Abstract

The frequency-tuning and -control properties of monolithic doubly resonant optical parametric oscillators are analyzed for stable single-mode pump radiation. Single-axial-mode operation is observed on the idler and the signal for both pulsed and continuous pumping. Projections are made for tuning-parameter tolerances that are required for maintenance of stable single-frequency oscillation. Continuous frequency tuning is possible through the simultaneous adjustment of two or three parameters; thus the synthesis of specific frequencies within the broad tuning range of the doubly resonant optical parametric oscillator is permitted.

© 1991 Optical Society of America

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Corrections

Robert C. Eckardt, C. D. Nabors, William J. Kozlovsky, and Robert L. Byer, "Optical parametric oscillator frequency tuning and control: errata," J. Opt. Soc. Am. B 12, 2322-2322 (1995)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-12-11-2322

References

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  1. J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3at optical frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).
    [CrossRef]
  2. J. A. Giordmaine, R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelley, B. Lax, P. E. Tannenwald, eds. (McGraw-Hill, New York, 1966), pp. 31–42.
  3. G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev. 146, 187–198 (1966).
    [CrossRef]
  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. S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
    [CrossRef]
  6. R. G. Smith, “Optical parametric oscillators,” in Advances in Lasers, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976), Vol. 4, pp. 189–307.
  7. R. L. Byer, “Parametric oscillators and nonlinear materials,” in Nonlinear Optics, P. G. Harper, B. S. Wherrett, eds. (Academic, San Francisco, Calif., 1977), pp. 47–160; R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, part B, pp. 587–702.
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    [CrossRef]
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    [CrossRef]
  11. 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]
  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. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), pp. 323–329.
  15. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 435–436.
  16. G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  17. W. J. Kozlovsky, C. D. Nabors, R. C. Eckardt, R. L. Byer, “Monolithic MgO:LiNbO3doubly resonant optical parametric oscillator pumped by a frequency-doubled diode-laser-pumped Nd:YAG laser,” Opt. Lett. 14, 66–68 (1989).
    [CrossRef] [PubMed]
  18. C. D. Nabors, R. C. Eckardt, W. J. Kozlovsky, R. L. Byer, “Efficient single-axial-mode operation of a monolithic MgO:LiNbO3optical parametric oscillator,” Opt. Lett. 14, 1134–1136 (1989).
    [CrossRef] [PubMed]
  19. T. J. Kane, R. L. Byer, “Monolithic, unidirectional, single-mode Nd:YAG ring laser,” Opt. Lett. 10, 65–67 (1985).
    [CrossRef] [PubMed]
  20. A. C. Nilsson, E. K. Gustafson, R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron. 25, 767–790 (1989).
    [CrossRef]
  21. W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
    [CrossRef]
  22. B.-K. Zhou, T. J. Kane, G. J. Dixon, R. L. Byer, “Efficient, frequency-stable laser-diode-pumped Nd:YAG lasers,” Opt. Lett. 10, 62–64 (1985).
    [CrossRef] [PubMed]
  23. T. J. Kane, A. C. Nilsson, R. L. Byer, “Frequency stability and offset locking of a laser-diode-pumped Nd:YAG monolithic nonplanar ring oscillator,” Opt. Lett. 12, 175–177 (1987).
    [CrossRef] [PubMed]
  24. G.-G. Zhong, J. Jian, Z.-K. Wu, in Eleventh International Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, New York, 1980), p. 631.
  25. D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
    [CrossRef]
  26. G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
    [CrossRef]
  27. D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
    [CrossRef]
  28. D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
    [CrossRef]
  29. J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).
  30. W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).
  31. A. Räuber, “Chemistry and physics of lithium niobate,” in Current Topics in Materials Science, E. Kaldis, ed. (North-Holland, Amsterdam, 1978), Vol. 1, pp. 481–601.
  32. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), chap. 7.
  33. J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
    [CrossRef]
  34. R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
    [CrossRef]
  35. F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
    [CrossRef]
  36. Y. S. Kim, R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
    [CrossRef]
  37. J. F. Nye, Physical Properties of Crystals (Oxford, London, 1985), Chap. 7.
  38. R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
    [CrossRef]
  39. H. Suche, W. Sohler, “Integrated optical parametric oscillators,” Optoelectron. Devices Technol. (Tokyo) 4, 1–20 (1989).
  40. A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
    [CrossRef]
  41. N. C. Wong, “Optical frequency division using an optical parametric oscillator,” Opt. Lett. 15, 1129–1131 (1990).
    [CrossRef] [PubMed]

1990 (2)

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

N. C. Wong, “Optical frequency division using an optical parametric oscillator,” Opt. Lett. 15, 1129–1131 (1990).
[CrossRef] [PubMed]

1989 (4)

1988 (3)

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
[CrossRef]

W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).

