Abstract

Two-beam coupling between orthogonally polarized waves is demonstrated by use of linear dichroism in Cu-doped potassium sodium strontium barium niobate. A maximum coupling gain coefficient of approximately 4 cm-1 is obtained at a grating spacing of 1 µm and a wavelength of 514.5 nm, where linear dichroism is moderate. The experimental results are compared with a theoretical model that allows a photorefractive grating to have an arbitrary phase shift with respect to an intensity-interference pattern. Fitting results indicate that the grating is not 90°-phase-shifted under open-circuit conditions. The contribution of the bulk photovoltaic field to the photorefractive phase shift is discussed.

© 1999 Optical Society of America

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References

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  1. R. R. Neurgaonkar and W. K. Cory, “Progress in photorefractive tungsten bronze crystals,” J. Opt. Soc. Am. B 3, 274–282 (1986).
    [CrossRef]
  2. H. Chen and Y. Xu, “Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6, (KNSBN) single crystals with tungsten–bronze structure,” J. Cryst. Growth 96, 357–362 (1989).
  3. Y. Tomita, J. Bergquist, and M. Shibata, “Photorefractive properties of undoped, Cr-doped and Cu-doped potassium sodium strontium barium niobate crystals,” J. Opt. Soc. Am. B 10, 94–99 (1993); Y. Tomita and J. Bergquist, “Photorefractive and thermooptic nonlinearities in potassium sodium strontium barium niobate single crystals,” Optoelectronics 8, 357–377 (1993); Y. Tomita and A. Suzuki, “Broadband photorefractivity of Cr-doped strontium barium niobate in the visible and near-infrared spectral regions,” Opt. Rev. 1, 233–236 (1994).
    [CrossRef]
  4. S. R. Montgomery, Y. Yarrison-Rice, D. O. Pederson, G. J. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “Self-pumped phase conjugation in the red in photorefractive Ba0.5Sr1.5K0.25Na0.75Nb5O15 and Sr0.6Ba0.4Nb2O6 with cerium in 9-fold coordinated sites,” J. Opt. Soc. Am. B 5, 1775–1782 (1988).
    [CrossRef]
  5. J. Xu, S. Liu, J. Y. Wu, G. Zhang, Y. Song, and H. Chen, “Observation of self-pumped phase-conjugate wave in Cu-KNSBN crystal,” Opt. Commun. 80, 239–241 (1991); J. Xu, Y. Wu, S. Liu, G. Zhang, D. Sun, Y. Song, and H. Chen, “High-performance self-pumped phase conjugator with a multichannel in KNSBN:Cu crystal,” Opt. Lett. 16, 1255–1257 (1991); Q. Jiang, X. Lu, Y. Song, D. Sun, H. Chen, J. Zhang, S. Bian, Y. Yuan, and K. Xu, “Enhanced self-pumped phase conjugation from 16°-cut KNSBN:Cu,” Appl. Opt. APOPAI 31, 6299–6302 (1992).
    [CrossRef] [PubMed]
  6. D. Sun, J. Chen, X. Lu, Y. Song, Z. Shao, H. Chen, J. Xu, Y. Wu, S. Liu, and G. Zhang, “Growth and self-pumped phase conjugation of Ce-doped KNa(Sr0.61Ba0.39)0.4Nb2O6,” J. Appl. Phys. 70, 33–35 (1991); S. Bian, J. Zhang, X. Su, W. Sun, Q. Jiang, H. Chen, and D. Sun, “Self-pumped phase conjugation of 18°-cut Ce-doped KNSBN crystal at 632.8 nm,” Opt. Lett. 18, 769–771 (1993).
    [CrossRef] [PubMed]
  7. S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
    [CrossRef]
  8. H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
    [CrossRef]
  9. Y. Li, S. Liu, M. Yang, K. Yang, K. Xu, and F. Hou, “Superior real-time holographic storage properties in doped potassium sodium strontium barium niobate crystal,” Opt. Lett. 22, 212–214 (1997).
    [CrossRef] [PubMed]
  10. F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
    [CrossRef]
  11. P. Jullien, P. Mathey, P. Lompré, A. Novikov, and S. Odoulov, “Coupling of ordinary and extraordinary waves in iron-doped BaTiO3 by a grating recorded by spatially oscillating photovoltaic currents,” J. Opt. Soc. Am. B 13, 2615–2621 (1996), and references therein.
    [CrossRef]
  12. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, UK, 1996), Chap. 2.
  13. R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, and M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium-doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1941 (1991).
    [CrossRef]
  14. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass. 1974), Chap. 9.
  15. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 2.
  16. X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
    [CrossRef]
  17. Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
    [CrossRef]
  18. The magnitude of the space-charge field under open-circuit conditions is approximately 1.2 kV/cm in the absence of Eph, while it is 1.1 kV/cm in the presence of Eph of −2.7 kV/cm. Therefore our estimated values for r13 and r33 without Eph differ only less than 10% from those with Eph of −2.7 kV/cm.

