Abstract

Photoinduced anisotropic Bragg diffraction in photorefractive coefficient KNbO3 using the electro-optic r42 = 380 pm/V has been studied. It has been demonstrated that, by using a noncritical configuration, a He–Ne laser beam with fixed incidence angle can be deflected within a range of 5.67 deg by changing the wavelength λr of the Ar+ laser beams used for recording the photorefractive grating (wavelength tuning range; 457.9 nm < λr < 514.5 nm). It is shown that for the reported interaction angles between recording and diffracted beams, the Bragg condition is noncritically fulfilled for the whole deflection range without any beam tilting being required.

© 1986 Optical Society of America

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References

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  1. P. Günter, Phys. Rep. 93, 199 (1982).
    [CrossRef]
  2. R. W. Dixon, IEEE J. Quantum Electron. QE-3, 85 (1967).
    [CrossRef]
  3. E. I. Gordon, Bell Syst. Tech. J. 44, 693 (1965).
  4. V. V. Lemanov, Ferroelectrics 7, 11 (1974).
    [CrossRef]
  5. G. T. Sincerbox, G. Roosen, Appl. Opt. 22, 690 (1983).
    [CrossRef] [PubMed]
  6. J. P. Huignard, B. Ledu, Opt. Lett. 7, 310 (1982).
    [CrossRef] [PubMed]
  7. S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).
  8. N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
    [CrossRef]
  9. P. Günter, Opt. Commun. 11, 285 (1974).
    [CrossRef]
  10. N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
    [CrossRef]
  11. J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).
  12. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  13. J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

1985

J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).

1984

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

1983

1982

1977

S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).

1974

V. V. Lemanov, Ferroelectrics 7, 11 (1974).
[CrossRef]

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
[CrossRef]

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

1969

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1967

R. W. Dixon, IEEE J. Quantum Electron. QE-3, 85 (1967).
[CrossRef]

1965

E. I. Gordon, Bell Syst. Tech. J. 44, 693 (1965).

Baumert, J.-C.

J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).

Chubachi, N.

N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
[CrossRef]

Dixon, R. W.

R. W. Dixon, IEEE J. Quantum Electron. QE-3, 85 (1967).
[CrossRef]

Gordon, E. I.

E. I. Gordon, Bell Syst. Tech. J. 44, 693 (1965).

Günter, P.

J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).

P. Günter, Phys. Rep. 93, 199 (1982).
[CrossRef]

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

Heaton, J. M.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Hoffnagle, J.

J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).

Huignard, J. P.

Kamshilin, A. A.

S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).

Kikuchi, Y.

N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kraetzig, E.

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

Kuelich, H. C.

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

Ledu, B.

Lemanov, V. V.

V. V. Lemanov, Ferroelectrics 7, 11 (1974).
[CrossRef]

Mills, P. A.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Paige, E. G. S.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Petrov, M. P.

S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).

Roosen, G.

Rupp, R. A.

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

Sincerbox, G. T.

Solymar, L.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Stepanov, S. J.

S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).

Watatsuki, N.

N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
[CrossRef]

Wilson, T.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Appl. Opt.

Appl. Phys. B

N. V. Kukhtarev, E. Kraetzig, H. C. Kuelich, R. A. Rupp, Appl. Phys. B, 35, 17 (1984).
[CrossRef]

Bell Syst. Tech. J.

E. I. Gordon, Bell Syst. Tech. J. 44, 693 (1965).

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Ferroelectrics

V. V. Lemanov, Ferroelectrics 7, 11 (1974).
[CrossRef]

IEEE J. Quantum Electron.

R. W. Dixon, IEEE J. Quantum Electron. QE-3, 85 (1967).
[CrossRef]

Jpn. J. Appl. Phys.

N. Watatsuki, N. Chubachi, Y. Kikuchi, Jpn. J. Appl. Phys. 13, 1754 (1974).
[CrossRef]

Opt. Acta

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 875 (1974).

Opt. Commun.

P. Günter, Opt. Commun. 11, 285 (1974).
[CrossRef]

Opt. Lett.

Phys. Rep.

P. Günter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

J.-C. Baumert, J. Hoffnagle, P. Günter, Proc. Soc. Photo-Opt. Instrum. Eng. 492, 374 (1985).

Sov. Tech. Phys. Lett.

S. J. Stepanov, M. P. Petrov, A. A. Kamshilin, Sov. Tech. Phys. Lett. 3, 345 (1977).

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Figures (4)

Fig. 1
Fig. 1

Wave-vector diagrams for a, isotropic and b, anisotropic Bragg-diffraction. c, Configuration for anisotropic Bragg diffraction used in the noncritical light deflector described in this work. d, Experimental situation for anisotropic Bragg diffraction in KNbO3. ki and kd, wave vectors of the incident and diffracted waves. θi and θd, angles of incidence and diffraction of the reading beam. K, wave vector of the induced photorefractive grating. 2θr is the angle between the two recording beams I+1 and K−1.

Fig. 2
Fig. 2

Wave-vector dependence of the angles of incidence and diffraction θi and θd for anisotropic Bragg diffraction using the geometry shown in Fig. 1d [calculated from Eqs. (5) by using refractive-index data from Ref. 11; angles measured inside the crystal].

Fig. 3
Fig. 3

Measured angles of incidence and diffraction θi′ and θd′ for anisotropic Bragg diffraction in KNbO3 as a function of the photoinduced grating wave number. (Solid lines, theoretical; angles measured outside the crystal.)

Fig. 4
Fig. 4

a, Photograph of the deflected readout beam (λ0 = 633 nm) by anisotropic Bragg scattering from photorefractive gratings recorded at eight different Ar laser lines at fixed recording angle 2θr = 36.9 deg. b, Diffraction efficiency and deflection angle for anisotropic Bragg diffraction at photorefractive gratings in KNbO3. ○, *: Recording at fixed wavelength λr = 488 nm and fixed angle of incidence θi′ = 56.23 deg only (○) and θi′ = 56.30 deg (*); tuning of angle of deflection by changing the angle 2θr between the recording beams. •, Recording at fixed angle between recording beams 2θr = 36.9 deg and fixed angle of incidence θi′ = 56.23 deg; tuning of angle of deflection by changing the recording wavelength.

Equations (12)

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Δ ( 1 n 2 ) i j ( r ) = r i j k E sc , k I ( r ) ,
E sc ( r ) = [ 0 , E 0 sin ( K x 2 ) , 0 ]
Δ ( 1 n 2 ) 23 ( x 2 ) = 2 r 232 E 0 sin ( K x 2 ) .
k d = k i ± K ,
K / k 0 = n sin θ i + n 3 sin θ d ,
cos θ d = ( n / n 3 ) cos θ i ,
n = ( cos 2 θ i n 2 2 + sin 2 θ i n 1 2 ) - 1 / 2 , θ i = sin - 1 [ n sin ( θ i ) ] ,             θ d = sin - 1 [ n 3 sin ( θ d ) ] .
Λ = λ r / 2 sin ( θ r )
Δ θ d Δ K / k 0 .
η = sin 2 ( ν 2 + ξ 2 ) 1 / 2 ( 1 + ξ 2 / ν 2 ) ,
ν = π L Δ n / λ 0 ,             ξ = L δ K / 2 ;
N = Δ θ d / δ θ = 100.

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