1987 (1)

1986 (1)

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

1985 (3)

1984 (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

1976 (1)

D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
[CrossRef]

1974 (1)

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[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 (2)

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

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

1970 (2)

R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
[CrossRef]

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

1969 (3)

Y. S. Kim, R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (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 (2)

R. Graham, H. Haken, “The quantum-fluctuations of the optical parametric oscillator. I,” Z. Phys. 210, 276–302 (1968).
[CrossRef]

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

1967 (1)

J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

1966 (1)

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev. 146, 187–198 (1966).
[CrossRef]

1965 (1)

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3at optical frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Ashkin, A.

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev. 146, 187–198 (1966).
[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]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), pp. 323–329.

Boyd, G. D.

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

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

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev. 146, 187–198 (1966).
[CrossRef]

Bridenbaugh, P. M.

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

Bryan, D. A.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Byer, R. L.

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

W. J. Kozlovsky, C. D. Nabors, R. C. Eckardt, R. L. Byer, “Monolithic MgO:LiNbO3doubly resonant optical parametric oscillator pumped by a frequency-doubled diode-laser-pumped Nd:YAG laser,” Opt. Lett. 14, 66–68 (1989).
[CrossRef] [PubMed]

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

A. C. Nilsson, E. K. Gustafson, R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron. 25, 767–790 (1989).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).

T. J. Kane, A. C. Nilsson, R. L. Byer, “Frequency stability and offset locking of a laser-diode-pumped Nd:YAG monolithic nonplanar ring oscillator,” Opt. Lett. 12, 175–177 (1987).
[CrossRef] [PubMed]

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

B.-K. Zhou, T. J. Kane, G. J. Dixon, R. L. Byer, “Efficient, frequency-stable laser-diode-pumped Nd:YAG lasers,” Opt. Lett. 10, 62–64 (1985).
[CrossRef] [PubMed]

T. J. Kane, R. L. Byer, “Monolithic, unidirectional, single-mode Nd:YAG ring laser,” Opt. Lett. 10, 65–67 (1985).
[CrossRef] [PubMed]

R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
[CrossRef]

R. L. Byer, “Parametric oscillators and nonlinear materials,” in Nonlinear Optics, P. G. Harper, B. S. Wherrett, eds. (Academic, San Francisco, Calif., 1977), pp. 47–160; R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, part B, pp. 587–702.

Chen, D.

J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Day, T.

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

Dixon, G. J.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Eckardt, R. C.

Edwards, G. J.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Edwin, R. P.

D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
[CrossRef]

Falk, J.

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

Feigelson, R. S.

R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
[CrossRef]

Gerson, R.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3at optical frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).
[CrossRef]

J. A. Giordmaine, R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelley, B. Lax, P. E. Tannenwald, eds. (McGraw-Hill, New York, 1966), pp. 31–42.

Graham, R.

R. Graham, H. Haken, “The quantum-fluctuations of the optical parametric oscillator. I,” Z. Phys. 210, 276–302 (1968).
[CrossRef]

Gustafson, E. K.

A. C. Nilsson, E. K. Gustafson, R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron. 25, 767–790 (1989).
[CrossRef]

W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).

Haken, H.

R. Graham, H. Haken, “The quantum-fluctuations of the optical parametric oscillator. I,” Z. Phys. 210, 276–302 (1968).
[CrossRef]

Halliburton, L. E.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Harris, S. E.

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

Jian, J.

G.-G. Zhong, J. Jian, Z.-K. Wu, in Eleventh International Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, New York, 1980), p. 631.

Kane, T. J.

Kim, Y. S.

Y. S. Kim, R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

Kleinman, D. A.

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

Kozlovsky, W. J.

W. J. Kozlovsky, C. D. Nabors, R. C. Eckardt, R. L. Byer, “Monolithic MgO:LiNbO3doubly resonant optical parametric oscillator pumped by a frequency-doubled diode-laser-pumped Nd:YAG laser,” Opt. Lett. 14, 66–68 (1989).
[CrossRef] [PubMed]

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

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

Lawrence, M.

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Mikulyak, R. M.

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Miller, R. C.

