Abstract

Using a modal theory, we study the dynamics of a two-dimensional finite beam reflected by a nonlinear grating coupler. Different algorithms are proposed to calculate the linear as well as the nonlinear coupling coefficients. We show that this nonlinear grating coupler can be optimized with respect to switching contrast and power. We compare our results with the experimentally determined switching behavior of a silicon-on-sapphire coupler and study its application as a fast saturable absorber.

© 1995 Optical Society of America

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    [CrossRef]
  3. G. M. Carter and Y. J. Chen, "Nonlinear optical coupling between radiation and confined modes," Appl. Phys. Lett. 42, 643–645 (1983).
    [CrossRef]
  4. Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
    [CrossRef]
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    [CrossRef]
  7. M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
    [CrossRef]
  8. B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
    [CrossRef]
  9. J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
    [CrossRef]
  10. R. W. Ziolkowski and J. B. Judkins, "NL-FDTD modeling of linear and nonlinear corrugated waveguides," in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 153–156.
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  14. G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, "Theory of pulsed excitation of nonlinear distributed prism couplers," J. Opt. Soc. Am. B 5, 432–442 (1988).
    [CrossRef]
  15. R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
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  16. T. Peschel and F. Lederer, "Optical response of nonlinear planar resonators under pulsed beam excitation," Phys. Rev. B 46, 7632–7643 (1992); G. Vitrant, M. Haeltermann, and R. Reinisch, Phys. Rev. B 48, 15465–15467 (1993).
    [CrossRef]
  17. F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
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    [CrossRef]
  19. G. Assanto, M. B. Marques, and G. I. Stegeman, "Grating coupling of light pulses into third-order nonlinear waveguides," J. Opt. Soc. Am. B 8, 553–561 (1991).
    [CrossRef]
  20. B. S. Wherrett, "Fabry–Perot bistable cavity optimization on reflection," IEEE J. Quantum Electron. QE-20, 646–651 (1984).
    [CrossRef]
  21. P. Vincent, H. Akhouaeyri, and M. Nevière, "Optical bistability by photothermal displacement in grating coupler configurations—a theoretical interpretation," J. Opt. Soc. Am. B 8, 1149–1156 (1991).
    [CrossRef]
  22. N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
    [CrossRef]
  23. H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.
  24. D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).
  25. R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
    [CrossRef]
  26. K. G. Svanteson, "Determination of interband and the free carrier absorption constants in silicon at high-level photoinjection," J. Phys. D 12, 425–436 (1979).
    [CrossRef]
  27. S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981).
  28. A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).
  29. W. G. Spitzer and H. Y. Fan, "Determination of optical constants and carrier effective mass of semiconductors," Phys. Rev. 106, 882–890 (1957).
    [CrossRef]
  30. G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
    [CrossRef]

1994

1993

F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
[CrossRef]

1992

T. Peschel and F. Lederer, "Optical response of nonlinear planar resonators under pulsed beam excitation," Phys. Rev. B 46, 7632–7643 (1992); G. Vitrant, M. Haeltermann, and R. Reinisch, Phys. Rev. B 48, 15465–15467 (1993).
[CrossRef]

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

1991

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
[CrossRef]

G. Assanto, M. B. Marques, and G. I. Stegeman, "Grating coupling of light pulses into third-order nonlinear waveguides," J. Opt. Soc. Am. B 8, 553–561 (1991).
[CrossRef]

P. Vincent, H. Akhouaeyri, and M. Nevière, "Optical bistability by photothermal displacement in grating coupler configurations—a theoretical interpretation," J. Opt. Soc. Am. B 8, 1149–1156 (1991).
[CrossRef]

1990

1989

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

1988

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, "Theory of pulsed excitation of nonlinear distributed prism couplers," J. Opt. Soc. Am. B 5, 432–442 (1988).
[CrossRef]

1986

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

1985

1984

B. S. Wherrett, "Fabry–Perot bistable cavity optimization on reflection," IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

1983

G. M. Carter and Y. J. Chen, "Nonlinear optical coupling between radiation and confined modes," Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

1979

K. G. Svanteson, "Determination of interband and the free carrier absorption constants in silicon at high-level photoinjection," J. Phys. D 12, 425–436 (1979).
[CrossRef]

1977

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).
[CrossRef]

1976

C. C. Ghizoni, B. Chen, and C. L. Tang, "Theory and experiments on grating couplers for thin-film waveguides," IEEE J. Quantum Electron. QE-12, 69–73 (1976).
[CrossRef]

1973

1970

1957

W. G. Spitzer and H. Y. Fan, "Determination of optical constants and carrier effective mass of semiconductors," Phys. Rev. 106, 882–890 (1957).
[CrossRef]

Akhouaeyri, H.

