Abstract

Distributed grating coupling of light pulses into planar waveguides, exhibiting third-order nonlinear-optical effects, is studied theoretically. The nonlinear interaction taking place between a beam that is Gaussian in time and space and one or more waveguide media with intensity-dependent refractive indexes or absorptions is analyzed, with emphasis on the different effects that result from the relative importance of two-photon absorption dispersive index changes, and their saturation. Criteria for the evaluation of real and imaginary parts of χ(3) by means of grating coupling are outlined.

© 1991 Optical Society of America

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    [CrossRef]
  9. J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl. Phys. 60, 1591 (1986).
    [CrossRef]
  14. G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
    [CrossRef]
  15. G. Vitrant and P. Arlot, J. Appl. Phys. 61, 4744 (1987).
    [CrossRef]
  16. F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
    [CrossRef]
  17. M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
    [CrossRef]
  18. G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 432 (1988).
    [CrossRef]
  19. W. Lukosz, V. Briguet, and J. Kramer, Opt. Commun. 69, 121 (1988).
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  20. K. Sasaki, K. Fujii, T. Tomioka, and T. Kinoshita, J. Opt. Soc. Am. B 5, 457 (1988).
    [CrossRef]
  21. R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 425 (1988).
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  22. R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
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  23. B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
    [CrossRef]
  24. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
    [CrossRef]
  25. G. Assanto, J. Mod. Opt. 36, 316 (1989).
    [CrossRef]
  26. P. Dannberg, T. Possner, A. Brauer, and U. Bartuch, Phys. Status Solidi B 150, 873 (1989).
    [CrossRef]
  27. G. Vitrant, R. Reinisch, J. Cl. Paumier, G. Assanto, and G. I. Stegeman, Opt. Lett. 14, 898 (1989).
    [CrossRef] [PubMed]
  28. G. Assanto and G. I. Stegeman, J. Appl. Phys. 67, 1188 (1990).
    [CrossRef]
  29. B. Svensson, G. Assanto, and G. I. Stegeman, J. Appl. Phys. 67, 3882 (1990).
    [CrossRef]
  30. J. Ehrlich, G. Assanto, and G. I. Stegeman, Opt. Commun. 75, 441 (1990).
    [CrossRef]
  31. V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, Opt. Lett. 14, 1140 (1989).
    [CrossRef] [PubMed]
  32. G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
    [CrossRef]
  33. M. Romagnoli and G. I. Stegeman, Opt. Commun. 64, 343 (1987); G. Assanto, J. P. Sabini, N. Finlayson, G. I. Stegeman, S. Trillo, and S. Wabnitz, Proc. Soc. Photo-Opt. Instrum. Eng. 1148, 162 (1989).
    [CrossRef]

1990 (3)

G. Assanto and G. I. Stegeman, J. Appl. Phys. 67, 1188 (1990).
[CrossRef]

B. Svensson, G. Assanto, and G. I. Stegeman, J. Appl. Phys. 67, 3882 (1990).
[CrossRef]

J. Ehrlich, G. Assanto, and G. I. Stegeman, Opt. Commun. 75, 441 (1990).
[CrossRef]

1989 (4)

1988 (9)

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
[CrossRef]

M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 432 (1988).
[CrossRef]

W. Lukosz, V. Briguet, and J. Kramer, Opt. Commun. 69, 121 (1988).
[CrossRef]

K. Sasaki, K. Fujii, T. Tomioka, and T. Kinoshita, J. Opt. Soc. Am. B 5, 457 (1988).
[CrossRef]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 425 (1988).
[CrossRef]

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
[CrossRef]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

1987 (4)

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

G. Vitrant and P. Arlot, J. Appl. Phys. 61, 4744 (1987).
[CrossRef]

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

M. Romagnoli and G. I. Stegeman, Opt. Commun. 64, 343 (1987); G. Assanto, J. P. Sabini, N. Finlayson, G. I. Stegeman, S. Trillo, and S. Wabnitz, Proc. Soc. Photo-Opt. Instrum. Eng. 1148, 162 (1989).
[CrossRef]

1986 (2)

1985 (2)

1984 (1)

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

1983 (2)

G. M. Carter and Y. J. Chen, Appl. Phys. Lett. 42, 643 (1983).
[CrossRef]

G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[CrossRef]

1982 (2)

Y. J. Chen and G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[CrossRef]

1977 (1)

T. Tamir and S. T. Peng, Appl. Phys. 14, 235 (1977).
[CrossRef]

1975 (1)

1973 (1)

1970 (1)

Andrejco, M. J.