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3at optical frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).
[CrossRef]

J. A. Giordmaine, R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelley, B. Lax, P. E. Tannenwald, eds. (McGraw-Hill, New York, 1966), pp. 31–42.

Nabors, C. D.

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

W. J. Kozlovsky, C. D. Nabors, R. C. Eckardt, R. L. Byer, “Monolithic MgO:LiNbO3doubly resonant optical parametric oscillator pumped by a frequency-doubled diode-laser-pumped Nd:YAG laser,” Opt. Lett. 14, 66–68 (1989).
[CrossRef] [PubMed]

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

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Nash, F. R.

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

Nelson, D. F.

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Nightingale, J. L.

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

Nilsson, A. C.

A. C. Nilsson, E. K. Gustafson, R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron. 25, 767–790 (1989).
[CrossRef]

T. J. Kane, A. C. Nilsson, R. L. Byer, “Frequency stability and offset locking of a laser-diode-pumped Nd:YAG monolithic nonplanar ring oscillator,” Opt. Lett. 12, 175–177 (1987).
[CrossRef] [PubMed]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford, London, 1985), Chap. 7.

Otto, G. N.

J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Pershan, S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Piskarskas, A.

A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
[CrossRef]

Räuber, A.

A. Räuber, “Chemistry and physics of lithium niobate,” in Current Topics in Materials Science, E. Kaldis, ed. (North-Holland, Amsterdam, 1978), Vol. 1, pp. 481–601.

Reade, G. E.

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

Riccius, H. D.

D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
[CrossRef]

Rice, R. R.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Rybicki, A.

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

Sargent, M.

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 435–436.

Silva, W. J.

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

Smil’gyavichyus, V.

A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
[CrossRef]

Smith, D. S.

D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
[CrossRef]

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]

R. G. Smith, “Optical parametric oscillators,” in Advances in Lasers, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976), Vol. 4, pp. 189–307.

Smith, R. T.

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Y. S. Kim, R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

Sohler, W.

H. Suche, W. Sohler, “Integrated optical parametric oscillators,” Optoelectron. Devices Technol. (Tokyo) 4, 1–20 (1989).

Suche, H.

H. Suche, W. Sohler, “Integrated optical parametric oscillators,” Optoelectron. Devices Technol. (Tokyo) 4, 1–20 (1989).

Sweeney, K. L.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Tomaschke, H. E.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Umbrasas, A.

A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
[CrossRef]

Welsh, F. S.

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), pp. 323–329.

Wong, N. C.

Wu, Z.-K.

G.-G. Zhong, J. Jian, Z.-K. Wu, in Eleventh International Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, New York, 1980), p. 631.

Yang, S. T.

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

Yariv, A.

For example, see A. Yariv, Quantum Electronics, 3rd. ed. (Wiley, New York, 1989), Chap. 17; Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), chap. 7.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), chap. 7.

Young, J. F.

R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
[CrossRef]

Zhong, G.-G.

G.-G. Zhong, J. Jian, Z.-K. Wu, in Eleventh International Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, New York, 1980), p. 631.

Zhou, B.-K.

Zook, J. D.

J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Appl. Phys. Lett. (1)

J. D. Zook, D. Chen, G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

IEEE J. Quantum Electron. (5)

A. C. Nilsson, E. K. Gustafson, R. L. Byer, “Eigenpolarization theory of monolithic nonplanar ring oscillators,” IEEE J. Quantum Electron. 25, 767–790 (1989).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

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

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

J. Appl. Phys. (6)

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

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

R. L. Byer, J. F. Young, R. S. Feigelson, “Growth of high-quality LiNbO3crystals from the congruent melt,” J. Appl. Phys. 41, 2320 (1970).
[CrossRef]

F. R. Nash, G. D. Boyd, M. Sargent, P. M. Bridenbaugh, “Effect of optical inhomogeneities on phase matching in nonlinear crystals,” J. Appl. Phys. 41, 2564–2575 (1970).
[CrossRef]

Y. S. Kim, R. T. Smith, “Thermal expansion of lithium tantalate and lithium niobate single crystals,” J. Appl. Phys. 40, 4637–4641 (1969).
[CrossRef]

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

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

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

Opt. Commun. (1)

D. S. Smith, H. D. Riccius, R. P. Edwin, “Refractive indices of lithium niobate,” Opt. Commun. 17, 332–335 (1976); errata, 20, 188 (1977).
[CrossRef]

Opt. Eng. (1)

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138–143 (1985).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

G. J. Edwards, M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–375 (1984).
[CrossRef]

Optoelectron. Devices Technol. (Tokyo) (1)

