Abstract

We present theoretical aspects of the study of nonlinear multilayered dielectric devices. Starting from Maxwell’s equations, we write the propagation equations for the pump and the harmonic fields without any approximation. We show that we can consider the two fundamental cases of TE and TM polarization. Using a suitable transfer matrix formalism, we solve the propagation equations for the undepleted cases for both a plane incident wave and a spatially limited incident beam. The case of a depleted-pump wave is also considered. Numerical simulations are carried out for a prism coupler. They show the limits of each approximation and also emphasize the advantages of multilayered devices for second-harmonic generation. Finally, we show the usefulness of the model compared with experimental results. We concentrate on second-harmonic generation by zinc sulfide thin films.

© 1998 Optical Society of America

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  3. H. Akhouayri, M. Nevière, P. Vincent, and R. Reinisch, “Second-harmonic generation in a corrugated waveguide,” Nonlinear Opt. 5, 127 (1993).
  4. R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
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  5. M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the pole and zero of the scattering operator,” J. Opt. Soc. Am. A 12, 513 (1995).
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  7. E. Popov, M. Nevière, R. Reinisch, J. L. Coutaz, and J. F. Roux, “Grating-enhanced second-harmonic generation in polymer waveguides: role of losses,” Appl. Opt. 34, 3398 (1995).
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  8. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques,” J. Opt. Soc. Am. B 6, 910 (1989).
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  10. N. Hashizume, M. Ohashi, T. Kondo, and R. Ito, “Optical harmonic generation in multilayered structures: a comprehensive analysis,” J. Opt. Soc. Am. B 12, 1894 (1995).
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  11. J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481 (1987).
    [CrossRef]
  12. R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297 (1994).
    [CrossRef]
  13. G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
    [CrossRef] [PubMed]
  14. S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622 (1994).
    [CrossRef] [PubMed]
  15. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. Byer, and W. R. Bosenberg, “Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3,” Opt. Lett. 21, 591 (1996).
    [CrossRef] [PubMed]
  16. Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
    [CrossRef]
  17. A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
    [CrossRef]
  18. A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
    [CrossRef]
  19. H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. F. Kajzar, “Organic molecules for guided wave quadratic and cubic optics,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 87–111.
  26. R. Reinisch, E. Popov, and M. Nevière, “Second-harmonic-generation-induced optical bistability in prism or grating couplers,” Opt. Lett. 20, 854 (1995).
    [CrossRef] [PubMed]
  27. S. Enoch and H. Akhouayri, “Bistable prism coupler with both second- and third-order nonlinearities,” J. Opt. Soc. Am. B 14, 588 (1997).
    [CrossRef]
  28. P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  29. F. Kazjar, “Organic molecules for guided wave quadratic and cubic optic,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 87–112.
  30. S. Enoch and H. Akhouayri, “Second-harmonic specular and scattered generated light: application to the experimental study of zinc sulfide thin films,” Appl. Opt. 36, 6319 (1997).
    [CrossRef]
  31. S. Enoch, “Theoretical an experimental study of second harmonic generation by optical thin films: multidielectric devices, prism and grating couplers,” Ph.D. dissertation (Université d’Aix Marseille III, Marseille, France, June 1997).
  32. The asymmetry that appears in the responses (Figs. 11 and 12) is due to the noncoincidence of the direction of polarization of the incident pump with that of the in-plane axis of the χ2 tensor that describes the thin film. This behavior is described in more detail in Ref. 30.

1997 (2)

1996 (2)

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. Byer, and W. R. Bosenberg, “Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3,” Opt. Lett. 21, 591 (1996).
[CrossRef] [PubMed]

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

1995 (9)

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

E. Popov, M. Nevière, R. Reinisch, J. L. Coutaz, and J. F. Roux, “Grating-enhanced second-harmonic generation in polymer waveguides: role of losses,” Appl. Opt. 34, 3398 (1995).
[CrossRef] [PubMed]

M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the pole and zero of the scattering operator,” J. Opt. Soc. Am. A 12, 513 (1995).
[CrossRef]

W. N. Herman and L. M. Hayden, “Maker fringes: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B 12, 416 (1995).
[CrossRef]

N. Hashizume, M. Ohashi, T. Kondo, and R. Ito, “Optical harmonic generation in multilayered structures: a comprehensive analysis,” J. Opt. Soc. Am. B 12, 1894 (1995).
[CrossRef]

R. Reinisch, E. Popov, and M. Nevière, “Second-harmonic-generation-induced optical bistability in prism or grating couplers,” Opt. Lett. 20, 854 (1995).
[CrossRef] [PubMed]

1994 (4)

1993 (1)

H. Akhouayri, M. Nevière, P. Vincent, and R. Reinisch, “Second-harmonic generation in a corrugated waveguide,” Nonlinear Opt. 5, 127 (1993).