Assanto, G.

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

G. Assanto, M. B. Marques, and G. I. Stegeman, "Grating coupling of light pulses into third-order nonlinear waveguides," J. Opt. Soc. Am. B 8, 553–561 (1991).
[CrossRef]

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, "Theory of pulsed excitation of nonlinear distributed prism couplers," J. Opt. Soc. Am. B 5, 432–442 (1988).
[CrossRef]

Ballantyne, J. M.

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

Berard, D.

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

Brown, T. G.

Burzynski, R.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Carter, G. M.

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

G. M. Carter and Y. J. Chen, "Nonlinear optical coupling between radiation and confined modes," Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Chen, B.

C. C. Ghizoni, B. Chen, and C. L. Tang, "Theory and experiments on grating couplers for thin-film waveguides," IEEE J. Quantum Electron. QE-12, 69–73 (1976).
[CrossRef]

Chen, Y. J.

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

G. M. Carter and Y. J. Chen, "Nonlinear optical coupling between radiation and confined modes," Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Chi, W.

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

Chi, W. D.

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

Chui, T. Heng

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

Dansas, P.

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

Ehrlich, J. E.

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

Erdhuisen, E. W. P.

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

Esser, A.

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

Ewertz, A.

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

Fan, H. Y.

W. G. Spitzer and H. Y. Fan, "Determination of optical constants and carrier effective mass of semiconductors," Phys. Rev. 106, 882–890 (1957).
[CrossRef]

Fortenberry, R. M.

Ghizoni, C. C.

C. C. Ghizoni, B. Chen, and C. L. Tang, "Theory and experiments on grating couplers for thin-film waveguides," IEEE J. Quantum Electron. QE-12, 69–73 (1976).
[CrossRef]

Gibson, U. J.

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
[CrossRef]

Gualous, H.

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

Haeltermann, M.

R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
[CrossRef]

Horsthuis, W. H. G.

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

Judkins, J. B.

R. W. Ziolkowski and J. B. Judkins, "NL-FDTD modeling of linear and nonlinear corrugated waveguides," in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 153–156.

Koster, A.

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

Kurz, H.

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

Kütt, W.

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

Laval, S.

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

Lederer, F.

F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
[CrossRef]

T. Peschel and F. Lederer, "Optical response of nonlinear planar resonators under pulsed beam excitation," Phys. Rev. B 46, 7632–7643 (1992); G. Vitrant, M. Haeltermann, and R. Reinisch, Phys. Rev. B 48, 15465–15467 (1993).
[CrossRef]

Liao, C.

Marques, M. B.

G. Assanto, M. B. Marques, and G. I. Stegeman, "Grating coupling of light pulses into third-order nonlinear waveguides," J. Opt. Soc. Am. B 8, 553–561 (1991).
[CrossRef]

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

Möhlmann, G. R.

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

Moshrefzadeh, R.

Neviere, M.

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

Nevière, M.

Paraire, N.

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

Paumier, J. C.

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

Peng, S. T.

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Peschel, T.

F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
[CrossRef]

T. Peschel and F. Lederer, "Optical response of nonlinear planar resonators under pulsed beam excitation," Phys. Rev. B 46, 7632–7643 (1992); G. Vitrant, M. Haeltermann, and R. Reinisch, Phys. Rev. B 48, 15465–15467 (1993).
[CrossRef]

Peschel, U.

F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
[CrossRef]

Prasad, P. N.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Prelewitz, D. F.

Reinisch, R.

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
[CrossRef]

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

Rousseau, M.

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

Seaton, C. T.

Shoemaker, R. L.

Singh, B. P.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Sonek, G. J.

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

Spitzer, W. G.

W. G. Spitzer and H. Y. Fan, "Determination of optical constants and carrier effective mass of semiconductors," Phys. Rev. 106, 882–890 (1957).
[CrossRef]

Stegeman, G. I.

