Abstract

Using beam propagation method calculations, we show that new effects occur for second-harmonic generation in the Čerenkov regime when it is optimized for efficient coupling to leaky modes. The fundamental throughput becomes independent of the input power over a few decades; i.e., optical power limiting is found. At even higher input powers, the fundamental throughput abruptly switches back to approximately the input power as a consequence of generating coupled second-harmonic–fundamental solitary waves in the waveguide because of the cascading effect.

© 1996 Optical Society of America

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References

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  1. SeeCompact Blue-Green Lasers, Vol. 6 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).
  2. For exampleG. I. Stegeman, in Proceedings of Erice Summer School on “Nonlinear Waves in Solid State Physics,”A. D. Boardman, T. Twardowski, eds., Vol. 247 of NATO ISI Series (Plenum, London, 1990), p. 463.
  3. For example, K. Chikuma, S. Umegaki, J. Opt. Soc. Am. B 9, 1083 (1992); T. Suhara, T. Morimoto, H. Nishihara, IEEE J. Quantum Electron. 29, 525 (1993).
    [CrossRef]
  4. G. J. M. Krijnen, H. J. W. M. Hoekstra, P. Lambeck, presented at the European Conference on Integrated Optics, Ville de Neuchatel, Neuchatel, Switzerland, April 18–23, 1993.
  5. G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.
  6. W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
    [CrossRef]
  7. G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
    [CrossRef]
  8. D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
    [CrossRef] [PubMed]
  9. For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
    [CrossRef] [PubMed]
  10. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).
  11. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
    [CrossRef] [PubMed]
  12. C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
    [CrossRef]

1996 (1)

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

1995 (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

1994 (2)

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

1992 (1)

1990 (1)

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

1985 (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Bjorklund, G.

Boggess, T. F.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Bosshard, C.

Chikuma, K.

DeMicheli, M.

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

Follonier, S.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Gunter, P.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

He, Q.

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

Hoekstra, H. J. W. M.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

G. J. M. Krijnen, H. J. W. M. Hoekstra, P. Lambeck, presented at the European Conference on Integrated Optics, Ville de Neuchatel, Neuchatel, Switzerland, April 18–23, 1993.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

Kang, J.

Kim, D. Y.

D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

Knopfle, G.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

Krijnen, G. J. M.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

G. J. M. Krijnen, H. J. W. M. Hoekstra, P. Lambeck, presented at the European Conference on Integrated Optics, Ville de Neuchatel, Neuchatel, Switzerland, April 18–23, 1993.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

Lambeck, P.

G. J. M. Krijnen, H. J. W. M. Hoekstra, P. Lambeck, presented at the European Conference on Integrated Optics, Ville de Neuchatel, Neuchatel, Switzerland, April 18–23, 1993.

Lambeck, P. V.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

Li, M. J.

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

Moerner, W.

Ostrowsky, D. B.

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

Pretre, P.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

Schiek, R.

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

Serbutoviez, C.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

Smirl, A. L.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Soileau, M. J.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Stegeman, G. I.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

For exampleG. I. Stegeman, in Proceedings of Erice Summer School on “Nonlinear Waves in Solid State Physics,”A. D. Boardman, T. Twardowski, eds., Vol. 247 of NATO ISI Series (Plenum, London, 1990), p. 463.

Torner, L.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

Torruellas, W.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

Twieg, R.

Umegaki, S.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Vidakovic, P.

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Zyss, J.

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, P. Vidakovic, J. Zyss, W. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, IEEE J. Quantum Electron. 32, 729 (1996).
[CrossRef]

For example, M. J. Li, M. DeMicheli, Q. He, D. B. Ostrowsky, IEEE J. Quantum Electron. 26, 1384 (1990); H. Sato, Y. Azumai, H. Nozawa, Opt. Lett. 19, 93 (1994).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

W. E. Torruellas, G. J. M. Krijnen, D. Y. Kim, R. Schiek, G. I. Stegeman, P. Vidakovic, J. Zyss, Opt. Commun. 112, 122 (1994).
[CrossRef]

Opt. Eng. (2)

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, P. Gunter, Opt. Eng. 34, 1951 (1995).
[CrossRef]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, Opt. Eng. 24, 613 (1985).

Opt. Lett. (1)

Phys. Rev. Lett. (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995); R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides,”Phys. Rev. A (to be published).
[CrossRef] [PubMed]

Other (4)

G. J. M. Krijnen, H. J. W. M. Hoekstra, P. Lambeck, presented at the European Conference on Integrated Optics, Ville de Neuchatel, Neuchatel, Switzerland, April 18–23, 1993.

G. J. M. Krijnen, W. Torruellas, G. I. Stegeman, H. J. W. M. Hoekstra, P. V. Lambeck, in Guided-Wave Optoelectronics: Device Characterization, Analysis, and Design, T. Tamir, H. Bertoni, G. Griffel, eds. (Plenum, New York, 1995), p. 381.

SeeCompact Blue-Green Lasers, Vol. 6 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).

For exampleG. I. Stegeman, in Proceedings of Erice Summer School on “Nonlinear Waves in Solid State Physics,”A. D. Boardman, T. Twardowski, eds., Vol. 247 of NATO ISI Series (Plenum, London, 1990), p. 463.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the numerically investigated structure. The waveguide is 5 mm long, has a thickness of 4 μm, and has refractive-index profiles as drawn schematically for ω and 2ω at the left-hand and the right-hand sides, respectively.

Fig. 2
Fig. 2

Logarithm of the transmission of the TE0(ω) mode as a function of the propagation distance for the three different input powers.

Fig. 3
Fig. 3

Output power of the guided fundamental mode (solid curve) and total power (dashed curve) versus input power.

Fig. 4
Fig. 4

Logarithm of the field profiles of the fundamental (left) and SH (right) fields after 5-mm propagation for cases I (top), II (middle), and III (bottom). The dashed lines represent the refractive-index profiles (not scaled).

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