Abstract

The output power and spectral characteristics of optical parametric oscillators (OPO’s) as they evolve from the doubly resonant to the singly resonant regime are examined. By assuming a high-Q signal cavity, we derive approximate analytical solutions of pump depletion and conversion efficiency for OPO’s with arbitrary idler Q. Using this set of solutions, we examine in detail amplitude and frequency instabilities of doubly resonant oscillators with low signal loss and arbitrary idler loss. We find that OPO’s with weak idler feedback, when operated at a few times above threshold, exhibit improved spectral stability. Experimental results are presented for LiNbO3 and KTP OPO’s operating with a fixed low signal loss and various idler losses, including the limiting case of the cw singly resonant oscillator with no idler feedback.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
    [Crossref]
  2. R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
    [Crossref]
  3. J. A. Giordmaine and R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelly, B. Lax, and P. E. Tannenwald, eds. (McGraw-Hill, New York, 1965), pp. 31–42.
  4. R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
    [Crossref]
  5. A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
    [Crossref] [PubMed]
  6. C. D. Nabors, R. C. Eckardt, W. J. Kozlovsky, and R. L. Byer, “Efficient single-axial-mode operation of a monolithic MgO:LiNbO3optical parametric oscillator,” Opt. Lett. 14, 1134–1136 (1989).
    [Crossref] [PubMed]
  7. D. Lee and N. C. Wong, “Tunable optical frequency division using a phase locked optical parametric oscillator,” Opt. Lett. 17, 13–15 (1992).
    [Crossref] [PubMed]
  8. C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 7, 815–820 (1990).
    [Crossref]
  9. R. C. Eckardt, C. D. Nabors, W. J. Kozlovsky, and R. L. Byer, “Optical parametric oscillator frequency tuning and control,” J. Opt. Soc. Am. B 8, 646–667 (1991).
    [Crossref]
  10. S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
    [Crossref]
  11. S. T. Yang, R. C. Eckardt, and R. L. Byer, “Continuous-wave singly resonant optical parametric oscillator pumped by a single-frequency resonantly doubled Nd:YAG laser,” Opt. Lett. 18, 971–973 (1993).
    [Crossref] [PubMed]
  12. J. Falk, “Instabilities in the doubly resonant parametric oscillator: a theoretical analysis,” IEEE J. Quantum Electron. QE-7, 230–235 (1971).
    [Crossref]
  13. J. E. Bjorkholm, “Analysis of the doubly resonant optical parametric oscillator without power-dependent reflections,” IEEE J. Quantum Electron. QE-5, 293–295 (1969).
    [Crossref]
  14. G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
    [Crossref]
  15. L. B. Kreuzer, “Single and multi-mode oscillation of the singly resonant optical parametric oscillator,” in Proceedings of the Joint Conference on Lasers and Opto-Electronics (Institution of Electrical and Radio Engineers, London, 1969), pp. 52–63.
  16. R. L. Byer, “Optical parametric oscillator,” in Treatise in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), pp. 587–702.
  17. C. D. Nabors, A. D. Farinas, T. Day, S. T. Yang, E. K. Gustafson, and R. L. Byer, “Injection locking of a 13-W cw Nd:YAG ring laser,” Opt. Lett. 14, 1189–1191 (1989).
    [Crossref] [PubMed]
  18. S. T. Yang, C. C. Pohalski, E. K. Gustafson, R. L. Byer, R. S. Feigelson, R. J. Raymakers, and R. K. Route, “6.5-W, 532-nm radiation by cw resonant external-cavity second-harmonic generation of an 18-W Nd:YAG laser in LiB3O5,” Opt. Lett. 16, 1493–1495 (1991).
    [Crossref] [PubMed]
  19. The MgO:LiNbO3 crystal is from Crystal Technology, Inc., Mountain View, Calif.
  20. K. Kato, “Parametric oscillation at 3.2 μ m in KTP pumped at 1.064 μ m,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
    [Crossref]
  21. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [Crossref]
  22. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
    [Crossref]
  23. H. Vanherzeele and J. D. Bierlein, “Magnitude of the nonlinear-optical coefficients of KTiOPO4,” Opt. Lett. 17, 982–984 (1992).
    [Crossref] [PubMed]
  24. T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-II continuous-wave optical parametric oscillators: oscillation and frequency-tuning characteristics,” J. Opt. Soc. Am. B 10, 1668–1680 (1993).
    [Crossref]
  25. J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
    [Crossref]
  26. S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
    [Crossref]
  27. A. I. Kovrigin and R. L. Byer, “Stability factor for optical parametric oscillators,” IEEE J. Quantum Electron. QE-5, 384–385 (1969).
    [Crossref]