H. Suche, W. Sohler, “Integrated optical parametric oscillators,” Optoelectron. Devices Technol. (Tokyo) 4, 1–20 (1989).

Phys. Rev. (2)

J. A. Armstrong, N. Bloembergen, J. Ducuing, S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

G. D. Boyd, A. Ashkin, “Theory of parametric oscillator threshold with single-mode optical masers and observation of amplification in LiNbO3,” Phys. Rev. 146, 187–198 (1966).
[CrossRef]

Phys. Rev. Lett. (1)

J. A. Giordmaine, R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3at optical frequencies,” Phys. Rev. Lett. 14, 973–976 (1965).
[CrossRef]

Proc. IEEE (1)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

J. L. Nightingale, W. J. Silva, G. E. Reade, A. Rybicki, W. J. Kozlovsky, R. L. Byer, “Fifty percent conversion efficiency second harmonic generation in magnesium oxide doped lithium niobate,” Proc. Soc. Photo-Opt. Instrum. Eng. 681, 20–24 (1986).

W. J. Kozlovsky, E. K. Gustafson, R. C. Eckardt, R. L. Byer, “OPO performance with a long pulse length, single frequency Nd:YAG laser pump,” Proc. Soc. Photo-Opt. Instrum. Eng. 912, 50–53 (1988).

Sov. J. Quantum Electron. (1)

A. Piskarskas, V. Smil’gyavichyus, A. Umbrasas, “Continuous parametric generation of picosecond light pulses,” Sov. J. Quantum Electron. 18, 155–156 (1988).
[CrossRef]

Z. Phys. (1)

R. Graham, H. Haken, “The quantum-fluctuations of the optical parametric oscillator. I,” Z. Phys. 210, 276–302 (1968).
[CrossRef]

Other (10)

J. A. Giordmaine, R. C. Miller, “Optical parametric oscillation in LiNbO3,” in Physics of Quantum Electronics, P. L. Kelley, B. Lax, P. E. Tannenwald, eds. (McGraw-Hill, New York, 1966), pp. 31–42.

R. G. Smith, “Optical parametric oscillators,” in Advances in Lasers, A. K. Levine, A. J. DeMaria, eds. (Dekker, New York, 1976), Vol. 4, pp. 189–307.

R. L. Byer, “Parametric oscillators and nonlinear materials,” in Nonlinear Optics, P. G. Harper, B. S. Wherrett, eds. (Academic, San Francisco, Calif., 1977), pp. 47–160; R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, part B, pp. 587–702.

For example, see A. Yariv, Quantum Electronics, 3rd. ed. (Wiley, New York, 1989), Chap. 17; Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9.

M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), pp. 323–329.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 435–436.

J. F. Nye, Physical Properties of Crystals (Oxford, London, 1985), Chap. 7.

A. Räuber, “Chemistry and physics of lithium niobate,” in Current Topics in Materials Science, E. Kaldis, ed. (North-Holland, Amsterdam, 1978), Vol. 1, pp. 481–601.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), chap. 7.

G.-G. Zhong, J. Jian, Z.-K. Wu, in Eleventh International Quantum Electronics Conference (Institute of Electrical and Electronics Engineers, New York, 1980), p. 631.

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Figures (19)

Fig. 1
Fig. 1

(a) Schematic representation of optical parametric amplification. Optical parametric oscillators can be formed by the addition of mirrors that are separate from the nonlinear material, as shown in (b). Monolithic oscillators (c) and (d), with highly reflecting coatings (M’s) applied directly to the nonlinear material, offer the advantages of low loss and rigidity that are important in stable, single-frequency DRO operation. Ring oscillators (d) offer the advantages of reduced feedback and improved conversion efficiency over standing-wave oscillators.

Fig. 2
Fig. 2

(a) Typical OPO tuning curve near the degeneracy frequency f0 = fp/2, where fp is the pump frequency. The signal and the idler frequencies are shown for a LiNbO3 OPO as a function of the tuning parameter, in this case temperature. For a fixed value of the tuning parameter, single-pass parametric gain exists in bands that are centered on the phase-matching wavelengths, as shown in (b). DRO’s have the added constraint that the signal and the idler cavity resonances must coincide in satisfying the condition fp = fs + fi, which results in output at cluster frequencies (c). Only two or three clusters, represented by open horizontal bars, are located within the gain bandwidth. Usually one cluster, represented by the longest open bar, dominates.

