Abstract

A new method is proposed for determining the two-beam coupling gain coefficients of photorefractive crystals with both o- and e-polarized lights. This method enables one to determine simultaneously and precisely the gain coefficients of a crystal for o- and e-polarized lights while the fanning effect is diminished. Experimental demonstrations are presented.

© 1998 Optical Society of America

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References

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  1. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I, Vol. 61 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1988); Photorefractive Materials and Their Applications II, Vol. 62 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1989).
  2. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  3. P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
    [CrossRef]
  4. P. Tayebati and D. Mahgerefteh, J. Opt. Soc. Am. B 8, 1053 (1991).
    [CrossRef]
  5. M. H. Garrett, J. Y. Chang, H. P. Jenssen, and C. Warde, J. Opt. Soc. Am. B 9, 1407 (1992).
    [CrossRef]
  6. R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, J. Opt. Soc. Am. B 9, 1416 (1992).
    [CrossRef]
  7. See, for example, K. R. MacDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
    [CrossRef]
  8. J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).
    [CrossRef]
  9. Q. B. He and P. Yeh, Appl. Opt. 33, 283 (1994).
    [CrossRef] [PubMed]
  10. J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
    [CrossRef]
  11. H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
    [CrossRef]
  12. See Ref.??7 for their definitions. The only difference is that the term eˆ1·eˆ2* in Eq.??(10) of Ref.??7, which comes from the interference of the coupling beams, is included in the expression of the modulation index m in Eq.??(2) in this Letter. This term is equal to 1 for the o polarization and to cos 2?e for the e polarization.

1996 (1)

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

1994 (1)

1993 (1)

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

1992 (2)

1991 (1)

1989 (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[CrossRef]

1983 (1)

1982 (1)

Chang, J. Y.

Ewbank, M. D.

Feinberg, J.

Gao, H.

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

Garrett, M. H.

He, Q. B.

Itoh, M.

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

Jenssen, H. P.

Kuroda, K.

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

MacDonald, K. R.

Mahgerefteh, D.

Neurgaonkar, R. R.

Ogura, I.

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

Okamura, H.

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

Shimura, T.

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

Tayebati, P.

Vazquez, R. A.

Warde, C.

Ye, P. X.

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

Yeh, P.

Q. B. He and P. Yeh, Appl. Opt. 33, 283 (1994).
[CrossRef] [PubMed]

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[CrossRef]

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

Zhang, J. S.

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

Zhu, Y.

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. S. Zhang, H. Gao, Y. Zhu, and P. X. Ye, Appl. Phys. Lett. 68, 2174 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

H. Okamura, T. Shimura, K. Kuroda, M. Itoh, and I. Ogura, Opt. Commun. 99, 230 (1993).
[CrossRef]

Other (3)

See Ref.??7 for their definitions. The only difference is that the term eˆ1·eˆ2* in Eq.??(10) of Ref.??7, which comes from the interference of the coupling beams, is included in the expression of the modulation index m in Eq.??(2) in this Letter. This term is equal to 1 for the o polarization and to cos 2?e for the e polarization.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I, Vol. 61 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1988); Photorefractive Materials and Their Applications II, Vol. 62 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

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

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Figures (4)

Fig. 1
Fig. 1

Schematic of beam coupling of two linearly polarized incident beams in a 0°-cut photorefractive crystal. θin, external incident angle; θo, internal incident angle for o light; θe, internal incident angle for e light. PBS, polarizing beam splitter.

Fig. 2
Fig. 2

Variations of Go, Ge, and R with β for different internal incident angles θ, calculated with Eqs.  (7) and (8). γoL and γeL are assumed to be 0.25 and 1, respectively, and to be independent of θ.

Fig. 3
Fig. 3

Measured steady-state gains Go (open circles) and Ge (open squares) and the ratio R (filled triangles) as a function of β of the two incident beams. The curves are theoretical results obtained with γo=1.57 cm-1, γe=5.76 cm-1, L=0.139 cm. Inset, time evolution of measured Go and Ge at β=30°.

Fig. 4
Fig. 4

TBC gain coefficients of the crystal for o- and e-polarized lights determined from the gains measured at different β as given in Fig.  3. γo=1.57 cm-1, γe=5.76 cm-1.

Equations (9)

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I=I01+m cos2πx/Λ+ϕ,
I0=A1o2+A1e2+A2o2+A2e2, m=2A1o*A2o+2A1e*A2ecos 2θe/I0,
dA1idz=12γimA2i-αi2 cos θiA1i,  i=o, e,
dA1idz=γisiAoe-αi2 cos θiA1i,  i=o, e,
A1iL=A1i0+siγi/γeffAoe0expγeffL-1×exp-αL/2 cos θ,  i=o, e,
γeff=so2γo+se2γe cos 2θ.
Go=1+soγo/γeffso+se tan β1 cos 2θ×expγeffL-12, Ge=1+seγe/γeffso cot β1+se cos 2θ×expγeffL-12,
RGe1/2-1Go1/2-1=tan β2tan β1γe/γo.
γeff=1/L lnso2Go1/2+se2Ge1/2 cos 2θso2+se2 cos 2θ, γo=γe/R=γeff/so2+Rse2 cos 2θ.

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