Abstract

Second-harmonic generation in Ti:LiNbO3 channel waveguide resonators is investigated both theoretically and experimentally as a means of enhancing the conversion efficiency. In particular, symmetric and matched resonators for the fundamental wave are studied. Matched resonators are shown to maximize the efficiency, which can surpass that of nonresonant guides by as many as several orders of magnitude. Experimentally, the theoretical predictions are confirmed by using a single-frequency argon-ion laser of λ = 1.09 μm emission wavelength as the fundamental source. With a matched resonator of 40-mm length a conversion efficiency of 10−3 is achieved with 100-μW fundamental power.

© 1988 Optical Society of America

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References

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  1. N. Uesugi and T. Kimura, “Efficient second-harmonic generation in three-dimensional LiNbO3optical waveguide,” Appl. Phys. Lett. 29, 572–574 (1976).
    [CrossRef]
  2. W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3optical waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978).
    [CrossRef]
  3. M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, and D. B. Ostrowsky, “Extension of second-harmonic phase-matching range in lithium niobate guides,” Opt. Lett. 8, 116–118 (1983).
    [CrossRef] [PubMed]
  4. M. M. Fejer, M. J. F. Digonnet, and R. L. Byer, “Generation of 22 mW of 532-nm radiation by frequency doubling in Ti:MgO:LiNbO3waveguides,” Opt. Lett. 11, 230–232 (1986).
    [CrossRef]
  5. G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29–36 (1986).
    [CrossRef]
  6. T. Taniuchi and K. Yamamoto, “Second-harmonic generation with GaAs laser diode in proton-exchanged LiNbO3waveguides,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. I, pp. 22–25.
  7. R. Regener and W. Sohler, “Efficient second-harmonic generation in matched waveguide resonators,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. III, postdeadline paper, pp. 49–52.
  8. W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
    [CrossRef]
  9. R. V. Schmidt and I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
    [CrossRef]
  10. J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
    [CrossRef]
  11. D. B. Ostrowsky, “Parametric processes in LiNbO3,” in Integrated Optics, H. P. Nolting and R. Ulrich, eds., Vol. 48 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985), pp. 146–151.
    [CrossRef]
  12. R. Regener, W. Sohler, and H. Suche, “Cw second-harmonic generation in optical waveguide resonators,” in Digest of 1st European Conference on Integrated Optics (Institution of Electrical Engineers, London, 1981), pp. 19–21.
  13. W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., Vol. II, No. 79 of NATO ASI Series (Nijhoff, The Hague, 1984), pp. 449–479.
  14. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
    [CrossRef]
  15. G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
    [CrossRef]
  16. E. Strake, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).
  17. St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
    [CrossRef]
  18. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  19. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
    [CrossRef]
  20. R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
    [CrossRef]
  21. R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).
  22. H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202.

1987 (1)

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

1986 (3)

M. M. Fejer, M. J. F. Digonnet, and R. L. Byer, “Generation of 22 mW of 532-nm radiation by frequency doubling in Ti:MgO:LiNbO3waveguides,” Opt. Lett. 11, 230–232 (1986).
[CrossRef]

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29–36 (1986).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

1985 (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[CrossRef]

1983 (1)

1982 (2)

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
[CrossRef]

1978 (1)

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3optical waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978).
[CrossRef]

1976 (1)

N. Uesugi and T. Kimura, “Efficient second-harmonic generation in three-dimensional LiNbO3optical waveguide,” Appl. Phys. Lett. 29, 572–574 (1976).
[CrossRef]

1974 (1)

R. V. Schmidt and I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Alferness, R. C.

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Arvidsson, G.

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29–36 (1986).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Bava, G. P.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

Botineau, J.

Boyd, G. D.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Buhl, L. C.

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Byer, R. L.

De Micheli, M.

Digonnet, M. J. F.

Divino, M. D.

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

Fejer, M. M.

Hampel, B.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

Jackel, J. L.

J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
[CrossRef]

Kaminow, I. P.

R. V. Schmidt and I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

Kimura, T.

N. Uesugi and T. Kimura, “Efficient second-harmonic generation in three-dimensional LiNbO3optical waveguide,” Appl. Phys. Lett. 29, 572–574 (1976).
[CrossRef]

Korotky, St. K.

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Laurell, F.

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29–36 (1986).
[CrossRef]

Minford, W. J.

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Montrosset, I.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

Neveu, S.

Ostrowsky, D. B.