Fig. 3
Fig. 3

Diagram2 that shows the relationship between the DRO signal and idler resonance frequencies and the conservation-of-energy condition. Signal resonances are plotted as a function of signal frequency ωs on an ordinary linear scale, with frequency increasing from left to right. The idler frequency scale is determined by that of the signal and the relationship ωp = ωs + ωs. In the display of idler resonances, therefore, frequency increases from right to left. A signal–idler pair that has both resonances centered on a vertical line are in coincidence, satisfying ωp = ωs + ωs. In general there will be some frequency mismatch Δω for each mode pair. The frequency mismatch is the frequency shift that is required in order for either signal or idler resonance to produce coincidence. The detail on the left-hand side shows the frequency mismatch Δω for a mode pair and its components Δωs and Δωi, which are the respective frequency displacements from the centers of the signal and the idler cavity resonances to the frequencies most favorable for parametric oscillation. Dispersion is exaggerated in this schematic representation. There are typically hundreds of cavity axial modes between the cluster frequencies for which Δω = 0.

Fig. 4
Fig. 4

Schematic representation of a detailed portion of an idealized tuning curve for a DRO. Oscillation progresses along cluster curves in discontinuous frequency change, a cluster jump, occurs when better phase matching exists on an adjacent cluster curve.

Fig. 5
Fig. 5

Phasor diagrams schematically show amplitude losses as and a and phase shifts ψs and ψi after one round-trip cavity transit for the signal and the idler, respectively. At threshold the increments of electric-field amplitude added by optical parametric amplification, ΔEs and ΔEi must restore the original fields.

Fig. 6
Fig. 6

Comparison of thresholds for DRO’s with differing cavity finesses. Thresholds are calculated as a function of the sum of the cavity-round-trip phase shifts ψ with Eq. (12) for two DRO’s with cavity finesse s = i = 360 and s = i = 960. The shape of the curve does not change, but the width, defined as the region over which threshold is less than twice its minimum value, decreases for higher finesse.

Fig. 7
Fig. 7

Signal–idler resonance diagram similar to Fig. 3, expanded in detail to show the relationships between quantities. The signal and the idler cavity resonances on which oscillation occurs are displaced from the respective cluster frequencies ωs,Cl and ωi,Cl for the general case of nonzero frequency mismatch. The DRO oscillating frequencies ωs,Osc and ωi,Osc divide the frequency mismatch Δω into the components Δωs and Δωi.

Fig. 8
Fig. 8

DRO geometry used for experimental observations.

Fig. 9
Fig. 9

Schematic representation of the setup used for DRO tuning measurements.

Fig. 10
Fig. 10

Oscillograms of cw-pumped DRO output, showing simultaneous output on three cluster curves. The signal displayed is that produced by a photodiode placed after a monochromator with slits adjusted for a 5-nm bandpass. Each of the oscillograms corresponds to the same portion of the ramped voltage applied to the DRO. The change in applied potential is indicated. The oscillograms differ only in the wavelength setting of the monochromator, indicated for the individual traces. The output on the central cluster dominates and is so strong that the oscilloscope trace does not return to the baseline.

Fig. 11
Fig. 11

Observed and calculated tuning for the pulsed-pumped DRO with finesse of 360. The open vertical bars in (a) show the extent of tuning observed as applied potential was ramped from 0 to 1150 V at a constant temperature. The solid curves behind the vertical bars are calculated phase-matching curves for the extreme voltages. Voltage tuning for three temperatures is shown in (b)–(d), where the bold central curves are the calculated phase-matching curves and the dashed curves indicate the limits of the phase-matching bandwidth. The dotted curves are calculated cluster curves, and the filled circles are observed operating points of the DRO. This DRO, which has only moderate finesse, exhibits few jumps between cluster curves as the voltage is ramped. The data are measurements of the applied potential for a limited sampling of output frequencies and do not represent individual mode hops.

Fig. 12
Fig. 12

Observed and calculated tuning for the cw-pumped DRO with finesse of 960. As in Fig. 11, the open bars in (a) indicate the range of tuning as voltage was ramped, in this case between −1150 V and 0, and the solid curves behind the vertical bars are the calculated phase-matching curves for the two extreme voltages. Voltage tuning is shown for three temperatures in (b)–(d). This DRO, which has higher finesse, exhibits a number of frequency jumps between three cluster curves as voltage is tuned.