1993 (2)

1992 (3)

1991 (3)

1990 (2)

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[Crossref]

C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 7, 815–820 (1990).
[Crossref]

1989 (2)

1987 (1)

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

1982 (1)

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

1973 (1)

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[Crossref]

1971 (1)

J. Falk, “Instabilities in the doubly resonant parametric oscillator: a theoretical analysis,” IEEE J. Quantum Electron. QE-7, 230–235 (1971).
[Crossref]

1970 (1)

J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
[Crossref]

1969 (3)

A. I. Kovrigin and R. L. Byer, “Stability factor for optical parametric oscillators,” IEEE J. Quantum Electron. QE-5, 384–385 (1969).
[Crossref]

J. E. Bjorkholm, “Analysis of the doubly resonant optical parametric oscillator without power-dependent reflections,” IEEE J. Quantum Electron. QE-5, 293–295 (1969).
[Crossref]

S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
[Crossref]

1968 (3)

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Ashkin, A.

J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
[Crossref]

Bava, G. P.

G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
[Crossref]

Bierlein, J. D.

Bjorkholm, J.

J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
[Crossref]

Bjorkholm, J. E.

J. E. Bjorkholm, “Analysis of the doubly resonant optical parametric oscillator without power-dependent reflections,” IEEE J. Quantum Electron. QE-5, 293–295 (1969).
[Crossref]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Byer, R. L.

S. T. Yang, R. C. Eckardt, and R. L. Byer, “Continuous-wave singly resonant optical parametric oscillator pumped by a single-frequency resonantly doubled Nd:YAG laser,” Opt. Lett. 18, 971–973 (1993).
[Crossref] [PubMed]

R. C. Eckardt, C. D. Nabors, W. J. Kozlovsky, and R. L. Byer, “Optical parametric oscillator frequency tuning and control,” J. Opt. Soc. Am. B 8, 646–667 (1991).
[Crossref]

S. T. Yang, C. C. Pohalski, E. K. Gustafson, R. L. Byer, R. S. Feigelson, R. J. Raymakers, and R. K. Route, “6.5-W, 532-nm radiation by cw resonant external-cavity second-harmonic generation of an 18-W Nd:YAG laser in LiB3O5,” Opt. Lett. 16, 1493–1495 (1991).
[Crossref] [PubMed]

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[Crossref]

C. D. Nabors, S. T. Yang, T. Day, and R. L. Byer, “Coherence properties of a doubly resonant monolithic optical parametric oscillator,” J. Opt. Soc. Am. B 7, 815–820 (1990).
[Crossref]

C. D. Nabors, R. C. Eckardt, W. J. Kozlovsky, and R. L. Byer, “Efficient single-axial-mode operation of a monolithic MgO:LiNbO3optical parametric oscillator,” Opt. Lett. 14, 1134–1136 (1989).
[Crossref] [PubMed]

C. D. Nabors, A. D. Farinas, T. Day, S. T. Yang, E. K. Gustafson, and R. L. Byer, “Injection locking of a 13-W cw Nd:YAG ring laser,” Opt. Lett. 14, 1189–1191 (1989).
[Crossref] [PubMed]

A. I. Kovrigin and R. L. Byer, “Stability factor for optical parametric oscillators,” IEEE J. Quantum Electron. QE-5, 384–385 (1969).
[Crossref]

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

R. L. Byer, “Optical parametric oscillator,” in Treatise in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), pp. 587–702.

Camy, G.

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Colucci, G.

G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
[Crossref]

Day, T.

Debuisschert, T.

Eckardt, R. C.

Fabre, C.

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-II continuous-wave optical parametric oscillators: oscillation and frequency-tuning characteristics,” J. Opt. Soc. Am. B 10, 1668–1680 (1993).
[Crossref]

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Falk, J.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

J. Falk, “Instabilities in the doubly resonant parametric oscillator: a theoretical analysis,” IEEE J. Quantum Electron. QE-7, 230–235 (1971).
[Crossref]

Fan, Y. X.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[Crossref]

Farinas, A. D.