M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, and D. B. Ostrowsky, “Extension of second-harmonic phase-matching range in lithium niobate guides,” Opt. Lett. 8, 116–118 (1983).
[CrossRef] [PubMed]

D. B. Ostrowsky, “Parametric processes in LiNbO3,” in Integrated Optics, H. P. Nolting and R. Ulrich, eds., Vol. 48 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985), pp. 146–151.
[CrossRef]

Regener, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[CrossRef]

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

R. Regener, W. Sohler, and H. Suche, “Cw second-harmonic generation in optical waveguide resonators,” in Digest of 1st European Conference on Integrated Optics (Institution of Electrical Engineers, London, 1981), pp. 19–21.

R. Regener and W. Sohler, “Efficient second-harmonic generation in matched waveguide resonators,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. III, postdeadline paper, pp. 49–52.

Rice, C. E.

J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
[CrossRef]

Ricken, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202.

Schmidt, R. V.

R. V. Schmidt and I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

Sibillot, P.

Sohler, W.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[CrossRef]

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3optical waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978).
[CrossRef]

H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202.

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

R. Regener and W. Sohler, “Efficient second-harmonic generation in matched waveguide resonators,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. III, postdeadline paper, pp. 49–52.

R. Regener, W. Sohler, and H. Suche, “Cw second-harmonic generation in optical waveguide resonators,” in Digest of 1st European Conference on Integrated Optics (Institution of Electrical Engineers, London, 1981), pp. 19–21.

W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., Vol. II, No. 79 of NATO ASI Series (Nijhoff, The Hague, 1984), pp. 449–479.

Strake, E.

E. Strake, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

Suche, H.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3optical waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978).
[CrossRef]

H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202.

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

R. Regener, W. Sohler, and H. Suche, “Cw second-harmonic generation in optical waveguide resonators,” in Digest of 1st European Conference on Integrated Optics (Institution of Electrical Engineers, London, 1981), pp. 19–21.

Taniuchi, T.

T. Taniuchi and K. Yamamoto, “Second-harmonic generation with GaAs laser diode in proton-exchanged LiNbO3waveguides,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. I, pp. 22–25.

Uesugi, N.

N. Uesugi and T. Kimura, “Efficient second-harmonic generation in three-dimensional LiNbO3optical waveguide,” Appl. Phys. Lett. 29, 572–574 (1976).
[CrossRef]

Veselka, J. J.

J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
[CrossRef]

Volk, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

Yamamoto, K.

T. Taniuchi and K. Yamamoto, “Second-harmonic generation with GaAs laser diode in proton-exchanged LiNbO3waveguides,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. I, pp. 22–25.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Appl. Phys. B (1)

R. Regener and W. Sohler, “Loss in low-finesse Ti:LiNbO3optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1985).
[CrossRef]

Appl. Phys. Lett. (4)

N. Uesugi and T. Kimura, “Efficient second-harmonic generation in three-dimensional LiNbO3optical waveguide,” Appl. Phys. Lett. 29, 572–574 (1976).
[CrossRef]

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3optical waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978).
[CrossRef]

R. V. Schmidt and I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

J. L. Jackel, C. E. Rice, and J. J. Veselka, “Proton exchange for high-index waveguides in LiNbO3,” Appl. Phys. Lett. 47, 607–608 (1982).
[CrossRef]

IEEE J. Lightwave Technol. (1)

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk; “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772–777 (1986).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second-harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–124 (1966).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. QE-9, 919–933 (1973).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42–51 (1987).
[CrossRef]

St. K. Korotky, W. J. Minford, L. C. Buhl, M. D. Divino, and R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3strip waveguides,” IEEE J. Quantum Electron. QE-18, 1796–1801 (1982).
[CrossRef]

Opt. Lett. (2)

Thin Solid Films (1)

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29–36 (1986).
[CrossRef]

Other (9)

T. Taniuchi and K. Yamamoto, “Second-harmonic generation with GaAs laser diode in proton-exchanged LiNbO3waveguides,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. I, pp. 22–25.

R. Regener and W. Sohler, “Efficient second-harmonic generation in matched waveguide resonators,” in Technical Digest of 12th European Conference on Optical Communications (Telefónica, Barcelona, 1986), Vol. III, postdeadline paper, pp. 49–52.