G. Assanto, M. B. Marques, and G. I. Stegeman, "Grating coupling of light pulses into third-order nonlinear waveguides," J. Opt. Soc. Am. B 8, 553–561 (1991).
[CrossRef]

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
[CrossRef]

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

G. Assanto, R. M. Fortenberry, C. T. Seaton, and G. I. Stegeman, "Theory of pulsed excitation of nonlinear distributed prism couplers," J. Opt. Soc. Am. B 5, 432–442 (1988).
[CrossRef]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, J. D. Valera, and H. G. Winful, "Nonlinear distributed waveguide couplers," J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

Svanteson, K. G.

K. G. Svanteson, "Determination of interband and the free carrier absorption constants in silicon at high-level photoinjection," J. Phys. D 12, 425–436 (1979).
[CrossRef]

Svensson, B. C.

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981).

Tamir, T.

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Tang, C. L.

C. C. Ghizoni, B. Chen, and C. L. Tang, "Theory and experiments on grating couplers for thin-film waveguides," IEEE J. Quantum Electron. QE-12, 69–73 (1976).
[CrossRef]

Ulrich, R.

Valera, J. D.

Vincent, P.

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

P. Vincent, H. Akhouaeyri, and M. Nevière, "Optical bistability by photothermal displacement in grating coupler configurations—a theoretical interpretation," J. Opt. Soc. Am. B 8, 1149–1156 (1991).
[CrossRef]

Vitrant, G.

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
[CrossRef]

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, "Fabry–Perot bistable cavity optimization on reflection," IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

Winful, H. G.

Zanoni, R.

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

Zettler, T.

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

Ziolkowski, R. W.

R. W. Ziolkowski and J. B. Judkins, "NL-FDTD modeling of linear and nonlinear corrugated waveguides," in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 153–156.

Ann. Phys.

D. Berard, N. Paraire, W. D. Chi, and A. Koster, "Using silicon nonlinearities in waveguides for passive nanosecond optical pulse shaping at λ = 1.064 μm," Ann. Phys. 16, 63–72 (1991).

Appl. Opt.

Appl. Phys.

T. Tamir and S. T. Peng, "Analysis and design of grating couplers," Appl. Phys. 14, 235–254 (1977).
[CrossRef]

Appl. Phys. Lett.

G. M. Carter and Y. J. Chen, "Nonlinear optical coupling between radiation and confined modes," Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Y. J. Chen, G. M. Carter, G. J. Sonek, and J. M. Ballantyne, "Nonlinear optical coupling to planar GaAs/AlGaAs waveguides," Appl. Phys. Lett. 48, 272–274 (1986).
[CrossRef]

R. Burzynski, B. P. Singh, P. N. Prasad, R. Zanoni, and G. I. Stegeman, "Nonlinear optical processes in a polymer waveguide: grating coupler measurement of electronic and thermal nonlinearities," Appl. Phys. Lett. 53, 2011–2013 (1988).
[CrossRef]

M. B. Marques, G. Assanto, G. I. Stegeman, G. R. Möhlmann, E. W. P. Erdhuisen, and W. H. G. Horsthuis, "Large, nonresonant, intensity dependent refractive index of 4-diakylamino-4′-nitro-diphenyl-polyene side chain polymers in waveguides," Appl. Phys. Lett. 58, 2613–2615 (1988).
[CrossRef]

B. C. Svensson, C. T. Seaton, U. J. Gibson, and G. I. Stegeman, "Optically controlled angular scanning via grating output couplers in nonlinear ZnS waveguides," Appl. Phys. Lett. 53, 941–943 (1988).
[CrossRef]

IEEE J. Quantum Electron.

J. E. Ehrlich, G. Assanto, G. I. Stegeman, and T. Heng Chui, "Guided-wave optical bistability in indium-antimonide thin films," IEEE J. Quantum Electron. QE-27, 809–816 (1991).
[CrossRef]

B. S. Wherrett, "Fabry–Perot bistable cavity optimization on reflection," IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

C. C. Ghizoni, B. Chen, and C. L. Tang, "Theory and experiments on grating couplers for thin-film waveguides," IEEE J. Quantum Electron. QE-12, 69–73 (1976).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. D

K. G. Svanteson, "Determination of interband and the free carrier absorption constants in silicon at high-level photoinjection," J. Phys. D 12, 425–436 (1979).
[CrossRef]

Opt. Commun.