1997 (2)

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

Y. Li, S. Liu, M. Yang, K. Yang, K. Xu, and F. Hou, “Superior real-time holographic storage properties in doped potassium sodium strontium barium niobate crystal,” Opt. Lett. 22, 212–214 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

1994 (2)

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

1991 (2)

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, and M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium-doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1941 (1991).
[CrossRef]

1989 (1)

H. Chen and Y. Xu, “Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6, (KNSBN) single crystals with tungsten–bronze structure,” J. Cryst. Growth 96, 357–362 (1989).

1988 (1)

1986 (1)

Bian, S.

Chen, H.

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

H. Chen and Y. Xu, “Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6, (KNSBN) single crystals with tungsten–bronze structure,” J. Cryst. Growth 96, 357–362 (1989).

Chen, H. C.

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

Clark III, W. W.

Cory, W. K.

Ewbank, M. D.

Frejlich, J.

Höhne, J.

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Hou, F.

Jiang, Q.

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Jullien, P.

Kahmann, F.

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Li, Y.

Liu, S.

Lompré, P.

Lu, X.

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Lu, X. L.

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

Mathey, P.

Miller, M. J.

Montgomery, S. R.

Neurgaonkar, R. R.

Novikov, A.

Odoulov, S.

Pankrath, R.

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Pederson, D. O.

Rupp, R. A.

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Salamo, G. J.

Shao, Z.

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Sharp, E. J.

Song, Y.

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Sun, D.

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Vachss, F. R.

Vazquez, R. A.

Wang, C. J.

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

Wood, G. L.

Xia, H. R.

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

Xu, K.

Xu, Y.

H. Chen and Y. Xu, “Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6, (KNSBN) single crystals with tungsten–bronze structure,” J. Cryst. Growth 96, 357–362 (1989).

Yang, K.

Yang, M.

Yarrison-Rice, Y.

Yue, X.

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

Appl. Phys. B (1)

X. Yue, X. Lu, Y. Song, Z. Shao, D. Sun, Q. Jiang, and H. Chen, “Studies of self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals,” Appl. Phys. B 53, 319–322 (1991).
[CrossRef]

J. Cryst. Growth (1)

H. Chen and Y. Xu, “Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6, (KNSBN) single crystals with tungsten–bronze structure,” J. Cryst. Growth 96, 357–362 (1989).

J. Opt. Soc. Am. B (5)

Opt. Lett. (1)

Phys. Rev. (2)

H. R. Xia, C. J. Wang, H. C. Chen, and X. L. Lu, “Photorefractive properties of manganese-modified potassium sodium strontium barium niobate crystals,” Phys. Rev. 55, 1292–1294 (1997).
[CrossRef]

F. Kahmann, J. Höhne, R. Pankrath, and R. A. Rupp, “Hologram recording with mutually orthogonal polarized waves in Sr0.61Ba0.39Nb2O6:Ce,” Phys. Rev. 50, 2474–2478 (1994).
[CrossRef]

Phys. Rev. B (1)

Q. Jiang, X. Lu, Y. Song, D. Sun, and H. Chen, “Copper–ion point defects in the photorefractive material (KxNa1−x)0.4(SryBa1−y)0.8Nb2O6,” Phys. Rev. B 50, 4185–4188 (1994).
[CrossRef]

Other (7)

The magnitude of the space-charge field under open-circuit conditions is approximately 1.2 kV/cm in the absence of Eph, while it is 1.1 kV/cm in the presence of Eph of −2.7 kV/cm. Therefore our estimated values for r13 and r33 without Eph differ only less than 10% from those with Eph of −2.7 kV/cm.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, UK, 1996), Chap. 2.

M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, Reading, Mass. 1974), Chap. 9.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 2.

Y. Tomita, J. Bergquist, and M. Shibata, “Photorefractive properties of undoped, Cr-doped and Cu-doped potassium sodium strontium barium niobate crystals,” J. Opt. Soc. Am. B 10, 94–99 (1993); Y. Tomita and J. Bergquist, “Photorefractive and thermooptic nonlinearities in potassium sodium strontium barium niobate single crystals,” Optoelectronics 8, 357–377 (1993); Y. Tomita and A. Suzuki, “Broadband photorefractivity of Cr-doped strontium barium niobate in the visible and near-infrared spectral regions,” Opt. Rev. 1, 233–236 (1994).
[CrossRef]