D. B. Ostrowsky, “Parametric processes in LiNbO3,” in Integrated Optics, H. P. Nolting and R. Ulrich, eds., Vol. 48 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985), pp. 146–151.
[CrossRef]

R. Regener, W. Sohler, and H. Suche, “Cw second-harmonic generation in optical waveguide resonators,” in Digest of 1st European Conference on Integrated Optics (Institution of Electrical Engineers, London, 1981), pp. 19–21.

W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., Vol. II, No. 79 of NATO ASI Series (Nijhoff, The Hague, 1984), pp. 449–479.

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

E. Strake, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

R. Regener, R. Ricken, W. Sohler, H. Suche, and R. Volk, Angewandte Physik, Universität Paderborn, Paderborn, Federal Republic of Germany (personal communication).

H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202.

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Figures (15)

Fig. 1
Fig. 1

The function h [see Eq. (10), left-hand ordinate] as h versus waveguide length l for several loss coefficients αω and α2ω as parameters. h is proportional to the conversion efficiency η (right-hand ordinate) given for a fundamental power of 1 mW and an effective interaction area of 260 μm2. The length-dependent bulk efficiency is plotted for comparison.

Fig. 2
Fig. 2

Resonator for the fundamental wave with mirrors M1 and M2 of (power) reflectivities Rf and Rr. P0, Pr, Pi+, Pi, and Pt are the incident, reflected, internal, and transmitted powers, respectively, and α is the loss coefficient of the LiNbO3 crystal (waveguide) of length l.

Fig. 3
Fig. 3

Calculated resonance factors fs and fm, characterizing the internal power enhancement of symmetric (Rf = Rr = R) and matched [Rf = Rr exp(−2αωl)] resonators versus the loss coefficient of the waveguide (lower abscissa, assuming a length l of 4 cm) and the a product (upper abscissa), respectively. The dashed line corresponds to a nonresonant waveguide (f = 1).

Fig. 4
Fig. 4

Calculated transmittance (left) and reflectivity (right) of a symmetric resonator versus the internal phase shift δ of half a round trip, assuming mirror reflectivities of 0.99, a device length of 4 cm, and various loss coefficients α, as shown. The length of the abscissa corresponds to 0.45 rad in both parts of the figure (λf = 1.09 μm).

Fig. 5
Fig. 5

Calculated transmittance (left) and reflectivity (right) of a matched resonator, using the same parameters as for the results given in Fig. 4 [with the exception that Rf is defined by Eq. (24)].

Fig. 6
Fig. 6

Comparison of calculated conversion efficiency η and generated second-harmonic power P2ω in a nonresonant guide and in a symmetric and a matched waveguide resonator as a function of the device length l, assuming a fundamental power (λf = 1.09 μm) of 1 mW, waveguide loss coefficients αω = 0.1 dB/cm, α2ω = 0.3 dB/cm, and Feff = 260 μm2. A nonlinear coupling of the lowest-order modes (TM00 and TE00) is considered.

Fig. 7
Fig. 7

Calculated conversion efficiency η and generated harmonic power P2ω in a matched waveguide resonator versus the loss coefficient of the fundamental wave (λf = 1.09 μm), assuming α2ω = 3αω, Pω = 1 mW, Feff = 260 μm2, and TM00–TE00 coupling.

Fig. 8
Fig. 8

Experimental setup: L1, single-frequency Ar-ion laser (λ = 1.09 μm); SF, spatial filter; OI, optical isolator, consisting of two Glan–Thompson polarizers (G\P’s), a YIG crystal, and a half-wave (λ/2) plate; L2, auxiliary He–Ne laser; OSA, optical spectrum analyzer; EOS, electro-optical shutter; MO’s, microscope objectives; TT, temperature-tuning element; BS’s, beam splitters; Fω and F2ω interference filters for fundamental and harmonic waves, respectively; TV, television system.

Fig. 9
Fig. 9

Second-harmonic generation in a nonresonant channel guide: harmonic power P2ω versus device temperature for 0.5 mW of fundamental power coupled to the waveguide. A theoretical curve is plotted as a dashed line, assuming an interaction length equal to the waveguide length.

Fig. 10
Fig. 10

Second-harmonic generation in a symmetric waveguide resonator of >99% mirror reflectivities and 0.035-dB/cm waveguide losses. Plot is of forward-generated harmonic power P2ω (left-hand ordinate) and reflected fundamental power Pωr (right-hand ordinate) versus the device temperature. The input power measured in front of the resonator was 1 mW.