Feigelson, R. S.

Geusic, J. E.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Giacobino, E.

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-II continuous-wave optical parametric oscillators: oscillation and frequency-tuning characteristics,” J. Opt. Soc. Am. B 10, 1668–1680 (1993).
[Crossref]

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Giordmaine, J. A.

J. A. Giordmaine and R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelly, B. Lax, and P. E. Tannenwald, eds. (McGraw-Hill, New York, 1965), pp. 31–42.

Guha, S.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

Gustafson, E. K.

Harris, S. E.

S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
[Crossref]

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

Heidmann, A.

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Herowicz, R. J.

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Kato, K.

K. Kato, “Parametric oscillation at 3.2 μ m in KTP pumped at 1.064 μ m,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[Crossref]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Kovrigin, A. I.

A. I. Kovrigin and R. L. Byer, “Stability factor for optical parametric oscillators,” IEEE J. Quantum Electron. QE-5, 384–385 (1969).
[Crossref]

Kozlovsky, W. J.

Kreuzer, L. B.

L. B. Kreuzer, “Single and multi-mode oscillation of the singly resonant optical parametric oscillator,” in Proceedings of the Joint Conference on Lasers and Opto-Electronics (Institution of Electrical and Radio Engineers, London, 1969), pp. 52–63.

Lee, D.

Levinstein, H. J.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Masuda, H.

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[Crossref]

Miller, R. C.

J. A. Giordmaine and R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelly, B. Lax, and P. E. Tannenwald, eds. (McGraw-Hill, New York, 1965), pp. 31–42.

Montrosset, I.

G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
[Crossref]

Nabors, C. D.

Oshman, M. K.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

Pohalski, C. C.

Raymakers, R. J.

Reynaud, S.

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Romano, D.

G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
[Crossref]

Route, R. K.

Rubin, J. J.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Singh, S.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Sizmann, A.

Smith, R. G.

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[Crossref]

J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
[Crossref]

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Van Uitert, L. G.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

Vanherzeele, H.

Wong, N. C.

Wu, F. J.

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

Yang, S. T.

Young, J. F.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

Appl. Phys. Lett. (2)

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb5O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[Crossref]

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[Crossref]

IEEE J. Quantum Electron. (9)

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[Crossref]

J. Falk, “Instabilities in the doubly resonant parametric oscillator: a theoretical analysis,” IEEE J. Quantum Electron. QE-7, 230–235 (1971).
[Crossref]

J. E. Bjorkholm, “Analysis of the doubly resonant optical parametric oscillator without power-dependent reflections,” IEEE J. Quantum Electron. QE-5, 293–295 (1969).
[Crossref]

G. Colucci, D. Romano, G. P. Bava, and I. Montrosset, “Analysis of integrated optics parametric oscillators,” IEEE J. Quantum Electron. 28, 729–738 (1992).
[Crossref]

K. Kato, “Parametric oscillation at 3.2 μ m in KTP pumped at 1.064 μ m,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).
[Crossref]

R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficient of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[Crossref]

J. Bjorkholm, A. Ashkin, and R. G. Smith, “Improvement of optical parametric oscillators by nonresonant pump reflection,” IEEE J. Quantum Electron. QE-6, 797–799 (1970).
[Crossref]

S. Guha, F. J. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907–912 (1982).
[Crossref]

A. I. Kovrigin and R. L. Byer, “Stability factor for optical parametric oscillators,” IEEE J. Quantum Electron. QE-5, 384–385 (1969).
[Crossref]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

A. Heidmann, R. J. Herowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, “Observation of quantum noise reduction on twin laser beams,” Phys. Rev. Lett. 59, 2555–2557 (1987).
[Crossref] [PubMed]

Proc. IEEE (1)

S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
[Crossref]

Other (4)

J. A. Giordmaine and R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelly, B. Lax, and P. E. Tannenwald, eds. (McGraw-Hill, New York, 1965), pp. 31–42.

The MgO:LiNbO3 crystal is from Crystal Technology, Inc., Mountain View, Calif.

L. B. Kreuzer, “Single and multi-mode oscillation of the singly resonant optical parametric oscillator,” in Proceedings of the Joint Conference on Lasers and Opto-Electronics (Institution of Electrical and Radio Engineers, London, 1969), pp. 52–63.