J. Xu, S. Liu, J. Y. Wu, G. Zhang, Y. Song, and H. Chen, “Observation of self-pumped phase-conjugate wave in Cu-KNSBN crystal,” Opt. Commun. 80, 239–241 (1991); J. Xu, Y. Wu, S. Liu, G. Zhang, D. Sun, Y. Song, and H. Chen, “High-performance self-pumped phase conjugator with a multichannel in KNSBN:Cu crystal,” Opt. Lett. 16, 1255–1257 (1991); Q. Jiang, X. Lu, Y. Song, D. Sun, H. Chen, J. Zhang, S. Bian, Y. Yuan, and K. Xu, “Enhanced self-pumped phase conjugation from 16°-cut KNSBN:Cu,” Appl. Opt. APOPAI 31, 6299–6302 (1992).
[CrossRef] [PubMed]

D. Sun, J. Chen, X. Lu, Y. Song, Z. Shao, H. Chen, J. Xu, Y. Wu, S. Liu, and G. Zhang, “Growth and self-pumped phase conjugation of Ce-doped KNa(Sr0.61Ba0.39)0.4Nb2O6,” J. Appl. Phys. 70, 33–35 (1991); S. Bian, J. Zhang, X. Su, W. Sun, Q. Jiang, H. Chen, and D. Sun, “Self-pumped phase conjugation of 18°-cut Ce-doped KNSBN crystal at 632.8 nm,” Opt. Lett. 18, 769–771 (1993).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for two-beam coupling between orthogonally polarized beams.

Fig. 2
Fig. 2

Spectral absorption coefficients for the nominally Cu-doped KNSBN sample with light polarization parallel with (αe) and perpendicular to (αo) the c axis. The anisotropy Δα, defined as αo-αe, is also plotted.

Fig. 3
Fig. 3

Measured exponential coupling gain ΓL versus θ at a grating spacing of 1 µm and with an input intensity ratio of 100. The solid and the dotted curves are the least-squares fit to Eqs. (6)–(8) with ϕ=-67° and ϕ=-90°, respectively.

Fig. 4
Fig. 4

Measured exponential coupling gains ΓoL and ΓeL as a function of θ, where Γ(o, e) are defined as (1/L) ln[Is(o, e)×(L)|with pump/Is(o, e)(L)|without pump]. The solid and the dotted curves are the theoretical results at ϕ=-67° and ϕ=-90°, respectively.

Equations (18)

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

Γ=1LlnIs(L)|withpumpIs(L)|withoutpump,
Io+e(x, z)=I0[1+12m(z)exp(iKx)+c.c.],
I0=Ip(1)+Ip(2)+Is(1)+Is(2),
m(z)=2eˆp(1)·eˆs(1)*Ep(1)Es(1)*+eˆp(2)·eˆs(2)*Ep(2)Es(2)*I0,
n1(o, e)=12[n(o, e)]3reff(o, e)Esc,
dI˜pedz=-dI˜sedz=+12Γem1(z, ϕ)I˜peI˜se,
dI˜podz=-dI˜sodz=-12Γom2(z, ϕ)I˜poI˜so,
dΔΨdz=14Γeme(z, ϕ)I˜peI˜se-I˜seI˜pe+Γom4(z, ϕ)I˜poI˜so-I˜soI˜po,
ΔΨ=Ψpe-Ψse-Ψpo+Ψso,
Γo=4πn1o|maxλ1cos φi,
Γe=4πn1e|maxλcos 2φicos φi,
m1(z, ϕ)=2I˜peI˜se cos 2φi sin ϕ-I˜poI˜so exp(-Δαz)sin(ϕ+ΔΨ)I˜pe+I˜se+(I˜po+I˜so)exp(-Δαz),
m2(z, ϕ)=2I˜peI˜se sin(ϕ-ΔΨ)-I˜poI˜so exp(-Δαz)cos 2φi sin ϕI˜pe+I˜se+(I˜po+I˜so)exp(-Δαz),
m3(z, ϕ)=2I˜peI˜se cos 2φi cos ϕ-I˜poI˜so exp(-Δαz)cos(ϕ+ΔΨ)I˜pe+I˜se+(I˜po+I˜so)exp(-Δαz),
m4(z, ϕ)=2I˜peI˜se cos(ϕ-ΔΨ)-I˜poI˜so exp(-Δαz)cos 2φi cos ϕI˜pe+I˜se+(I˜po+I˜so)exp(-Δαz),
Esc=-imEq[Ed-i(E0+Eph)]Eq+Ed-iE0,
dΔΨdz=f(z)sin ΔΨ,
f(z)=-Γe exp(-Δαz)(I˜pe-I˜se)(I˜poI˜so/I˜peI˜se)1/2+o(I˜po-I˜so)(I˜peI˜se/I˜poI˜so)1/22[I˜pe+I˜se+(I˜po+I˜so)exp(-Δαz)],

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