Fig. 11
Fig. 11

Second-harmonic generation in a matched waveguide resonator of 68 and 98% front- and rear-mirror reflectivities, respectively, and 0.1-dB/cm waveguide losses. Plot is of forward-generated harmonic power P2ω (left-hand ordinate) and reflected fundamental power Pωr (right-hand ordinate) versus the device temperature. The input power measured in front of the resonator was 100 μW. The right part of the figure is an enlarged view of the central resonance on the left.

Fig. 12
Fig. 12

Harmonic (peak) power, generated in a matched waveguide resonator in a pulsed-mode operation as a function of the square of the harmonic power Pω2: dashed line, η = 10−2/mW; solid line, η = 4 × 10−3/mW.

Fig. 13
Fig. 13

Representation of phase-matching curve (x = Δβl/2) and resonances of the reflected fundamental power of a 4-cm-long nearly matched resonator versus the device temperature with optimized (dashed curves) and arbitrary (dashed–dotted curves) relative positions.

Fig. 14
Fig. 14

Electro-optically induced shift of the phase-match temperature ΔTpm and of the shift ΔTR of the resonances of a Ti:LiNbO3 waveguide resonator of 4.4-cm length.

Fig. 15
Fig. 15

Second-harmonic generation in a matched waveguide resonator at higher fundamental power levels. The plot is of harmonic (P2ω, left-hand ordinate) and reflected fundamental (Pωr, right-hand ordinate) powers versus the device temperature.

Equations (30)

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E ω ( x , y , z , t ) = ½ { A ω ( z ) E ω ( x , y ) exp [ i ( ω t - β ω z ) ] + c . c . } , E 2 ω ( x , y , z , t ) = ½ { A 2 ω ( z ) E 2 ω ( x , y ) exp [ i ( 2 ω t - β 2 ω z ) ] + c . c . } ,
P ω = A ω 2 2 Z ω - + E ω 2 ( x , y ) d x d y ,
Z ω = 1 0 c n eff , ω ,
- + E 2 ( x , y ) d x d y = 1.
P ω = A ω 2 2 Z ω
η = P 2 ω P ω = tanh 2 ( g l ) ,
X = - + E 2 ω ( x , y ) E ω 2 ( x , y ) d x d y [ - + E 2 ω 2 ( x , y ) d x d y ] 1 / 2 E ω 2 ( x , y ) d x d y .
X = - + E 2 ω ( x , y ) E ω 2 ( x , y ) d x d y ,
F eff = 1 X 2 ,
I eff = P ω F eff = X 2 P ω .
η = g 2 l 2 = K I eff l 2 ,
η = K I eff ( z = 0 ) h ( α ω , α 2 ω , l ) ,
h ( α ω , α 2 ω , l ) = [ exp ( - α ω l ) - exp ( - α 2 ω l / 2 ) α ω - α 2 ω / 2 ] 2 ,
η bulk = K 2 n l λ P ω .
l c = F eff 2 n λ .
η ˜ = η P ω ( z = 0 ) = K h ( α ω , α 2 ω , l ) F eff .
P r = P 0 { [ ( R f ) 1 / 2 - ( R r ) 1 / 2 exp ( - α ω l ) ] 2 + 4 ( R f R r ) 1 / 2 exp ( - α ω l ) sin 2 δ } / N 1 ,
P i + = P 0 ( 1 - R f ) / N 1 ,
P i - = P 0 ( 1 - R f ) exp ( - α ω l ) R r / N 1 ,
P t = P 0 ( 1 - R f ) ( 1 - R r ) exp ( - α ω l ) / N 1 ,
P r = P 0 [ ( R f ) 1 / 2 - ( R r ) 1 / 2 exp ( - α ω l ) ] 2 / N 2 < P 0 ,
P i + = P 0 ( 1 - R f ) / N 2 = P 0 f ,
P i - = P 0 ( 1 - R f ) exp ( α ω l ) R r / N 2 = P 0 f exp ( - α ω l ) R r ,
P t = P 0 ( 1 - R f ) ( 1 - R r ) exp ( - α ω l ) / N 2 < P 0 ,
f = 1 - R f [ 1 - ( R f R r ) 1 / 2 exp ( - α ω l ) ] 2 .
f s = 1 - R [ 1 - R exp ( - α ω l ) ] 2 .
R fm = R r exp ( - 2 α ω l ) .
f m = 1 1 - R fm .
f m , max = 1 1 - exp ( - 2 α ω l ) .
η res = η f 2 ,

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