R. Reinisch, M. Neviere, P. Vincent, and G. Vitrant, "Radiated and diffracted orders in Kerr-type grating couplers," Opt. Commun. 91, 51–56 (1992).
[CrossRef]

Opt. Lett.

G. Vitrant, R. Reinisch, J. C. Paumier, G. Assanto, and G. I. Stegeman, "Nonlinear prism coupling with nonlocality," Opt. Lett. 14, 899–900 (1989).
[CrossRef]

Phys. Rev.

W. G. Spitzer and H. Y. Fan, "Determination of optical constants and carrier effective mass of semiconductors," Phys. Rev. 106, 882–890 (1957).
[CrossRef]

Phys. Rev. B

R. Reinisch, G. Vitrant, and M. Haeltermann, "Coupled mode theory of diffraction induced transverse effects in nonlinear optical resonators," Phys. Rev. B 44, 7870–7878 (1991).
[CrossRef]

T. Peschel and F. Lederer, "Optical response of nonlinear planar resonators under pulsed beam excitation," Phys. Rev. B 46, 7632–7643 (1992); G. Vitrant, M. Haeltermann, and R. Reinisch, Phys. Rev. B 48, 15465–15467 (1993).
[CrossRef]

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F. Lederer, T. Peschel, and U. Peschel, "The effect of excited leaky waves on the transient non-linear optical response of planar semiconductor resonators," Pure Appl. Opt. 2, 635–658 (1993).
[CrossRef]

Other

N. Paraire, P. Dansas, A. Koster, M. Rousseau, and S. Laval, "Sensitivity and switching contrast optimization in an optical signal processing waveguide structure," in Optical Information Technology, State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 350–357.
[CrossRef]

H. Gualous, A. Koster, W. Chi, N. Paraire, and S. Laval, "Thermo-optical logic gate array using SOS waveguide," in Optical Information Technology State-of-the-Art-Report, S. D. Smith and R. F. Neale, eds. (Springer-Verlag, Berlin, 1993), pp. 358–366.

S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981).

A. Esser, A. Ewertz, T. Zettler, W. Kütt, and H. Kurz, "Femtosecond spectroscopic study of free carrier induced optical nonlinearities in crystalline silicon," in Ultrafast Phenomena in Spectroscopy, A. Laubereau and A. Seilmeier, eds., Inst. Phys. Conf. Ser. 126, 299–302 (1992).

R. W. Ziolkowski and J. B. Judkins, "NL-FDTD modeling of linear and nonlinear corrugated waveguides," in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), pp. 153–156.

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Figures (5)

Fig. 1
Fig. 1

Grating coupler. (a) Geometry: for the configuration used in the experiment the parameters are cladding, sapphire = (3.06, 0); guide, silicon = (12.56, 0.0028); substrate, silver = (−38.4, 5.5). λ = 325 nm, h = 50 nm, d = 575 nm. The transmitted field is evanescent. (b) Experimentally determined angular reflection spectrum of the silver-clad grating coupler.

Fig. 2
Fig. 2

Critical parameters of a silver-clad grating coupler as a function of its grating depth (h). The grating is assumed to have a sinusoidal shape. Left-hand scale, normalizing power per transverse width Pin0; right-hand scale, maximum achievable contrast in reflection.

Fig. 3
Fig. 3

Evolution of a central strip of the near field along the propagation direction. Incident peak intensity 3.6 MW/cm2, pulse duration 200 ps, beam diameter 800 μm; guided intensity, arbitrary units; reflected intensity, one line corresponds to 450 kW/cm2.

Fig. 4
Fig. 4

Time- and space-dependent far-field pattern of a central strip of the reflected field for different incident peak intensities. Left-hand figures, experimental results (left, incident field; right, reflected field. 10 enlarged). Right-hand figures, numerical simulations of the reflected far field.

Fig. 5
Fig. 5

Reflection of Gaussian pulses as a function of their peak energy density: (a) for different pulse durations (Tpuls), (b) for different detuning (Δ).

