–2579 (1996).
    [Crossref]
  5. 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]
  6. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [Crossref] [PubMed]
  7. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [Crossref]
  8. Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [Crossref]
  9. E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at large modulation depths,” J. Opt. Soc. Am. B 11, 670–675 (1994).
    [Crossref]
  10. J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
    [Crossref]
  11. A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
    [Crossref]

1996 (1)

1995 (2)

1994 (2)

1993 (1)

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
[Crossref]

1991 (1)

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

1990 (1)

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

1985 (1)

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

1982 (2)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

J.-P. Huignard and B. Ledu, “Collinear Bragg diffraction in photorefractive Bi12SiO20,” Opt. Lett. 7, 310–312 (1982).
[Crossref] [PubMed]

Agulló-López, F.

Alvarez-Bravo, J. V.

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
[Crossref]

Andersen, P. E.

Arizmendi, L.

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
[Crossref]

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[Crossref] [PubMed]

Bauschulte, S.

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

Buchhave, P.

Carrascosa, M.

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at large modulation depths,” J. Opt. Soc. Am. B 11, 670–675 (1994).
[Crossref]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
[Crossref]

Fries, S.

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

Günter, P.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Habiby, S. F.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[Crossref] [PubMed]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[Crossref] [PubMed]

Hubbard, W. M.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

Huignard, J.-P.

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

J.-P. Huignard and B. Ledu, “Collinear Bragg diffraction in photorefractive Bi12SiO20,” Opt. Lett. 7, 310–312 (1982).
[Crossref] [PubMed]

Johansen, P. M.

Krätzig, E.

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

Ledu, B.

López, V.

Marrakchi, A.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

Patel, J. S.

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

Pedersen, H. C.

Petersen, P. M.

Rajbenbach, H.

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Refrégier, Ph.

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Ringhofer, K.

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

Serrano, E.

Solymar, L.

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

Vasnetsov, M. V.

Yacoby, Y.

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

J. Appl. Phys. (1)

Ph. Refrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103, 22–28 (1993).
[Crossref]

S. Fries, S. Bauschulte, E. Krätzig, K. Ringhofer, and Y. Yacoby, “Spatial frequency mixing in lithium niobate,” Opt. Commun. 84, 251–257 (1991).
[Crossref]

Opt. Eng. (1)

A. Marrakchi, W. M. Hubbard, S. F. Habiby, and J. S. Patel, “Dynamic holographic interconnects with analog weights in photorefractive crystals,” Opt. Eng. 29, 215–225 (1990).
[Crossref]

Opt. Lett. (1)

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Science (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic of recording and readout in the three-wave mixing configuration. In the experiments recording and readout are carried out simultaneously, but they are shown here separately for clarity. (a) Recording of gratings, (b) readout of gratings. BSO, Bi12SiO20.

Fig. 2
Fig. 2

Schematic of the spatial frequencies of the space-charge field and their relation to the index gratings. The amplitudes of the grating components relative to one another do not resemble the real values.

Fig. 3
Fig. 3

Diffraction pattern of ordinary second-harmonic G22 and combinational index grating G23 for β=0.245. Solid curves, the diffraction pattern without phase modulation applied to I1; dotted curves, the diffraction pattern with phase modulation applied to I1.

Fig. 4
Fig. 4

Normalized diffraction efficiency η(t) versus time for the three index gratings: G2 (circles), G22 (triangles), and G23 (squares). The parameters obtained from the experimental setup are β=0.255, κ=0.80, fringe spacings Λ1=0.925 μm and Λ2=0.933 μm, and separation angle δθ=2.7 mrad. The steady-state values of the diffraction efficiencies have been normalized to unity to facilitate the comparison.

Fig. 5
Fig. 5

Rise times t1090 as a function of intensity ratio β for the three index gratings: G2 (circles), G22 (triangles), and G23 (squares). The parameters obtained from the experimental setup are κ=0.80, fringe spacings Λ1=0.925 μm and Λ2=0.933 μm, and separation angle δθ=2.7 mrad.

Tables (1)

Tables Icon

Table 1 Nonlinear Cross Talk Δη as a Function of Intensity Ratio β for Non-Phase-Modulated Index Grating Components G2 and G22

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