Arlot, P.

G. Vitrant and P. Arlot, J. Appl. Phys. 61, 4744 (1987).
[CrossRef]

Assanto, G.

G. Assanto and G. I. Stegeman, J. Appl. Phys. 67, 1188 (1990).
[CrossRef]

B. Svensson, G. Assanto, and G. I. Stegeman, J. Appl. Phys. 67, 3882 (1990).
[CrossRef]

J. Ehrlich, G. Assanto, and G. I. Stegeman, Opt. Commun. 75, 441 (1990).
[CrossRef]

G. Vitrant, R. Reinisch, J. Cl. Paumier, G. Assanto, and G. I. Stegeman, Opt. Lett. 14, 898 (1989).
[CrossRef] [PubMed]

G. Assanto, J. Mod. Opt. 36, 316 (1989).
[CrossRef]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 425 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 432 (1988).
[CrossRef]

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

G. Assanto, B. Svensson, D. Kuchibhatla, U. J. Gibson, C. T. Seaton, and G. I. Stegeman, Opt. Lett. 11, 644 (1986).
[CrossRef] [PubMed]

Bartuch, U.

P. Dannberg, T. Possner, A. Brauer, and U. Bartuch, Phys. Status Solidi B 150, 873 (1989).
[CrossRef]

Brauer, A.

P. Dannberg, T. Possner, A. Brauer, and U. Bartuch, Phys. Status Solidi B 150, 873 (1989).
[CrossRef]

Briguet, V.

W. Lukosz, V. Briguet, and J. Kramer, Opt. Commun. 69, 121 (1988).
[CrossRef]

Burzynski, R.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
[CrossRef]

Carter, G. M.

G. M. Carter and Y. J. Chen, Appl. Phys. Lett. 42, 643 (1983).
[CrossRef]

G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[CrossRef]

Y. J. Chen and G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

Chelli, H.

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

Chen, Y. J.

G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[CrossRef]

G. M. Carter and Y. J. Chen, Appl. Phys. Lett. 42, 643 (1983).
[CrossRef]

Y. J. Chen and G. M. Carter, Appl. Phys. Lett. 41, 307 (1982).
[CrossRef]

Cullen, T. J.

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

Dalgoutte, D. G.

Dannberg, P.

P. Dannberg, T. Possner, A. Brauer, and U. Bartuch, Phys. Status Solidi B 150, 873 (1989).
[CrossRef]

Delisle, C.

S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl. Phys. 60, 1591 (1986).
[CrossRef]

DeLong, K. W.

Ehrlich, J.

J. Ehrlich, G. Assanto, and G. I. Stegeman, Opt. Commun. 75, 441 (1990).
[CrossRef]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
[CrossRef]

Fortenberry, R. M.

Fujii, K.

Gabel, A.

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

Garmire, E.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

Gibson, U. J.

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
[CrossRef]

G. Assanto, B. Svensson, D. Kuchibhatla, U. J. Gibson, C. T. Seaton, and G. I. Stegeman, Opt. Lett. 11, 644 (1986).
[CrossRef] [PubMed]

Heeger, A. J.

M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
[CrossRef]

Ironside, C. N.

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

Jerominiek, H.

S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl. Phys. 60, 1591 (1986).
[CrossRef]

Kinoshita, T.

Koster, A.

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

P. Vincent, N. Paraire, N. Neviere, A. Koster, and R. Reinisch, J. Opt. Soc. Am. B 2, 1106 (1985).
[CrossRef]

Kramer, J.

W. Lukosz, V. Briguet, and J. Kramer, Opt. Commun. 69, 121 (1988).
[CrossRef]

Kuchibhatla, D.