Tables (1)

Tables Icon

Table 1 Determination of Characteristic Constants of the Investigated Silver-Clad Grating Coupler

Equations (54)

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g = 2 π / Λ ,
E j ( y , z , t ) = - d β y - d β z - d ω E ^ j ( β , ω ) × exp { i [ β y y + β z z - ( ω - ω 0 ) t ] } ,             j = t , r , in ,
E ^ r / t ( β , ω ) = σ r / t E ^ in ( β , ω ) + α in a r / t × { 1 [ β g ( ω ) + i Γ ] 2 - β + g 2 } E ^ in ( β , ω ) ,
{ [ β g ( ω ) + i Γ ] 2 - β 2 } E ^ g ( β , ω ) = α in E ^ in ( β - g , ω ) ,
E ^ r / t ( β , ω ) = σ r / t E ^ in ( β , ω ) + a r / t E ^ g ( β + g , ω ) .
[ i Γ ( ω ) + β g ( ω ) ] 2 [ i Γ ( ω 0 ) + β g ( ω 0 ) ] 2 + 2 R β g v g ( ω - ω 0 ) ,
v g = [ ω β g ( ω ) | ω = ω 0 ] - 1 .
E r / t / in ( y , z , t ) = A r / t / in ( y , z , t ) exp [ i ( β in y y + β in z z ) ] ,
E g ( y , z , t ) = A g ( y , z , t ) × exp { i [ ( β in y + g y ) y + ( β in z + g z ) z ] } ,
[ i ( 1 v g t + z ) + R β g ( ω 0 ) - β in + g + i [ Γ ( ω 0 ) + T β g ( ω 0 ) ] + 1 2 R β g ( 2 y 2 + 2 z 2 ) ] A g ( y , z , t ) = a in A in ( y , z , t ) ,
A r / t ( y , z , t ) = σ r / t A in ( y , z , t ) + a r / t A g ( y , z , t ) ,
a in = α in 2 R β g .
Y 0 2 = 1 2 ( T β g + Γ ) R β g ,
β g ( χ NL ; ω 0 ) = β g ( χ NL = 0 ; ω 0 ) + ω 0 c a NL ( ω 0 ) χ NL ( y , z , t ) = β g ( ω 0 ) + ω 0 c a NL ( ω 0 ) χ NL ( y , z , t ) ,
a NL = c ω 0 β g χ NL | χ NL = 0 .
χ NL = - α N ,
[ t - D amb ( 2 y 2 + 2 z 2 ) + 1 τ R ] N ( y , z , t ) = 0 2 NL d x f g ( x ) 2 d T χ silicon A g ( y , z , t ) 2 ,
Z = z Z 0 ,             Y = y Z 0 ,             T = t T 0 ,             U g = A g A g 0 , U in = A in A in 0 ,             U r / t = A r σ r / t A in 0 ,
Z 0 = [ T β g + Γ ] - 1 ,             T 0 = Z 0 / v g
A g 0 = [ 2 c ω 0 0 d ( T β g + Γ ) τ R α a NL T χ silicon NL d x f g ( x ) 2 ] 1 / 2 ,
A in 0 = A g 0 ( T β g + Γ ) a in ,             A r / t 0 = A g 0 σ r / t ,
[ i ( T + Z ) + Δ + i - χ ( Z , T ) ] U g ( Z , T ) = U in ( Z , T ) ,
U r / t ( Z , T ) = U in ( Z , T ) - i δ r / t U g ( Z , T ) ,
[ T R T + 1 - L 2 ( 2 Z 2 + 2 Y 2 ) ] χ ( Z , T ) = U g ( Z , T ) 2 .
Δ = R β g - g + β in T β g + Γ , δ r / t = i a r / t a in σ r / t ( T β g + Γ ) , L = 1 Z 0 τ R D amb , T R = τ R T 0 .
a r / t = - ω 0 2 c 2 grating d x G ± ( x , β in , ω ) χ - 1 ( x ) f g ( x ) ,
a in = - ω 0 2 c 2 τ ¯ 2 R β g grating d x g g ( x ) χ 1 ( x ) f 0 ( x ) ,
