Abstract

We demonstrate that recording thick holographic phase gratings in photorefractive polymers can lead not only to very efficient Bragg diffraction but also to rather strong diffraction into non-Bragg orders. We show that this effect has features drastically different from those of Raman–Nath diffraction on thin gratings. We compare the experimental results with a model based on the theory of dynamic self-diffraction in a photorefractive medium. Applications of this effect in devices for optical image processing are proposed.

© 1996 Optical Society of America

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References

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  1. B. Goss Lev, “New compound brightens outlook for photorefractive polymers,” Phys. Today 48(1), 17 (1995).
    [CrossRef]
  2. K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
    [CrossRef]
  3. W. E. Moerner, S. M. Silence, Chem. Rev. 94, 127 (1994).
    [CrossRef]
  4. P. Günter, J. P. Huignard, eds., Photorefractive Materials and Their Applications I and II (Springer-Verlag, Berlin, 1989).
  5. S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
    [CrossRef]
  6. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  7. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  8. A. Roy, K. Singh, J. Appl. Phys. 71, 5332 (1992).
    [CrossRef]
  9. L. B. Au, L. Solymar, IEEE J. Quantum Electron. 24, 162 (1988).
    [CrossRef]
  10. B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
    [CrossRef]
  11. B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.
  12. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

1995

B. Goss Lev, “New compound brightens outlook for photorefractive polymers,” Phys. Today 48(1), 17 (1995).
[CrossRef]

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

1994

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

W. E. Moerner, S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

1992

A. Roy, K. Singh, J. Appl. Phys. 71, 5332 (1992).
[CrossRef]

1988

L. B. Au, L. Solymar, IEEE J. Quantum Electron. 24, 162 (1988).
[CrossRef]

1979

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

1969

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

Au, L. B.

L. B. Au, L. Solymar, IEEE J. Quantum Electron. 24, 162 (1988).
[CrossRef]

Caulfield, H. J.

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Goss Lev, B.

B. Goss Lev, “New compound brightens outlook for photorefractive polymers,” Phys. Today 48(1), 17 (1995).
[CrossRef]

Kippelen, B.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Kogelnik, H.

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

Kukhtarev, N.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Meerholz, K.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Moerner, W. E.

W. E. Moerner, S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Peyghambarian, N.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Roy, A.

A. Roy, K. Singh, J. Appl. Phys. 71, 5332 (1992).
[CrossRef]

Sandalphon,

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Silence, S. M.

W. E. Moerner, S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

Singh, K.

A. Roy, K. Singh, J. Appl. Phys. 71, 5332 (1992).
[CrossRef]

Solymar, L.

L. B. Au, L. Solymar, IEEE J. Quantum Electron. 24, 162 (1988).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Volodin, B. L.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Bell Syst. Tech. J.

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

Chem. Rev.

W. E. Moerner, S. M. Silence, Chem. Rev. 94, 127 (1994).
[CrossRef]

Ferroelectrics

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron.

L. B. Au, L. Solymar, IEEE J. Quantum Electron. 24, 162 (1988).
[CrossRef]

J. Appl. Phys.

A. Roy, K. Singh, J. Appl. Phys. 71, 5332 (1992).
[CrossRef]

Nature

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, Nature (London) 371, 497 (1994).
[CrossRef]

Opt. Eng.

B. L. Volodin, Sandalphon, K. Meerholz, B. Kippelen, N. Kukhtarev, N. Peyghambarian, Opt. Eng. 34, 2213 (1995).
[CrossRef]

Phys. Today

B. Goss Lev, “New compound brightens outlook for photorefractive polymers,” Phys. Today 48(1), 17 (1995).
[CrossRef]

Rep. Prog. Phys.

S. I. Stepanov, Rep. Prog. Phys. 57, 39 (1994).
[CrossRef]

Other

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

B. L. Volodin, B. Kippelen, K. Meerholz, N. V. Kukhtarev, H. J. Caulfield, N. Peyghambarian, “Study of non-Bragg orders in dynamic self-diffraction in a photorefractive polymer: experiment, theory, and applications,” submitted to J. Opt. Soc. Am. B.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (3)

Fig. 1
Fig. 1

Asymmetric energy exchange between the ±0 beams in dynamic self-diffraction. The inset shows a schematic of the geometry of the dynamic self-diffraction experiments. Beams +0 and −0 are the writing beams, and beams +1 and −1 are the non-Bragg (higher-order) diffracted beams. K is the grating vector.

Fig. 2
Fig. 2

Diffraction efficiency into the +1 (filled circles) and −1 (open triangles) non-Bragg orders as a function of the applied field. The field polarity convention is illustrated in Fig. 1. The inset shows the calculated diffraction efficiency for the ±1 orders according to Eq. (2).

Fig. 3
Fig. 3

Photograph of the ±0 beams transmitted through the sample and the ±1 non-Bragg diffraction orders. The −0 beam is collimated, the +0 beam is diverging, the −1 beam is converging (demonstrating the phase-conjugate relation to the +0 beam), and the +1 beam is diverging approximately two times faster than the +0 beam (demonstrating the phase doubling).

Equations (4)

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± 1 = - i k 0 Δ n K ( cos  ξ ± i sin  ξ ) ± 0 2 0 * I 0 + I b × exp ( i Q ± 1 z ) - 1 Q ± 1 ,
Q ± 1 Δ k 1 cos  α ± 1 - k 0 Δ n 0 cos  ψ + δ , δ = k 0 Δ n K cos  ξ cos  ψ I ± 0 ( z ) - I 0 ( z ) I 0 + I b ,
η ± 1 I ± 1 ( d ) I 0 = ( k 0 d Δ n K cos  α ± 1 ) 2 I ± 0 2 ( d ) I 0 ( d ) I 0 ( I 0 + I b ) 2 × [ sin ( Q ± 1 d / 2 ) Q ± 1 d / 2 ] 2 .
Q ± 1 d / 2 κ k 0 d Δ n K / cos  α ± 1 .

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