Fig. 13
Fig. 13

Observed and calculated tuning for the cw-pumped DRO as a function of temperature. The same tuning data that were used in Fig. 12 are used here. A fixed voltage of −200 V was chosen. For the cases in which oscillation on a cluster curve was observed at voltages both higher and lower than this voltage, frequencies were obtained by interpolation and are represented by filled circles. For the cases in which cluster tuning came near but did not reach this voltage, frequencies were obtained by extrapolation and are represented by open circles. The dotted curves are portions of the calculated temperature-dependent cluster curves. The calculated phase-matching curve is the central bold curve, and the dashed curves show the approximate gain-bandwidth limits.

Fig. 14
Fig. 14

Mode-hop spacing in an applied potential as a function of detuning from degeneracy. The dots are data points, and the solid line is calculated from theory.

Fig. 15
Fig. 15

Detailed display of calculated DRO tuning as a function of applied potential for conditions that would produce output similar to that shown in Fig. 10. All calculations are for a fixed temperature of 107.540°C. Detailed calculations of tuning for three cluster curves are shown in (b)–(d). Here the DRO output frequency is indicated by the open horizontal bars. A finesse of 960 is used. The slope of the continuous portions of the detailed tuning curves (b)–(d) is dependent on the relative values of finesse at the signal and the idler frequencies, but in all cases this slope is much less than the slope of the cluster curves.

Fig. 16
Fig. 16

Calculated detailed tuning as a function of temperature. For this calculation temperature is adjusted while other parameters are held constant at values that correspond to a point near the center of Fig. 15(c). Here, also, the slope of the continuous portions of the tuning curve are dependent on the relative values of signal and idler finesse, and this slope is small compared with the slope of the cluster curve.

Fig. 17
Fig. 17

Calculated detailed tuning as a function of pump frequency. For this calculation pump frequency is adjusted while other parameters are held constant at values that correspond to a point near the center of Fig. 15(c). For pump-frequency tuning with equal signal and idler cavity finesse, the slope of the continuous portions of the tuning curve is ~0.5. Because of the scale necessary to display the much greater slope of the cluster curve, the continuous portions of the tuning curve appear to be horizontal.

Fig. 18
Fig. 18

Calculated tuning for varying the voltage and the pump frequency simultaneously so as to maintain Δm = 0 and Δms = 0. The dashed line is the cluster curve of Fig. 17. Tuning limits taken are the points at which Δk = ±π/l in the 1.25-cm-long crystal.

Fig. 19
Fig. 19

Calculated tuning for varying the voltage, the pump frequency, and the temperature simultaneously so as to maintain Δm = 0, Δms = 0, and Δk = 0.

Tables (5)

Tables Icon

Table 1 Derivatives Used to Calculate Tuning of a Monolithic DRO

Tables Icon

Table 2 Derivatives used to Model Tuning of MgO:LiNbO3 Monolithic DRO’sa

Tables Icon

Table 3 Calculated Single-Parameter Continuous Tuning Rates and Parameter Tolerances for Stable Operation of the Finesse = 960 DRO Pumped at 563.6 THz with Signal Frequency 287.44 THz

Tables Icon

Table 4 Calculated Values for Two-Parameter Tuning of a Monolithic MgO:LiNbO3 DRO at fs = 287.44 THz or λs = 1043 nm

Tables Icon

Table 5 Comparison of Measured and Calculated Values for Parametric Fluorescence in MgO:LiNbO3

Equations (88)