1991 (1)

1989 (2)

1988 (1)

R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
[CrossRef]

1987 (1)

1977 (1)

R. Petit and M. Cadilhac, “Theorie électromagnetique du coupleur a prisme,” J. Opt. (Paris) 8, 41 (1977).
[CrossRef]

1962 (2)

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effect of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Akhouayri, H.

S. Enoch and H. Akhouayri, “Second-harmonic specular and scattered generated light: application to the experimental study of zinc sulfide thin films,” Appl. Opt. 36, 6319 (1997).
[CrossRef]

S. Enoch and H. Akhouayri, “Bistable prism coupler with both second- and third-order nonlinearities,” J. Opt. Soc. Am. B 14, 588 (1997).
[CrossRef]

H. Akhouayri, M. Nevière, P. Vincent, and R. Reinisch, “Second-harmonic generation in a corrugated waveguide,” Nonlinear Opt. 5, 127 (1993).

R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
[CrossRef]

Amra, C.

Assanto, G.

Beaulieu, Y.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

Bethune, D. S.

Bosenberg, W. R.

Boyd, R. W.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297 (1994).
[CrossRef]

Byer, R.

Cadilhac, M.

R. Petit and M. Cadilhac, “Theorie électromagnetique du coupleur a prisme,” J. Opt. (Paris) 8, 41 (1977).
[CrossRef]

Chatenoud, F.

Chui, H. C.

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

Coutaz, J. L.

E. Popov, M. Nevière, R. Reinisch, J. L. Coutaz, and J. F. Roux, “Grating-enhanced second-harmonic generation in polymer waveguides: role of losses,” Appl. Opt. 34, 3398 (1995).
[CrossRef] [PubMed]

R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
[CrossRef]

Dai, H.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Dela?ge, A.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Dion, M.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Eckardt, R. C.

Enoch, S.

Fejer, M. M.

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. Byer, and W. R. Bosenberg, “Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3,” Opt. Lett. 21, 591 (1996).
[CrossRef] [PubMed]

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

Fernando, C.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

Fischer, G. L.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Frlan, E.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Gehr, R. J.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Harris Jr., J. S.

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

Hashizume, N.

Hayden, L. M.

Herman, W. N.

Ito, R.

Janz, S.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622 (1994).
[CrossRef] [PubMed]

Jenekhe, S. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Kondo, T.

Laurent, N.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effect of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Martinet, E. L.

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

Maystre, D.

R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
[CrossRef]

Myers, L. E.

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

Nevière, M.

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effect of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Normandin, R.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

S. Janz, F. Chatenoud, and R. Normandin, “Quasi-phase-matched second-harmonic generation from asymmetric coupled quantum wells,” Opt. Lett. 19, 622 (1994).
[CrossRef] [PubMed]

Ohashi, M.

Osaheni, J. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Paumier, J. C.

Petit, R.

R. Petit and M. Cadilhac, “Theorie électromagnetique du coupleur a prisme,” J. Opt. (Paris) 8, 41 (1977).
[CrossRef]

Pic, E.

R. Reinisch, M. Nevière, H. Akhouayri, J. L. Coutaz, D. Maystre, and E. Pic, “Grating enhanced second harmonic generation through electromagnetic resonances,” Opt. Eng. 27, 961 (1988).
[CrossRef]

Popov, E.

Reinisch, R.

Rosencher, E.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

Roux, J. F.

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effect of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Sipe, J. E.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297 (1994).
[CrossRef]

J. E. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481 (1987).
[CrossRef]

Stegeman, G. I.

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effect of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Theilmann, S.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

Van Der Meer, P.

Y. Beaulieu, S. Janz, H. Dai, E. Frlan, C. Fernando, A. Dela⁁ge, P. Van Der Meer, M. Dion, and R. Normandin, “Surface emitted harmonic generation for sensor and display applications,” J. Nonlinear Opt. Phys. Mater. 4, 893 (1995).
[CrossRef]

Vincent, P.

H. Akhouayri, M. Nevière, P. Vincent, and R. Reinisch, “Second-harmonic generation in a corrugated waveguide,” Nonlinear Opt. 5, 127 (1993).