Laval, S.

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

Liao, C.

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
[CrossRef]

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

Lukosz, W.

W. Lukosz, V. Briguet, and J. Kramer, Opt. Commun. 69, 121 (1988).
[CrossRef]

Mai, X.

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

Maradudin, A. A.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

McBranch, D.

M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
[CrossRef]

Mizrahi, V.

Moses, D.

M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
[CrossRef]

Moshrefzadeh, R.

Neviere, N.

Paraire, N.

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

P. Vincent, N. Paraire, N. Neviere, A. Koster, and R. Reinisch, J. Opt. Soc. Am. B 2, 1106 (1985).
[CrossRef]

Pardo, F.

F. Pardo, H. Chelli, A. Koster, N. Paraire, and S. Laval, IEEE J. Quantum Electron. QE-23, 545 (1987).
[CrossRef]

Patela, S.

S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl. Phys. 60, 1591 (1986).
[CrossRef]

Paumier, J. Cl.

Peng, S. T.

T. Tamir and S. T. Peng, Appl. Phys. 14, 235 (1977).
[CrossRef]

Possner, T.

P. Dannberg, T. Possner, A. Brauer, and U. Bartuch, Phys. Status Solidi B 150, 873 (1989).
[CrossRef]

Prasad, P. N.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
[CrossRef]

Reinisch, R.

Romagnoli, M.

M. Romagnoli and G. I. Stegeman, Opt. Commun. 64, 343 (1987); G. Assanto, J. P. Sabini, N. Finlayson, G. I. Stegeman, S. Trillo, and S. Wabnitz, Proc. Soc. Photo-Opt. Instrum. Eng. 1148, 162 (1989).
[CrossRef]

Saifi, M. A.

Sasaki, K.

Seaton, C. T.

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 432 (1988).
[CrossRef]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 425 (1988).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
[CrossRef]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
[CrossRef]

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

G. Assanto, B. Svensson, D. Kuchibhatla, U. J. Gibson, C. T. Seaton, and G. I. Stegeman, Opt. Lett. 11, 644 (1986).
[CrossRef] [PubMed]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
[CrossRef]

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

Shoemaker, R. L.

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
[CrossRef]

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

Sinclair, M.

M. Sinclair, D. McBranch, D. Moses, and A. J. Heeger, Appl. Phys. Lett. 53, 2374 (1988).
[CrossRef]

Singh, B. P.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
[CrossRef]

Stegeman, G. I.

G. Assanto and G. I. Stegeman, J. Appl. Phys. 67, 1188 (1990).
[CrossRef]

J. Ehrlich, G. Assanto, and G. I. Stegeman, Opt. Commun. 75, 441 (1990).
[CrossRef]

B. Svensson, G. Assanto, and G. I. Stegeman, J. Appl. Phys. 67, 3882 (1990).
[CrossRef]

V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, Opt. Lett. 14, 1140 (1989).
[CrossRef] [PubMed]

G. Vitrant, R. Reinisch, J. Cl. Paumier, G. Assanto, and G. I. Stegeman, Opt. Lett. 14, 898 (1989).
[CrossRef] [PubMed]

R. M. Fortenberry, G. Assanto, R. Moshrefzadeh, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 425 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, J. Opt. Soc. Am. B 5, 432 (1988).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
[CrossRef]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
[CrossRef]

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
[CrossRef]

G. Assanto, A. Gabel, C. T. Seaton, G. I. Stegeman, C. N. Ironside, and T. J. Cullen, Electron. Lett. 23, 484 (1987).
[CrossRef]

M. Romagnoli and G. I. Stegeman, Opt. Commun. 64, 343 (1987); G. Assanto, J. P. Sabini, N. Finlayson, G. I. Stegeman, S. Trillo, and S. Wabnitz, Proc. Soc. Photo-Opt. Instrum. Eng. 1148, 162 (1989).
[CrossRef]

G. Assanto, B. Svensson, D. Kuchibhatla, U. J. Gibson, C. T. Seaton, and G. I. Stegeman, Opt. Lett. 11, 644 (1986).
[CrossRef] [PubMed]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
[CrossRef]

J. D. Valera, C. T. Seaton, G. I. Stegeman, R. L. Shoemaker, X. Mai, and C. Liao, Appl. Phys. Lett. 45, 1013 (1984).
[CrossRef]

G. I. Stegeman, IEEE J. Quantum Electron. QE-18, 1610 (1982).
[CrossRef]

Svensson, B.