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ω p = ω s + ω i .
Δ k = k p - k s - k i = ( n p ω p - n s ω s - n i ω i ) / c ,
Δ ω = Δ ω s + Δ ω i .
E j ( z , t ) = ½ [ E j ( z ) exp i ( k j z - ω j t ) + c . c . ] ,
d E s d z = i κ s E p E i * exp ( i Δ k z ) ,
d E i d z = i κ i E p E s * exp ( i Δ k z ) ,
d E p d z = i κ p E s E i exp ( - i Δ k z ) ,
Δ E s = i κ s E p E i * l sinc ( Δ k l / 2 )
Δ E i = i κ i E p E s * l sinc ( Δ k l / 2 ) .
( 1 - a s ) exp ( i ψ s ) E s + Δ E s = E s
( 1 - a i ) exp ( i ψ i ) E i + Δ E i = E i .
Δ E s = E s ( a s 2 + ψ s 2 ) 1 / 2 exp ( i ϕ s - i γ s )
Δ E i = E i ( a i 2 + ψ i 2 ) 1 / 2 exp ( i ϕ i - i γ i ) ,
ϕ s + ϕ i = γ s + π / 2
ϕ s + ϕ i = γ i + π / 2 ,
ψ s a s = ψ i a i .
ψ = ψ s + ψ i ,
ψ s = a s a s + a i ψ
ψ i = a i a s + a i ψ .
[ ( a s 2 + ψ s 2 ) ( a i 2 + ψ i 2 ) ] 1 / 2 = κ s κ i E p 2 l 2 sinc 2 ( Δ k l / 2 ) = Γ 2 l 2 sinc 2 ( Δ k l / 2 ) .
Γ 2 l 2 = a s a i sinc 2 ( Δ k l / 2 ) [ 1 + ψ 2 ( a s + a i ) 2 ] .
F s π / a s ,             F i π / a i .
Δ ω s = δ ω s ψ s 2 π ,             Δ ω i = δ ω i ψ i 2 π .
Γ 2 l 2 = π 2 F i F s sinc 2 ( Δ k l / 2 ) [ 1 + ( 2 Δ ω F i F s F i δ ω s + F s δ ω i ) 2 ] .
Γ 2 l 2 2 = B sin [ 2 tan - 1 ( sin ψ C + cos ψ ) - ψ ] sin [ tan - 1 ( sin ψ C + cos ψ ) ] sinc 2 ( Δ k l 2 ) - 1 sinc 2 ( Δ k l 2 ) ,
B = R i ( 1 - R s 2 ) R i 2 - R s 2 ,             C = R s R i 1 - R i 2 1 - R s 2 .
m s = 2 l n s / λ s = l n s ω s / ( π c )
m i = 2 l n i / λ i = l n i ω i / ( π c ) ,
m s ω s = l π c ( n s + ω s n s ω s ) = δ ω s - 1
m i ω i = l π c ( n i + ω i n i ω i ) = δ ω i - 1 .
m = m s + m i ,
Δ m = m - ROUND ( m )
Δ m s = m s - ROUND ( m s ) .
Δ k = ( Δ k ω s ) ω p ( ω s - ω s , 0 ) + 1 2 ( 2 Δ k ω s 2 ) ω p ( ω s - ω s , 0 ) 2 + ( Δ k ω p ) ω s ( ω p - ω p , 0 ) + Δ k T ( T - T 0 ) + Δ k V V + Δ k 0 ,
m = ( m m s ) ω p ( ω s - ω s , 0 ) + 1 2 ( 2 m ω s 2 ) ω p ( ω s - ω s , 0 ) 2 + ( m ω p ) ω s ( ω p - ω p , 0 ) + m t ( T - T 0 ) + m V V + m 0 ,
m s = m s m s ( ω s - ω s , 0 ) + 1 2 2 m s ω s 2 ( ω s - ω s , 0 ) 2 + m s T ( T - T 0 ) + m s V V + m s , 0 .
( f ω s ) ω p = f ω s - f ω i ,
( f ω p ) ω s = f ω p + f ω i .
Δ m ( cluster ) = ± 1 = ( m ω s ) ω p Ω S ± + 1 2 ( 2 m ω s 2 ) ω p Ω S ± 2 .
Ω S ± ± ( m ω s ) ω p - 1 = ± δ ω i δ ω s δ ω i - δ ω s ,
Δ ω s ( Gain FWHM ) | 2 π l ( Δ k ω s ) ω p - 1 | .
Δ ω = Δ m s , Cl ( δ ω s - δ ω i ) .
Δ ω s = Δ ω δ ω s F i / ( δ ω s F i + δ ω i F s )
Δ ω i = Δ ω δ ω i F s / ( δ ω s F i + δ ω i F s ) .
ω s , Osc = ω s , Cl - Δ m s , Cl δ ω s + Δ ω s = ω s , Cl - Δ m s , Cl δ ω s δ ω i ( F s + F i ) δ ω s F i + δ ω i F s .
Δ ω ζ = δ ω s m s ζ + δ ω i m i ζ = ( δ ω s - δ ω i ) m s ζ + δ ω i m ζ .