Vitrant, G.

Vodjdani, N.

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

Weller-Brophy, L. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. A. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871 (1995).
[CrossRef] [PubMed]

Woods, G. L.

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (3)

A. Fiore, V. Berger, E. Rosencher, N. Laurent, S. Theilmann, N. Vodjdani, and J. Nagle, “Huge birefringence in selectively oxidized GaAs/AlAs optical waveguides,” Appl. Phys. Lett. 68, 1320 (1996).
[CrossRef]

A. Fiore, E. Rosencher, V. Berger, and J. Nagle, “Electric field induced interband second harmonic generation in GaAs/AlGaAs quantum wells,” Appl. Phys. Lett. 67, 3765 (1995).
[CrossRef]

H. C. Chui, G. L. Woods, M. M. Fejer, E. L. Martinet, and J. S. Harris, Jr., “Tunable mid-infrared generation by difference frequency mixing of diode laser wavelengths in the intersubband InGaAs/AlAs quantum wells,” Appl. Phys. Lett. 66, 265 (1995).
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G. Vitrant, “Third order nonlinear integrated optical resonators,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 285–303.

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F. Kajzar, “Organic molecules for guided wave quadratic and cubic optics,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 87–111.

F. Kazjar, “Organic molecules for guided wave quadratic and cubic optic,” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), pp. 87–112.

S. Enoch, “Theoretical an experimental study of second harmonic generation by optical thin films: multidielectric devices, prism and grating couplers,” Ph.D. dissertation (Université d’Aix Marseille III, Marseille, France, June 1997).

The asymmetry that appears in the responses (Figs. 11 and 12) is due to the noncoincidence of the direction of polarization of the incident pump with that of the in-plane axis of the χ2 tensor that describes the thin film. This behavior is described in more detail in Ref. 30.

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Figures (16)

Fig. 1
Fig. 1

Schematic representation of a multilayered device, showing the coordinate axes and the incidence angle.

Fig. 2
Fig. 2

Schematic representation of the prism couplers. Device 1 (left): e1=0.73 μm, e2=0.7 μm, e3=0.97 μm. Device 2 (middle): e1=0.73 μm, e2=0.7 μm, e3=0.73 μm, e4=0.725 μm, e5=0.73 μm, e6=0.7 μm, e7=0.73 μm. Device 3 (right): e1=0.7 μm, e2=0.8 μm; Superstrate indices: n1(ω)=n1(2ω)=1.0; high-index layers (light-colored layers) n2(ω)=2.27+j2 10-4, n2(2ω)=2.38+j2 10-4; low-index layers (gray-colored layers) n3(ω)n3(2ω)=1.3+j3 10-4; prism indices n4(ω)=2.51, n4(2ω)=2.52.

Fig. 3
Fig. 3

Amplitudes of the electric field in the high-index layer of device 1: The enhancement of the field for the resonance angles is as much as 7000 times.

Fig. 4
Fig. 4

Device 1. Dashed curves, second-harmonic TE intensity generated for TE (lower curve) and TM (upper curve) incident fields; solid curves, reflectivity for the two cases.

Fig. 5
Fig. 5

Device 1. Dashed curves, second-harmonic TM intensity generated for TE (lower curve) and TM (upper curve) incident fields; solid curves, reflectivity for the two cases.

Fig. 6
Fig. 6

Device 2. Dotted curves, second-harmonic TE intensity generated for TE (lower curve) and TM (upper curve) incident fields; solid curves, reflectivity for the two cases.

Fig. 7
Fig. 7

Device 2. Dotted curves, second-harmonic TM intensity generated for TE (lower curve) and TM (upper curve) incident fields; solid curves, reflectivity for the two cases.

Fig. 8
Fig. 8

Comparison of depleted (solid curves) and undepleted (dashed curve) solutions. The harmonic curves are superimposed. Both the pump and the harmonic fields are TE polarized.

Fig. 9
Fig. 9

Spatially limited beam response, near field. The incident beam is a rectangular sheet with a width of 0.1 mm (dashed curve), 0.5 mm (dotted curve), or 1 mm (solid curve). The amplitudes are normalized to the maximum amplitude of the near field. Both the pump and the harmonic fields are TE polarized.

Fig. 10
Fig. 10

Response of the device when the incidence angle is close to the resonance angle: plane-wave response (solid curve); beam sizes 1 mm (+), 0.1 mm (×). Both the pump and the harmonic fields are TE polarized.