Svensson, B. C.

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, Appl. Phys. Lett. 53, 941 (1988).
[CrossRef]

Tamir, T.

T. Tamir and S. T. Peng, Appl. Phys. 14, 235 (1977).
[CrossRef]

Tomioka, T.

Tremblay, R.

S. Patela, H. Jerominiek, C. Delisle, and R. Tremblay, J. Appl. Phys. 60, 1591 (1986).
[CrossRef]

Tripathy, S. K.

G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett. 43, 891 (1983).
[CrossRef]

Ulrich, R.

Valera, J. D.

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, J. Opt. Soc. Am. A 2, 590 (1985).
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G. Vitrant, R. Reinisch, J. Cl. Paumier, G. Assanto, and G. I. Stegeman, Opt. Lett. 14, 898 (1989).
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G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
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G. Vitrant and P. Arlot, J. Appl. Phys. 61, 4744 (1987).
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Wright, E. M.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
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Zanoni, R.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
[CrossRef]

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
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R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, Appl. Phys. Lett. 53, 2011 (1988).
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Appl. Opt. (1)

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G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, Appl. Phys. Lett. 52, 869 (1988).
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G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, IEEE J. Lightwave Technol. 6, 953 (1988); G. Assanto, J. Mod. Opt. 37, 855 (1990).
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Figures (18)

Fig. 1
Fig. 1

Geometry of a grating coupler. The grating is at the film–substrate interface, with the input beam I incident from the cladding at an angle θ from the normal. Note how the beam is displaced by a distance Δx from the edge of the coupler at x = 0. A transverse profile corresponding to a typical TE0 mode is sketched for the guided-wave field propagating along x. See text.

Fig. 2
Fig. 2

Evolution of a TE0 guided-field amplitude along a bidimensional coupler under cw excitation. The abscissa x = 500 (arbitrary units) corresponds to the rightmost edge of the grating coupler in Fig. 1. The curves refer to a grating coupler optimized at low powers in the absence of nonlinear effects (solid curve), with a dispersive Kerr-like nonlinearity (short-dashed curve) and n2,f = 10−17 m2/W, and in the case of a two-photon absorptive nonlinearity (long-dashed curve) with α2,f = 8.2 cm/GW (the subscript f stands for film).

Fig. 3
Fig. 3

Evolution of guided-field phase along the coupler described in Fig. 2. The solid line refers to the linear and TPA cases, while the dotted curve refers to the Kerr nonlinearity with n2,f = 10−17 m2/W. Note the large variations in the phase, exceeding π/2 in the nonlinear dispersive case. The phase value at x = 0 (corresponding to x ≃ −4.5w0 in the coordinate system in Fig. 1) depends on the phase of the coupling coefficient γm in Eq. (3) in the text.

Fig. 4
Fig. 4

Imaginary versus real part (arbitrary units) of the guidedwave field under a bidimensional grating coupler for dispersive Kerr-like nonlinearities with n2,f = 10−17 m2/W (solid curve), with n2,f = 10−16 m2/W (long-dashed curve), and for a TPA nonlinearity with α2,f = 0.1 cm/GW (short-dashed curve). The curves originate at x ≃ −∞ in the origin (0, 0) of the plane and evolve up to x = 0, the rightmost edge of the coupler (see Fig. 1). Each point marks an equal distance along the grating. The coupling -was optimized at low-powers.

