Abstract

A nonperturbative analytical solution for steady-state photorefractive recording in the diffusion approximation has been obtained. It applies to any arbitrary modulation depth m and includes, as limit cases, the perturbation solutions reported by previous authors.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [Crossref]
  2. M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Appl. Phys. 50, 5642 (1979).
    [Crossref]
  3. E. Ochoa, F. Vachss, L. Hesselink, J. Opt. Soc. Am. A 3, 181 (1986).
    [Crossref]
  4. Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
    [Crossref]
  5. R. Saxena, T. Y. Chang, J. Opt. Soc. Am. B 9, 1467 (1992).
    [Crossref]
  6. L. Boutsikaris, F. Davidson, Opt. Commun. 105, 411 (1994).
    [Crossref]
  7. M. Cronin-Golomb, Opt. Commun. 89, 276 (1993).
    [Crossref]
  8. K. Ratnam, P. P. Banerjee, Opt. Commun. 107, 522 (1994).
    [Crossref]
  9. O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
    [Crossref]
  10. E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
    [Crossref]

1995 (1)

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

1994 (3)

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

L. Boutsikaris, F. Davidson, Opt. Commun. 105, 411 (1994).
[Crossref]

K. Ratnam, P. P. Banerjee, Opt. Commun. 107, 522 (1994).
[Crossref]

1993 (1)

M. Cronin-Golomb, Opt. Commun. 89, 276 (1993).
[Crossref]

1992 (1)

1986 (1)

1985 (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

1979 (2)

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

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

Agullo-Lopez, F.

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

Banerjee, P. P.

K. Ratnam, P. P. Banerjee, Opt. Commun. 107, 522 (1994).
[Crossref]

Boutsikaris, L.

L. Boutsikaris, F. Davidson, Opt. Commun. 105, 411 (1994).
[Crossref]

Carrascosa, M.

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

Chang, T. Y.

Cronin-Golomb, M.

M. Cronin-Golomb, Opt. Commun. 89, 276 (1993).
[Crossref]

Daniel, O.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

Davidson, F.

L. Boutsikaris, F. Davidson, Opt. Commun. 105, 411 (1994).
[Crossref]

Gaylord, T. K.

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

Hesselink, L.

Huignard, J. P.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Jonathan, J.-M. C.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

Kukhtarev, N. V.

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

Lopez, V.

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

Magnusson, R.

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

Markov, V. B.

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

Moharam, M. G.

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

Ochoa, E.

Odulov, S. G.

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

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Ratnam, K.

K. Ratnam, P. P. Banerjee, Opt. Commun. 107, 522 (1994).
[Crossref]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Roosen, G.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

Saxena, R.

Serrano, E.

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Soskin, M.

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

Stelmach, A.

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

Vachss, F.

Vinetskii, V. L.

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

Ferroelectrics (1)

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

IEEE J. Quantum Electron. (1)

E. Serrano, V. Ĺopez, M. Carrascosa, F. Agulĺo-Ĺopez, IEEE J. Quantum Electron. 30, 875 (1994).
[Crossref]

J. Appl. Phys. (2)

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

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

L. Boutsikaris, F. Davidson, Opt. Commun. 105, 411 (1994).
[Crossref]

M. Cronin-Golomb, Opt. Commun. 89, 276 (1993).
[Crossref]

K. Ratnam, P. P. Banerjee, Opt. Commun. 107, 522 (1994).
[Crossref]

O. Daniel, A. Stelmach, J.-M. C. Jonathan, G. Roosen, Opt. Commun. 113, 559 (1995).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Dependence of the amplitude of the (a) first, (b) second, and (c) third harmonic components of the field on the grating vector K with Λ = 2π/K. The analytical solution is represented by the solid curves, and the exact numerical solution by the dashed curves. As a reference, the amplitude of the fundamental grating corresponding to the linear solution is displayed with a dotted curve in (a).

Equations (25)

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

N D + ( r ) t = s I ( r ) N D 0 - γ n N D + ( r ) ,
n ( r ) t = N D + ( r ) t - 1 e J ( r ) ,
J ( r ) = e μ n E ( r + μ k b T n ( r ) ,
[ 0 E ( r ) ] = - e [ n ( r ) + N A - N D + ( r ) ] ,
I ( r ) = I 0 [ 1 + m 2 exp ( i Kr ) + c . c . ] ,
E ( r ) = - k b T e log [ n ( r ) ] .
E ( r ) - k b T e [ E ( r ) ] k d 2 k b T / e + E ( r ) = - k b T e log [ I ( r ) ] ,
k d 2 = e N A k b T .
E ( r ) - 1 k d 2 [ E ( r ) ] = - k b T e log I ( r ) .
E ( r ) - 1 k d 2 [ E ( r ) ] = m k b T e K F ( r ) sin ( Kr ) ,
F ( r ) = 1 1 + m cos ( Kr )
E ( r ) = E 0 + j = 1 E j exp ( i j Kr ) + c . c . ,
F ( r ) = A 0 + j = 1 A j exp ( i j Kr ) + c . c . ,
A j = 1 2 π / K 0 2 π / K 1 1 + m cos ( Kr ) cos ( j Kr ) d r .
A 0 = 1 1 - m 2 ,
A 1 = 1 - 1 - m 2 m 1 - m 2 ,
A 2 = 2 - m 2 - 2 1 - m 2 m 2 1 - m 2 ,
A 3 = 4 - 3 m 2 - 4 1 - m 2 + m 2 1 - m 2 m 3 1 - m 2 ,
A 4 = 8 - 8 m 2 - 8 1 - m 2 + 4 m 2 1 - m 2 + m 4 m 4 1 - m 2 .
j = 1 [ 1 + ( j K k d ) 2 ] [ E j exp ( i j Kr ) + E j * exp ( - i j Kr ) ] = m E D ( A 0 sin ( Kr ) + j = 1 { A j sin [ K ( j + 1 ) r ] - A j sin [ K ( j - 1 ) r ] } ) ,
E D = K T k b e .
E j = - i 2 E D m 1 + ( j K k d ) 2 ( A j - 1 - A j + 1 )             j 1.
E 1 = - i 2 E D m 1 + K 2 k d 2 × ( 1 1 - m 2 - 2 - m 2 - 2 1 - m 2 m 2 1 - m 2 ) ,
E 2 = i 2 E D m 1 + 4 K 2 k d 2 ( 1 - 1 - m 2 m 1 - m 2 - 4 - 3 m 2 - 4 1 - m 2 + m 2 1 - m 2 m 3 1 - m 2 ) ,
E 3 = - i 2 E D m 1 + 9 K 2 k d 2 ( 2 - m 2 - 2 1 - m 2 m 2 1 - m 2 - 8 - 8 m 2 - 8 1 - m 2 + 4 m 2 1 - m 2 + m 4 m 4 1 - m 2 ) .

Metrics