Fig. 11
Fig. 11

Experimental TM-polarized harmonic normalized transmitted intensity as a function of the angle of incidence. The incident pump field (λ=1.064 μm) is TE polarized.

Fig. 12
Fig. 12

Theoretical TM-polarized harmonic normalized transmitted intensity. The incident pump field (λ=1.064 μm) is TE polarized.

Fig. 13
Fig. 13

FP resonant at 1.064 μm. Experimental TE-polarized normalized transmitted intensity as a function of the angle of incidence. The incident pump field is TE polarized.

Fig. 14
Fig. 14

FP resonant at 1.064 μm. Solid curve, theoretical modulus of the transmitted harmonic field; dashed curve, transmittivity at 1.064 μm. The pump and the harmonic fields are TE polarized.

Fig. 15
Fig. 15

FP resonant at 0.532 μm. Experimental TE-polarized normalized transmitted intensity as a function of the angle of incidence. The incident pump field is TE polarized.

Fig. 16
Fig. 16

FP resonant at 0.532 μm. Solid curve, theoretical modulus of the transmitted harmonic field; dashed curve, transmittivity at 1.064 μm. The pump and the harmonic fields are TE polarized.

Equations (83)

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rot E(ω, r)=jωμ0H(ω, r),
rot H(ω, r)=-jω[0ωE(ω, r)+PNL(ω, r)],
rot E(2ω, r)=2jωμ0H(2ω, r),
rot H(2ω, r)=-2jω[0ωE(2ω, r)+PNL(2ω, r)],
PNL(2ω, r)=0χ2ω(2):E(ω, r)E(ω, r),
PNL(ω, r)=0χω(2):E(2ω, r)E*(ω, r),
Einc(ω, r)=Exinc(ω, r)ex+Eyinc(ω, r)ey+Ezinc(ω, r)ez,
Einc(ω, r)=A(ω, r)exp(jαz),
d2Ex,l(ω)dy2+[kl2(ω)-a2(ω)]Ex,l(ω)
=-μ0ω2Px,lNL(ω),
ddy 1kl2(ω) dHx,l(ω)dy+1-α2(ω)kl2(ω)Hx,l(ω)
=iω ddy Pz,lNL(ω)kl2(ω)+α(ω)ωkl2(ω) Py,lNL(ω),
d2Ex,l(2ω)dy2+[kl2(2ω)-α2(2ω)]Ex,l(2ω)
=-4μ0ω2Px,lNL(2ω),
ddy 1kl2(2ω) dHx,l(2ω)dy+1-α2(2ω)kl2(2ω)Hx,l(ω)
=2iω ddy Pz,lNL(2ω)kl2(2ω)+2α(2ω)ωkl2(2ω) Py,lNL(2ω),
Ex,l(Ω, yl)=Ex,l-1(Ω, yl),
Ez,l(Ω, yl)=Ez,l-1(Ω, yl),
Hx,l(Ω, yl)=Hx,l-1(Ω, yl),
Hz,l(Ω, yl)=Hz,l-1(Ω, yl),
dEx,l(Ω, yl)dy=dEx,l-1(Ω, yl)dy,
1kl2(Ω) dHx,l(Ω, yl)dy-jΩPz,lNL(Ω, yl)
=1kl-12(Ω) dHx,l-1(Ω, yl)dy-jΩPz,l-1NL(Ω, yl).
U(ω, y)=f(α, y)exp(iαz),
f(α, y)=A+(α)exp[iβ(α)y]+A-(α)exp[-iβ(α)y],
f(α, y)=f0(α, y)α-αp,
A±(α)B(αp)αp-α.
