Abstract

Recent analytical results in the frame of photorefractive spatial-soliton propagation are exploited to derive a novel scheme for the investigation of space-charge field formation in photorefractive crystals. The procedure is specialized to describe a two-wave mixing configuration. To test our predictions, we have performed an experiment in a sample of BaTiO3.

© 1998 Optical Society of America

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References

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  1. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
    [CrossRef]
  2. P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1988); Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).
  3. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  4. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, UK, 1996).
  5. L. B. Au and L. Solymar, Opt. Lett. 13, 660 (1988).
    [CrossRef]
  6. M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
    [CrossRef]
  7. N. V. Kukhtarev, P. Buchhave, and S. F. Lyuksyutov, Phys. Rev. A 55, 3133 (1997).
    [CrossRef]
  8. Y. H. Lee and R. W. Hellwarth, J. Appl. Phys. 71, 916 (1992).
    [CrossRef]
  9. A. Bledowski, J. Otten, and K. H. Ringhofer, Opt. Lett. 16, 672 (1991).
    [CrossRef] [PubMed]
  10. M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  11. M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef]
  12. B. Crosignani, P. Di Porto, A. Degasperis, M. Segev, and S. Trillo, J. Opt. Soc. Am. B 14, 3078–3090 (1997).
    [CrossRef]
  13. F. Vachss and L. Hesselink, J. Opt. Soc. Am. A 5, 690 (1988).
    [CrossRef]
  14. Conditions (17) express in a compact form the limitations imposed by our resolving scheme. The first is quite restrictive. Apart from the possibility of being relaxed at the cost of greater algebraic complexity, it has the advantage of being valid for all values of 0<m1<1. The condition on the drift field is related to the so-called saturation field and is easily verified in most doped crystals for standard applied voltages.
  15. A. Yariv, Optical Electronics, 5th ed. (Wiley, New York, 1995).
  16. J. H. Hong and R. Saxena, Opt. Lett. 16, 180 (1991).
    [PubMed]

1997

1996

1994

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1992

Y. H. Lee and R. W. Hellwarth, J. Appl. Phys. 71, 916 (1992).
[CrossRef]

1991

1988

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Au, L. B.

Bledowski, A.

Buchhave, P.

N. V. Kukhtarev, P. Buchhave, and S. F. Lyuksyutov, Phys. Rev. A 55, 3133 (1997).
[CrossRef]

Crosignani, B.

B. Crosignani, P. Di Porto, A. Degasperis, M. Segev, and S. Trillo, J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Degasperis, A.

Di Porto, P.

B. Crosignani, P. Di Porto, A. Degasperis, M. Segev, and S. Trillo, J. Opt. Soc. Am. B 14, 3078–3090 (1997).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Hellwarth, R. W.

Y. H. Lee and R. W. Hellwarth, J. Appl. Phys. 71, 916 (1992).
[CrossRef]

Hesselink, L.

Hong, J. H.

Kukhtarev, N. V.

N. V. Kukhtarev, P. Buchhave, and S. F. Lyuksyutov, Phys. Rev. A 55, 3133 (1997).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

Lee, Y. H.

Y. H. Lee and R. W. Hellwarth, J. Appl. Phys. 71, 916 (1992).
[CrossRef]

Lyuksyutov, S. F.

N. V. Kukhtarev, P. Buchhave, and S. F. Lyuksyutov, Phys. Rev. A 55, 3133 (1997).
[CrossRef]

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

Otten, J.

Ringhofer, K. H.

Saxena, R.

Segev, M.

Shih, M.

Solymar, L.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

Trillo, S.

Vachss, F.

Valley, G. C.

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Vinetski, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Young, L.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetski, Ferroelectrics 22, 961 (1979).
[CrossRef]

J. Appl. Phys.

M. G. Moharam, T. K. Gaylord, R. Magnusson, and L. Young, J. Appl. Phys. 50, 5642 (1979).
[CrossRef]

Y. H. Lee and R. W. Hellwarth, J. Appl. Phys. 71, 916 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

N. V. Kukhtarev, P. Buchhave, and S. F. Lyuksyutov, Phys. Rev. A 55, 3133 (1997).
[CrossRef]

Phys. Rev. Lett.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Other

P. Günter and J. P. Huignard, eds., Photorefractive Materials and Their Applications I (Springer-Verlag, Berlin, 1988); Photorefractive Materials and Their Applications II (Springer-Verlag, Berlin, 1989).