R. L. Byer, “Optical parametric oscillator,” in Treatise in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), pp. 587–702.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Theoretical signal-photon-conversion efficiency plotted as a function of pumping intensity relative to threshold. Calculation is done for DRO’s with fixed round-trip signal-power reflectance of 100% and various round-trip idler-power reflectances Ri. Note that the 100% conversion-efficiency point moves continuously from N = 4 to N = (π/2)2 as the OPO’s evolve from the DRO to the SRO regime.

Fig. 2
Fig. 2

Calculated normalized signal intensity versus detuning of the signal and idler resonances expressed as the sum of the round-trip phase shift Ψs + Ψi. The calculation is done for DRO’s with a signal-power reflectance of 99%, except for the dashed curve, for which Rs = 89.1%. The peak of calculated signal intensity is normalized to unity. The pumping levels are at three times above their respective thresholds. Perfect phase matching is assumed for these calculations. Note the widely different phase-detuning tolerance range for Ri ranging from 99% to 0%. For Ri = 99% the tolerance range is so small that it appears as a spike. In the other extreme, when Ri = 0% the SRO amplitude remains flat regardless of phase detuning.

Fig. 3
Fig. 3

Calculated parametric gain, (Γlc)2 = κsκi|Es|2lc2, versus detunings from an exact overlap of signal- and idler-cavity resonances. The calculation is done for DRO’s with fixed round-trip signal-power reflectance of 99% and idler-power reflectance of 25%. The phase-detuning range over which the OPO remains above threshold increases as the pumping level is raised. Perfect phase matching is assumed for these calculations.

Fig. 4
Fig. 4

Calculated OPO Δklc operating point for OPO’s with Rs = 99% and Ri = 1% as a function of cavity-detuning parameter Ψ0 and at different pumping levels. The dashed curve is calculated by Falk’s prescription, which assigns the minimum-threshold point as the OPO operating point. In this study we calculated the solid curves assuming that the OPO oscillates at the highest signal output point.

Fig. 5
Fig. 5

Calculated maximum Δklc operating-point excursion of the OPO relative to the phase-matching peak as a function of idler-field reflectance ri. The OPO has fixed signal power reflectance of 99%. The dashed curve is from Falk’s calculation. The solid curves are calculated assuming that the OPO operating point corresponds to the maximum signal point. They are calculated for pumping at 1.1, 1.5, 2.0, 2.5, and 3.0 times above threshold. Pumping at 2.5 times above threshold, the maximum operating-point excursions are insignificant for ri < 0.1.

Fig. 6
Fig. 6

DRO experimental setup. The two flat mirrors of the bow-tie ring cavity are spaced 45 cm apart between the two flat mirrors, and the space between the two mirrors (each with a 10-cm radius of curvature) is 11 cm. The incident angle on all the mirrors is 3 deg. To introduce loss preferentially for the idler in a LiNbO3 OPO, we replace one of the flat mirrors with a Ti: sapphire mirror. For KTP OPO one or two Brewster plates are introduced into the long leg of the cavity to couple out the p-polarized idler waves preferentially.

Fig. 7
Fig. 7

Measured LiNbO3 DRO threshold as a function of round-trip idler-power loss. We observed minimum threshold of 20 mW. The curve is calculated by the threshold-ratio formula [Eq. (14)], assuming a 17-mW threshold for round-trip signal- and idler-power loss of 0.8%. The extrapolated SRO threshold is 8.5 W.

Fig. 8
Fig. 8

Cw KTP SRO experimental setup. Mirrors M1 and M2 each have a 5-cm radius of curvature. Mirror M3 is flat. Mirrors M2 and M3 and the pump mirror are mounted on PZT’s. The pump and idler waves are reflected back through the crystal. The LiNbO3 Brewster prism rejects the idler wave when one achieves true SRO operation.

Fig. 9
Fig. 9

Generated SRO-idler power versus pump power. The threshold is 1.07 W. At 3.2 W of 532-nm pump power, the non-resonant idler output power is 1.1 W for an idler conversion efficiency of 33%.