d2Ex,l(ω)dy2+[kl2(ω)-α2(ω)]Ex,l(ω)=0,
ddy 1kl2(ω) dHx,l(ω)dy+1-α2(ω)kl2(ω)Hx,l(ω)=0,
1k2(ω) dHx(ω)dy.
Einc(y, z)=-+p(α-α0)exp(-iβy)exp(iαz)dα,
E(y, z)=-+p(α-α0)f(α, y)exp(iαz)dα.
E2(y, z)=-+-+p(α-α0)f(α, y)×exp(iαz)p(α-α0)f(α, y)×exp(iαz)dαdα.
E2(y, z)=2-+ exp(2iαz)dα×-+p(α-α0)f(α, y)×p(α-2α-α0)f(α-2α, y)dα.
ΔE2ω(y, z)+k2(2ω)E2ω(y, z)
=-k02(2ω)χ(2)-+F(y, α)exp(2iαz)dα,
E2ω(y, z)=-+F2(y, α)exp(2iαz)dα,
d2F2(y, α)dy2+[k2(2ω)-α2(ω)]F2(y, α)
=-k02(2ω)χ(2)F(y, α),
F(y, α)=2-+p(α-α0)p(α-2α-2α0)×f(α, y)f(α-2α, y)dα.
f(α, y)=f0(αp, y)α-αp,
f(α-2α, y)=f0(αp, y)α-2α-αp,
F(α, y)=G(y, α)2(α-αp),
Ez(ω)y-Ey(ω)z=jωμ0Hx(ω),
Ex(ω)z=jωμ0Hy(ω),
Ex(ω)y=-jωμ0Hz(ω),
Hz(ω)y-Hy(ω)z=-jω0(ω)Ex-jωPxNL(ω),
Hx(ω)z=-jω0(ω)Ey(ω)-jωPyNL(ω),
Hx(ω)y=jω0(ω)Ez(ω)+jωPzNL(ω).
div1k2(ω) grad Hx(ω)+Hx(ω)=jω rotPNL(ω)k2(ω)ex.
ΔEx(ω)+k2(ω)Ex(ω)=-μ0ω2PxNL(ω).
div1k2(2ω) grad Hx(2ω)+Hx(2ω)
=2jω rotPNL(2ω)k2(2ω)ex,
ΔEx(2ω)+k2(2ω)Ex(2ω)=-4μ0ω2PxNL(2ω)
Hy(ω)=1jωμ0 Ex(ω)z,
Hz(ω)=-1jωμ0 Ex(ω)y
Ey(ω)=-1jω0(ω) Hx(ω)z-10(ω) PyNL(ω),
Ez(ω)=1jω0(ω) Hx(ω)y-10(ω) PzNL(ω)
Fl(yl)=u2ω,l1Cl du2ω,ldyy=yl,
Fl(yl+1)=MlFl-1(yl)+Vl(yl+1)-Ml[Vl(y1)+Tl(yl)].
Ml=cos[βl(2ω)dl]Clβl(2ω) sin[βl(2ω)dl]-βl(2ω)Cl sin[βl(2ω)dl]cos[βl(2ω)dl],
Tl(yl)=-2jω0Pz,lNL(2ω, yl)k2ω,l2-Pz,l-1NL(2ω, yl-1)k2ω,l-12.
FN(yN)=MF0(y1)+S,
M=l=1N-1Ml,
S=l=1N-1k=l+1N-1MkVl(yl+1)-k=lN-1Mk[Vl(yl)+Tl(yl)].
I(α, y)=-+p(α-α0)f(α, y)p(α-2α-α0)×f(α-2α, y)dα.
f(α, y)=f0(αp, y)α-αp,
f(α-2α, y)=f0(αp, y)α-2α-αp;
A+(α)exp[iβ(α)y]+A-(α)exp[-iβ(α)y],
β(α)=kω2-α2.
A+(α)=A+(αp)α-αp=C+α-αp,
A-(α)=A-(αp)α-αp=C-α-αp.
β(α)β(αr)-αr(α-αr)(kω2-αr2)1/2,
αp=αr+jαIm.
X=α-α,Δ=2αr(kω2-αr2)1/2.
I(α, y)=-+p(α-α0+X)f(α-α0+X, y)×p(α-α0-X)f(α-α0-X, y)dX.
I(α, y)=-+ p(α-α0+X)α-α0+X p(α-α0-X)α-α0-X ×[g(α, y)+K cos(ΔXy)]dX,
K=2C+C-,
g(α, y)=C+2 exp{j[2β(αr)-Δ(α-αr)]y}+C-2 exp{-j[2β(αr)-Δ(α-αr)]y}.
I1(α, y)=-+ p(α-α0+X)α-α0+X p(α-α0-X)α-α0-X K×exp(iΔXy)dX.
S(α, y)=-8jπk2ω2χ(2) p(jαIm)p(2α-2αp-jαIm)2α-2αp×{g(α, y)+K cos[(α-αp)y]},
S(α, y)=-k2ω2χ(2) G(y, α)2(α-αp),
G(α, y)=8jπp(jαIm)p(2α-2αp-jαIm)×{g(α, y)+K cos[(α-αp)y]}.

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