Fig. 5
Fig. 5

Coupling efficiency versus input pulse energy for a three-dimensional grating coupler optimized at low powers with a purely dispersive nonlinearity n2,f = 10−17 m2/W (solid curve), with a combined TPA and Kerr nonlinearity α2,f = 1.0 cm/GW and the same n2,f (long-dashed curve), with a purely absorptive nonlinearity α2,f = 1.0 cm/GW (short-dashed curve), and with an integrating nonlinearity n2,f = 2.3 × 10−13 m2/W with relaxation time τ = 1 μsec (dotted curve). The input pulse duration is 100 psec (FWHM).

Fig. 6
Fig. 6

Coupling efficiency versus input pulse energy for a nonlinear coupler with n2,f = 10−16 m2/W and various α2,f and index saturation Δnsat. a, Purely dispersive Kerr nonlinearity, Δnsat = ∞, no TPA; b, Δnsat = 0.001, no TPA; c, Δnsat = 0.0005, no TPA; d, Δnsat = 0.0005, α2,f = 0.01 cm/GW; e, Δnsat = 0.0005, α2,f = 0.1 cm/GW.

Fig. 7
Fig. 7

Coupling efficiency η versus input pulse energy for a detuned coupler with n2,f = 10−16 m2/W and no TPA. The other coupling parameters are optimized at low powers. a, Δθ = 0.0; b, Δθ = 0.025°; c, Δθ = 0.05°; d, Δθ = −0.05°; e, Δθ = 0.1°; f, Δθ = 0.15°.

Fig. 8
Fig. 8

Same as in Fig. 7 but with n2,f = 0.0 m2/W and α2,f = 10.0 cm/GW. a, Δθ = 0.0°; b, Δθ = 0.025°; c, Δθ = 0.05°; d, Δθ = 0.1°; e, Δθ = 0.15°.

Fig. 9
Fig. 9

η versus input pulse energy for a detuned coupler with n2,f = 10−16 m2/W and index saturation. a, Kerr case; b, Δnsat = ∞, Δθ = 0.05°; c, Δnsat = 0.0005, Δθ = 0.05°; d, Δnsat = 0.001, Δθ = 0.05°.

Fig. 10
Fig. 10

η versus input pulse energy for a coupler optimized at low powers and various time constants. (a) Kerr n2,f = 10−17 m2/W and pulse duration Δt = 10 psec (solid curve), 100 psec (dotted curve), and 1 nsec (dashed curve). (b) Integrating nonlinearity n2,f = 2.3 × 10−12 m2/W, with Δt = 100 psec and relaxation time τ = 1 μsec (solid curve), 100 nsec (dotted curve), and 10 nsec (dashed curve).

Fig. 11
Fig. 11

Normalized coupled power versus time for a distributed coupler optimized at low powers. a, Gaussian input profile; b, Kerr n2,f = 10−17 m2/W, α2,f = 0.0 cm/GW; c, n2,f = 0.0 m2/W, α2,f = 8.2 cm/GW; d, n2,f = 9.0 × 10−18 m2/W, α2,f = 2.5 cm/GW; e, integrating n2,f = 2.3 × 10−13 m2/W and τ = 1 μsec. The input energy is 0.4 mJ in all cases, and the nonlinear coefficients are chosen to give approximately the same coupling efficiency.

Fig. 12
Fig. 12

Normalized coupled power versus time for a detuned coupler with Δθ = 0.1°, n2,f = 10−17 m2/W α2,f = 0.0 cm/GW, and various input energies in. Solid curve, input profile with Δt = 100 psec (FWHM); dotted curve, in = 3.0 μJ; short-dashed curve, in = 4.5 μJ; long-dashed curve, in = 6.0 μJ. The best compression is obtained for in = 4.5 μJ.

Fig. 13
Fig. 13

Coupled power (watts per meter) versus y and time for a coupler with n2,f = 10−17 m2/W, α2,f = 0.0 cm/GW, and an input energy of 0.4 mJ.

Fig. 14
Fig. 14

Coupled power (watts) versus time and versus angular detuning. The coupler has a dispersive Kerr nonlinearity as in Fig. 13, and the input energy is in = 0.4 mJ. The time axis is equivalent to a y axis, provided that the vertical coordinate is in units of joules per meter.