Fig. 10
Fig. 10

OPO temporal output recorded versus cavity-length change. The superimposed ramp is the voltage drive for the PZT. With 100 V applied to the PZT, the cavity length changes by 0.9 μm. (a) Output intensity from a high-Q KTP DRO. As the cavity length is scanned, the output intensity modulation reaches a peak of 75% for pumping at 1.38 times above threshold. (b) Output intensity fluctuation of a KTP OPO with one Brewster plate inserted to discriminate against the idler wave. Note the reduced intensity modulation of 43%. (c) SRO output intensity the position of mirror M3 is scanned (see Fig. 8). Fast amplitude fluctuations have disappeared in this case. Slow amplitude variations are due to pump-mirror position fluctuations.

Fig. 11
Fig. 11

Free-running output of KTP OPO with one Brewster plate inserted as observed at three different pumping levels. The cavity length is swept in these traces: (a), (b), and (c) represent pumping at 1.1, 1.8, and 2.5 times above threshold, respectively. When the pump power is increased, the intensity modulation resulting from cavity-length fluctuation is reduced. Note that the time interval for (a) is much shorter than the time duration displayed in (b) and (c). The steplike amplitude changes shown in (c) correspond to axial mode hops.

Fig. 12
Fig. 12

KTP SRO output spectrum as observed by a 300-MHz scanning-confocal Fabry–Perot interferometer. The observed single-axial-mode output linewidth of 1 MHz is instrument-resolution limited.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