ω s , Osc ζ = ω s δ ω i ω s F i + δ ω i F s ( F i m ζ - ( F s + F i ) m s ζ ) .
Δ ζ Hop spacing = | ( m s , Cl ζ ) - 1 | .
ω s , Cl ζ = - m ζ ( m ω s ) ω p - 1 = - δ ω s δ ω i δ ω i - δ ω s m ζ .
m s , Cl ζ = m s ζ + m s ω s ω s , Cl ζ = m s ζ - δ ω i δ ω i - δ ω s m ζ .
ω s , Hop - ω s , Cl = ± 1 2 δ ω i δ ω s ( F i + F s ) δ ω i F s + δ ω s F i .
Δ ω = ± F i δ ω s + F s δ ω i 2 F i F s .
ω s , Fin - ω s , Cl = ± F s + F i 2 F s F i δ ω s δ ω i δ ω i - δ ω s .
Δ ζ Hop tolerance = ± 1 2 ( m s , c l ζ ) - 1 .
m s , Cl ζ - δ ω 0 ω i - δ ω s m ζ ,
δ ω i - δ ω s 2 δ ω 0 2 2 m s ω s 2 ( ω s - ω 0 ) .
Δ ζ Hop tolerance ± δ ω 0 2 m s ω s 2 ( ω s - ω 0 ) / m ζ .
ψ Fin = ± π ( 1 F i + 1 F s ) .
Δ ζ Fin tolerance ± ½ ( 1 / F i + 1 / F s ) m / ζ .
ω s , Osc ζ = ω s δ ω i δ ω i F s + δ ω s F i ( F i m s ζ - F s m i ζ ) .
m i ζ ( m i ω p ) ω s = m i ω i
m s ζ ( m s ω p ) ω s = 0.
d m d ζ 1 = 0 = ( m ω s ) ω p d ω s d ζ 1 + m ζ 1 + m ζ 2 d ζ 2 d ζ 1 ,
d m s d ζ 1 = 0 = m s ω s d ω s d ζ 1 + m s ζ 1 + m s ζ 2 d ζ 2 d ζ 1 ,
d Δ k d ζ 1 = ( Δ k ω s ) ω p d ω s d ζ 1 + Δ k ζ 1 + Δ k ζ 2 d ζ 2 d ζ 1 .
d Δ k d ω p = 0 = ( Δ k ω s ) ω p d ω s d ω p + ( Δ k ω p ) ω s + Δ k T d T d ω p + Δ k V d V d ω p ,
d m d ω p = 0 = ( m ω s ) ω p d ω s d ω p + ( m ω p ) ω s + m T d T d ω p + m V d V d ω p ,
d m s d ω p = 0 = m s ω s d ω s d ω p + m s ω p + m s T d T d ω p + m s V d V d ω p .
n 2 = A 1 + A 2 + B 1 F λ 2 - ( A 3 - B 2 F ) 2 + B 3 F - A 4 λ 2 ,
F = ( T - T 0 ) ( T + T 0 + 546 ) ,
x 2 n x 2 + y 2 n y 2 + z 2 n z 2 = 1.
( 1 n x 2 + r 1 k E k ) x 2 + ( 1 n y 2 + r 2 k E k ) y 2 + ( 1 n z 2 + r 3 k E k ) z 2 + 2 r 4 k E k y z + 2 r 5 k E k x z + 2 r 6 k E k x y = 1 ,
r i k E k = k = 1 3 r i k E k ,             i = 1 , 6.
( r i k ) = ( 0 - r 22 r 13 0 r 22 r 13 0 0 r 33 0 r 51 0 r 51 0 0 - r 22 0 0 ) .
( 1 n o 2 - r 22 E y ) x 2 + ( 1 n o 2 + r 22 E y ) y 2 + z 2 n e 2 + 2 r 51 E y y z = 1.
n y ( 1 n o 2 + r 22 E y ) - 1 / 2 n o - n o 3 r 22 E y 2
n z n e .
r 22 ( 633 nm ) = 6.8 × 10 - 12 m / V , r 22 ( 1.15 μ m ) = 5.4 × 10 - 12 m / V , r 22 ( 3.39 μ m ) = 3.1 × 10 - 12 m / V .
Δ l l = α ( T - T R ) + β ( T - T R ) 2 ,
α 11 = ( 1.54 × 10 - 5 ) ° C - 1
β 11 = ( 5.3 × 10 - 9 ) ° C - 2 ,
P i = d i j k T j k ,
S j k = d i j k E i .
( d j m ) = ( 0 0 0 0 d 15 - 2 d 22 - d 22 d 22 0 d 15 0 0 d 31 d 31 d 33 0 0 0 ) .
S 11 = d 211 E 2 = d 21 E 2 = - d 22 E y .
Δ k V = ( ω s n s 3 + ω i n i 3 ) r 22 2 c t ,
m V = - l π c t [ ( n s ω s + n i ω i ) d 22 + ( ω s n s 3 + ω i n i 3 ) r 22 2 ] ,
m s V = - l π c t ( n s ω s d 22 + ω s n s 3 r 22 2 ) .

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