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

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

Conditions (17) express in a compact form the limitations imposed by our resolving scheme. The first is quite restrictive. Apart from the possibility of being relaxed at the cost of greater algebraic complexity, it has the advantage of being valid for all values of 0<m1<1. The condition on the drift field is related to the so-called saturation field and is easily verified in most doped crystals for standard applied voltages.

A. Yariv, Optical Electronics, 5th ed. (Wiley, New York, 1995).

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Figures (4)

Fig. 1
Fig. 1

Basic experimental arrangement for measuring TWM, Bragg diffraction and TWM beam size dependence.

Fig. 2
Fig. 2

Measured values of first harmonic Bragg diffraction efficiency for an expected m1=0.3 with He–Ne, as a function of external bias voltage. The fit is obtained by taking of the first harmonic of Eq. (20) and use of relation (28). (b) Measured values of second harmonic Bragg diffraction efficiency. The fit is obtained by taking of the second harmonic of Eq. (20).

Fig. 3
Fig. 3

(a) Measured values of TWM gain ratio of the amplified beam for m1=0.84. Superimposed is the fitting curve obtained by taking of the first harmonic of Eq. (20) and use of Eq. (29). (b) TWM gain ratio for m1=0.92.

Fig. 4
Fig. 4

Measured values of σ=g2/(V/lEDb)2 for various values of lb/l. The fitting curve is obtained for m10.2 and Q01.7. Beam coupling higher than first-harmonic is neglected.

Equations (46)

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γNeNd+=(β+sI)(Nd-Nd+),
(d/dx)(E)=ρ,
ρ=q(Nd+-Na-Ne),
(d/dx)J=0,
J=qμNeE+μkbT(d/dx)Ne,
V=--l/2l/2E dx,
qμ(β+sI)Nd-q ddx E-Naγq ddx E+Na E
+ddx μkbT(β+sI)Nd-q ddx E-Naγq ddx E+Na=Jc.
YEEDb,ξkDbx,
Q1+IId,GJcqμβ1EDb,
QYα-δ ddξ Y1+δ ddξ Y+ddξ Q α-δ ddξ Y1+δ ddξ Y=G.
QY1+ddξ Y+ddξ Q1+ddξ Y=Gαg.
I=I0[1+m cos(Kx)],
Q=1+I0Ib+Id [1+m cos(χξ)]=1+Q0[1+m cos(χξ)]=(1+Q0)[1+m1 cos(χξ)],
Y=-QQ+gQ+gQ Y+Y1+Y,
|Y|1,
|Y|-QQ+gQ+gQ Y.
Y(0)=-QQ+gQYd+Ydr,
|Y0|1,
|Y(0)|-QQ+gQ+gQ Y(0).
1,|Ydr|1,
=χm11-m1m1>12χm1<12.
Y=gQ+o().
Y=-QQ+gQ-gQ2 QQ+o(2).
g=-VlEDb 1(1-lb/l)+(lb/l)/[(1+Q0)(1-m12)1/2],
g=-VlEDb(1+Q0)(1-m12)1/2=gmax,for lbl=1,
g=-VlEDb=gmin,for lb=0.
gmin1 1-m1(1-m12)1/2.
Y=-QQ+o(2).
Δ[1/n2]ij=rijkEk,
Δn-½ rn3E,
ηin2rkR4 cos(θi) LE(i)2,
γ=πn3rλ cos(θ) |E(1)a|.
I2(L)I2(0)=1+M1+Me-γL exp(-αL),
Y(0)=-QQ+QQ2-YdrQQ,
Y(0)QQ+QQ2+|Ydr|QQ.
Y(0)m1χ21-m1+m12χ2(1-m1)2+|Ydr| m1χ1-m1,
|Y(0)|m1χ3(1-m1)+3m12χ3(1-m1)2+2m1χ(1-m1)3+|Ydr| m1χ2(1-m1)+2|Ydr|m1χ(1-m1)2.
|Ydr| m1χ2(1-m1)+2|Ydr|m1χ(1-m1)2
-QQ+gQ+gQ Y(0).
|Ydr| m1χ2(1-m1)+2|Ydr|m1χ(1-m1)2|Ydr|,
-kDbEDb V=-lkDb/2lkDb/2Ydξ.
-kDbEDb V=-lkDb/2lkDb/2 gQ dξ=-lkDb/2lkDb/2 g(1+Q0)[1+m1 cos(χξ)] dξ.
-lkDb/2lkDb/2 g(1+Q0)[1+m1 cos(χξ)] dξ
=(l-lb)gkDb+g(1+Q0) -lkDb/2lkDb/2 1[1+m1 cos(χξ)] dξ.
-lkDb/2lkDb/2 1[1+m1 cos(χξ)] dξlbkDb(1-m12)1/2.

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