E s ( z ) z = i κ s E p ( z ) E i * ( z ) exp ( i Δ k z ) ,
E i ( z ) z = i κ i E p ( z ) E s * ( z ) exp ( i Δ k z ) ,
E p ( z ) z = i κ p E s ( z ) E i ( z ) exp ( i Δ k z ) .
E i ( z ) = { E i 0 cos ( Γ z ) E i 0 [ i Δ k / ( 2 Γ ) ] sin ( Γ z ) + ( i κ i / Γ ) E p 0 E s 0 * sin ( Γ z ) } exp ( i Δ k z / 2 ) ,
E p ( z ) = { E p 0 cos ( Γ z ) E p 0 [ i Δ k / ( 2 Γ ) ] sin ( Γ z ) + ( i κ p / Γ ) E s 0 E i 0 sin ( Γ z ) } exp ( i Δ k z / 2 ) ,
E i 0 = i κ i Γ E p 0 E s 0 * sin ( Γ l c ) r i exp ( i Δ k l c / 2 + i Ψ i ) 1 [ cos ( Γ l c ) i Δ k 2 Γ sin ( Γ l c ) ] r i exp [ i ( Δ k l c / 2 + Ψ i ) ] .
E s ( z = l c ) E s 0 = 1 + N C F * sin ( x ) x × { 1 + sin ( 2 x ) 2 x + i Δ k l c sin 2 ( x ) x 2 ( Δ k l c ) 2 4 x 2 [ 1 sin ( 2 x ) 2 x ] } + N C 2 x 2 { 1 [ 1 ( Δ k l c 2 x ) 2 ] sin 2 ( x ) | F | 2 } × { 2 sin 2 ( x ) + i Δ k l c [ 1 sin ( 2 x ) 2 x ] } N C F sin ( x ) x [ 1 ( Δ k l c 2 x ) 2 ] [ 1 sin ( 2 x ) 2 x ] ,
F = r i exp [ i ( Δ k l c / 2 + Ψ i ) ] 1 [ cos ( x ) i Δ k l c / ( 2 x ) sin ( x ) ] exp [ i ( Δ k l c / 2 + Ψ i ) ] r i .
1 r s exp i Ψ s = 1 + N C F * sin ( x ) x × { 1 + sin ( 2 x ) 2 x + i Δ k l c sin 2 ( x ) x 2 ( Δ k l c ) 2 4 x 2 [ 1 sin ( 2 x ) 2 x ] } + N C 2 x 2 { 1 [ 1 ( Δ k l c 2 x ) 2 ] sin 2 ( x ) | F | 2 } × { 2 sin 2 ( x ) + i Δ k l c [ 1 sin ( 2 x ) 2 x ] } N C F sin ( x ) x [ 1 ( Δ k l c 2 x ) 2 ] [ 1 sin ( 2 x ) 2 x ] ,
1 r s = 2 1 r i r s + r i N ( r i sinc ( x ) sinc ( 2 x ) 1 cos ( x ) r i + 1 2 sinc 2 ( x ) { 1 sin 2 ( x ) r i 2 [ 1 cos ( x ) r i ] 2 } ) .
E p ( z ) = E p 0 [ cos ( Γ z ) sin ( Γ l c ) r i 1 cos ( Γ l c ) r i sin ( Γ z ) ] .
| E p ( z = l c ) | 2 | E p 0 | 2 = [ cos ( x ) sin 2 ( x ) r i 1 cos ( x ) r i ] 2 .
ω p ω s n s n p | E s 0 | 2 | E p 0 | 2 = 2 r s x 2 ( r i sinc ( x ) sinc ( 2 x ) 1 cos ( x ) r i + 1 2 sinc 2 ( x ) { 1 sin 2 ( x ) r i 2 [ 1 cos ( x ) r i ] 2 } ) .
| E p th | 2 | E p 0 | 2 = sinc 2 ( x ) ,
| E p ( z = l c ) | 2 | E p 0 | 2 = cos 2 ( x ) ,
Ψ s + Ψ i = Ψ 0 + 2 Δ k l c , Ψ 0 = 2 ω p c [ n p l c + ( L l c ) ] .
P DROth P hi Q th = 2 ( 1 r i ) α i ( 1 + r i ) ,
P s P i = γ s ( γ i + μ i ) γ i ( γ s + μ s ) ,
| δ ν p | = k i ν i | ν i 0 k s ν s | ν s 0 k p ν p | ν p 0 k i ν i | ν i 0 Δ ν s .
k s ν s = 3.723 × 10 14 , k i ν i = 3.922 × 10 14 , k p ν p = 3.997 × 10 14 .
E i ( z ) z = i κ i E p ( z ) E s * ( z ) exp ( i Δ k z ) ,
E p ( z ) z = i κ p E s ( z ) E i ( z ) exp ( i Δ k z ) .
E i + ( z ) = i κ i Γ E p 0 E s 0 * sin ( Γ z ) exp i ( Δ k z / 2 + Δ φ + ) , E p + ( z ) = E p 0 [ cos ( Γ z ) + i Δ 2 Γ sin ( Γ z ) ] exp ( i Δ k z / 2 ) ,
E i ( z = 0 ) = R i exp ( i Δ φ ) E i + ( z = l c ) , E i ( z = 0 ) = R p exp ( i Δ φ ) E p + ( z = l c ) ,
E i ( z ) = { i R i κ i Γ sin ( Γ l c ) [ cos ( Γ z ) i Δ k 2 Γ sin ( Γ z ) ] + i κ i R p Γ [ cos ( Γ l c ) + i Δ k 2 Γ sin ( Γ l c ) ] × sin ( Γ z ) exp i Δ φ } × E s 0 * E p 0 exp [ i ( Δ k z / 2 + Δ k l c / 2 + Δ φ + ) ] , E p ( z ) = { R p [ cos ( Γ l c ) + i Δ k 2 Γ sin ( Γ l c ) ] × [ cos ( Γ z ) + i Δ k 2 Γ sin ( Γ z ) ] κ i κ p R i Γ 2 | E s 0 | 2 sin ( Γ l c ) sin ( Γ z ) exp i Δ φ } × E p 0 exp i ( Δ k z / 2 + Δ k l c / 2 ) .
n p [ | E p 0 | 2 ( 1 R p ) | E p + ( z = l c ) | 2 | E p ( z = l c ) | 2 ] = ( 1 R i ) n i | E i + ( z = l c ) | 2 + n i | E i ( z = l c ) | 2 + 2 a s n s | E s 0 | 2 ,
n p | E p 0 | 2 [ sin 2 ( Γ l c ) R i sin 2 ( Γ l c ) + ( R i + R p ) cos 2 ( Γ l c ) sin 2 ( Γ l c ) + ( R i + R p ) ( Δ k 2 Γ ) 2 + 2 R i R p cos 2 ( Γ l c ) sin 2 ( Γ l c ) cos ( Δ φ ) 2 ( Δ k 2 Γ ) 2 R i R p sin 4 ( Γ l c ) cos ( Δ φ ) 2 Δ Γ R i R p cos ( Γ l c ) sin ( Γ l c ) sin 2 ( Γ l c ) sin ( Γ φ ) ] = n p 2 a s Γ 2 κ s κ i .
| E p 0 | th 2 = 2 a s κ s κ i l c 2 ( Δ k l c / 2 ) 2 sin 2 ( Δ k l c / 2 ) × [ 1 1 + R p + 2 R i R p cos ( Δ k l c + Δ φ ) ] .

Metrics