Γ = i 2 R β g ω 0 4 c 4 grating d x grating d x g g ( x ) × G ( x , x , β in , ω 0 ) χ 1 ( x ) χ - 1 ( x ) f g ( x ) ,
Γ = R γ s a t 2 + R γ c a r 2 2 R β g - d x f g ( x ) 2 ,
a in = - 2 i Γ R γ s τ 0 a t * + R γ c ρ 0 a r * R γ s a t 2 + R γ c a r 2 ,
δ r = ρ 0 ρ ¯ 2 Γ T β g + Γ ,
R ( β in ) = E r 2 E in 2 = | ρ ¯ ( 1 - ρ 0 ρ ¯ 2 i Γ β g + i Γ - β in + g ) | 2 ,
R β g = β min + g ,             guided - wave resonance ,
T β g + Γ = ½ Δ β ,             linewidth ,
ρ ¯ 2 = R max ,             maximum reflectivity ,
2 Γ ρ ¯ [ T β g + Γ ] = 1 ± ( R min / R max ) 1 / 2 = δ r ,             contrast .
Γ = T β g ( 2 cos ϕ ρ ¯ - 1 ) - 1 ,
P in 0 = 1 2 0 γ c c 2 ω A in 0 2 Z 0 = c 3 2 ω 2 τ R α T χ silicon × - + d x f g ( x ) 2 NL d x f g ( x ) 2 d R β g ( T β g + Γ ) 2 a NL Γ ,
a in 2 = 2 Γ γ c R β g - d x f g ( x ) 2 .
τ D = d 2 4 π 2 D amb 6.5 ps ,
L d = τ R D amb 0.75 μ m ,
[ 2 x 2 - β 2 + ω 2 c 2 ( x , ω ) ] E ^ ( x , β , ω ) = - μ 0 ω 2 P ^ ( x , β , ω ) .
E ^ ( x , β , ω ) = E ^ ext ( x , β , ω ) - μ 0 ω 2 x - x + G ( x , x , β , ω ) P ^ ( x , β , ω ) d x ,
[ 2 x 2 - β 2 + ω 2 c 2 ( x , ω ) ] G ( x , x , β , ω ) = δ ( x - x ) ,
G ( x , x , β , ω ) = { G + ( x , β , ω ) exp [ i γ c ( x - x + ) ] for x > x + G - ( x , β , ω ) exp [ i γ s ( x - - x ) ] for x < x - .
E ^ 0 ( x , β , ω ) = τ ¯ f 0 ( x ) E ^ in ( β , ω ) - μ 0 ω 2 x - x + d x G ( x , x , β , ω ) P ^ 0 ( x , β , ω ) ,
E ^ n ( x , β , ω ) = - μ 0 ω 2 x - x + d x G ( x , x , β , ω ) P ^ n ( x , β , ω ) .
G ( x , x , β , ω ) f g ( x ) g g ( x ) β g 2 ( ω ) - β 2             for β R β g ,
[ β g 2 ( ω ) - β 2 ] E ^ g ( β , ω ) = - μ 0 ω 0 2 x - x + d x g g ( x ) P ^ 1 ( x , β , ω ) ,
E ^ 0 ( x , β , ω ) = τ ¯ f 0 ( x ) E ^ in ( β , ω ) - μ 0 ω 0 2 x - x + d x G ( x , x , β , ω ) P ^ 0 ( x , β , ω ) .
χ ( x , z ) = l χ l ( x ) exp ( i l g z z ) .
E ^ 0 ( x , β , ω ) = τ ¯ f 0 ( x ) E ^ in ( β + g , ω ) - ω 0 2 c 2 x - x + d x G ( x , x , β in , ω 0 ) f g ( x ) × χ - 1 ( x ) E ^ g ( β + g , ω ) .
a r / t = - ω 0 2 c 2 x - x + d x G ± ( x , β in , ω 0 ) χ - 1 ( x ) f g ( x ) , ρ ¯ = τ ¯ f 0 ( x + ) - 1.
[ ( β g + i Γ ) 2 - β 2 ] E ^ g ( β , ω ) = α in E ^ in ( β - g , ω ) , α in = 2 R β g a in = - ω 0 2 c 2 τ ¯ x - x + d x g g ( x ) χ 1 ( x ) f 0 ( x ) , Γ = i 2 R β g ω 0 4 c 4 x - x + d x x - x + d x g g ( x ) χ 1 ( x ) × G ( x , x , β in , ω 0 ) χ - 1 ( x ) ,

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