Fig. 15
Fig. 15

Coupled power (watts) versus time and versus angular detuning for a TPA coupler with α2,f = 8.2 cm/GW and in = 0.4 mJ.

Fig. 16
Fig. 16

Same as in Figs. 14 and 15 for a coupler with n2,f = 10−17 m2/W and α2,f = 8.2 cm/GW.

Fig. 17
Fig. 17

Coupling efficiency η versus incidence angle for a Kerr coupler with n2,f = 10−17 m2/W and no TPA. The vertical dashed line indicates the optimum coupling angle at low powers, while the solid curve a represents the linear response of the system. The angular response of the nonlinear grating exhibits a lower peak value of η and a larger shift in angle when the input pulse energy is increased from b, 10 μJ to c, 20 μJ; d, 40 μJ; e, 80 μJ; and f, 160 μJ.

Fig. 18
Fig. 18

Same as in Fig. 17 for an input energy of 40 μJ and various nonlinearities at low-power optimum coupling. a, Linear response, reduced by factor 2; b, α2,f = 1.0 cm/GW, n2,f = 0.0 m2/W; c, α2,f = 8 cm/GW, n2,f = 0.0 m2/W; d, α2,f = 0.0 cm/GW, n2,f = 10−17 m2/W; e, α2,f = 2.5 cm/GW, n2,f = 9.0 × 10−17 M2/W.

Equations (20)

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E in ( x , y , t ) = ½ e ^ in a in ( x , y , t ) exp [ i ( ω t - k 0 x sin θ ) ] + c . c .
E gw m ( x , y , z , t ) = ½ e ^ gw C m a gw m ( x , y , t ) f m ( z ) × exp { i [ ω t - Re ( β 0 m ) x ] } + c . c . ,
d d x a gw m ( x , y , t ) = γ m a in ( x , y , t ) + i [ β 0 m - k 0 sin θ ± K + Δ β m ( x , y , t ) + i α gw m ] a g m ( x , y , t ) ,
γ m = ω 0 δ ( n f 2 - n s 2 ) C m f m ( h ) E y ( 0 ) 8 i ,
E y ( 0 ) = 4 q f exp ( i q f h ) q f + i q s + ( q f - i q s ) exp ( 2 i q f h ) - q f q s [ q f + i q s - ( q f - i q s ) exp ( 2 i q f h ) ]
q f 2 = k 0 2 ( n f 2 - n c 2 sin 2 θ ) ,
q s 2 = k 0 2 ( n c 2 sin 2 θ - n s 2 ) .
α g = γ 2 2 .
Im ( β 0 m ) = - α ( z ) f m ( z ) 2 d z - f m ( z ) 2 d z + α sc m .
n ( E ) = n 0 + n 2 E 2 = n 0 + n 2 , I I ,
Re [ Δ β m ( x , y , t ) ] = k 0 c 0 2 ( C m ) 4 - n 0 ( z ) n 2 ( z ) f m ( z ) 4 dz a gw m ( x , y , t ) 2
Re [ Δ β m ( x , y , t ) ] = k 0 c 0 2 ( C m ) 4 - n 0 ( z ) n 2 ( z ) × { 2 3 [ f x m ( z ) 2 + f z m ( z ) 2 ] 2 + 1 3 [ f x m ( z ) ] 2 + [ f z m ( z ) ] 2 2 } d z a gw m ( x , y , t ) 2
α ( I ) = α 0 + α 2 I ,
Im [ Δ β m ( x , y , t ) ] = - α 2 ( z ) f m ( z ) 4 d z 2 [ - f m ( z ) 2 d z ] 2 a gw m ( x , y , t ) 2
Re [ Δ β m ( x , y , t ) ] = Δ β sat m ( 1 - exp { - Re [ Δ β m ( x , y , t ) ] Δ β sat m } ) ,
Δ β sat m = j P j P tot k 0 Δ n sat , j ,
a in ( x , y , t ) = a in , x ( x ) a in , y ( y ) a in , t ( t ) ,
θ = sin - 1 { [ Re ( β 0 m ) K ] / k 0 }
w 0 0.805 l ,
Δ x = - l / 2

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