Abstract

We use a plane-wave analysis to examine a singly resonant, cavity-enhanced, frequency doubler containing an intracavity sum-frequency interaction that frequency sums the resonant fundamental with the second harmonic to produce the third harmonic of the resonant field. We derive expressions for the steady-state performance of the device. We determine the input coupler intensity reflectivity and the ratio of nonlinear drives between the second-harmonic generation (SHG) and sum-frequency generation (SFG) stages for optimum third-harmonic conversion efficiency. We also examine the optimum SHG interaction length under conditions of limited total interaction length. We find that numerical simulations modeling three spatial dimensions can be closely approximated by appropriately scaled plane-wave results. As an example, we consider frequency tripling of a 350-mW, 1319-nm, cw laser in two consecutive nonlinear gratings in periodically poled lithium niobate and find third-harmonic power-conversion efficiency of 85.3% when first-order quasi-phase-matching (QPM) is used for the SFG process and 51.0% when third-order SFG QPM is used. We also consider frequency tripling of a 20-W, 1064-nm, continuous-wave mode-locked laser in two lithium triborate crystals and find a time-averaged third-harmonic power-conversion efficiency of 56.0% from modeling three spatial dimensions.

© 1999 Optical Society of America

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  1. A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
    [CrossRef]
  2. W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12, 1014–1016 (1987).
    [CrossRef] [PubMed]
  3. W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
    [CrossRef]
  4. G. T. Maker and A. I. Ferguson, “Efficient frequency doubling of a diode-laser-pumped Nd:YAG laser using an external resonant cavity,” Opt. Commun. 76, 369–375 (1990).
    [CrossRef]
  5. D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
    [CrossRef]
  6. E. S. Polzik and H. J. Kimble, “Frequency doubling with KNbO3 in an external cavity,” Opt. Lett. 16, 1400–1402 (1991).
    [CrossRef] [PubMed]
  7. Z. Y. Ou and H. J. Kimble, “Enhanced conversion efficiency for harmonic generation with double resonance,” Opt. Lett. 18, 1053–1055 (1993).
    [CrossRef] [PubMed]
  8. K. Fiedler, S. Schiller, R. Paschotta, P. Kürz, and J. Mlynek, “Highly efficient frequency doubling with a doubly resonant monolithic total-internal-reflection ring resonator,” Opt. Lett. 18, 1786–1788 (1993).
    [CrossRef] [PubMed]
  9. M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
    [CrossRef]
  10. J. Knittel and A. H. Kung, “39.5% conversion of low-power Q-switched Nd:YAG laser radiation of 266 nm by use of a resonant ring cavity,” Opt. Lett. 22, 366–368 (1997).
    [CrossRef] [PubMed]
  11. J. Knittel and A. H. Kung, “Fourth harmonic generation in a resonant ring cavity,” IEEE J. Quantum Electron. QE-33, 2021–2028 (1997).
    [CrossRef]
  12. Notation and properties of elliptic integrals and Jacobi elliptic functions taken from M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chaps. 16–17, pp. 576–626.
  13. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  14. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  15. G. T. Moore and K. Koch, “Efficient frequency conversion at low power using periodic refocusing,” J. Opt. Soc. Am. B (to be published).
  16. G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
    [CrossRef]
  17. G. T. Moore and K. Koch, “The tandem optical parametric oscillator,” IEEE J. Quantum Electron. QE-32, 2085–2094 (1996).
    [CrossRef]
  18. G. T. Moore and K. Koch, “Optical parametric oscillation with detuned intracavity sum-frequency generation,” IEEE J. Quantum Electron. QE-29, 2334–2341 (1993).
    [CrossRef]
  19. K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
    [CrossRef]
  20. G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
    [CrossRef]
  21. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
    [CrossRef]
  22. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  23. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
    [CrossRef]
  24. R. Asby, “Optical-mode interaction in nonlinear media,” Phys. Rev. 187, 1062–1069 (1969).
    [CrossRef]
  25. R. Asby, “Theory of optical parametric amplification from a focused Gaussian beam,” Phys. Rev. B 2, 4273–4282 (1970).
    [CrossRef]
  26. K. Drühl, “Dispersion-induced generation of higher order transversal modes in singly-resonant optical parametric oscillators,” Opt. Commun. 145, 5–8 (1998).
    [CrossRef]

1998 (1)

K. Drühl, “Dispersion-induced generation of higher order transversal modes in singly-resonant optical parametric oscillators,” Opt. Commun. 145, 5–8 (1998).
[CrossRef]

1997 (4)

J. Knittel and A. H. Kung, “Fourth harmonic generation in a resonant ring cavity,” IEEE J. Quantum Electron. QE-33, 2021–2028 (1997).
[CrossRef]

K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
[CrossRef]

J. Knittel and A. H. Kung, “39.5% conversion of low-power Q-switched Nd:YAG laser radiation of 266 nm by use of a resonant ring cavity,” Opt. Lett. 22, 366–368 (1997).
[CrossRef] [PubMed]

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
[CrossRef]

1996 (1)

G. T. Moore and K. Koch, “The tandem optical parametric oscillator,” IEEE J. Quantum Electron. QE-32, 2085–2094 (1996).
[CrossRef]

1995 (2)

G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
[CrossRef]

1993 (4)

G. T. Moore and K. Koch, “Optical parametric oscillation with detuned intracavity sum-frequency generation,” IEEE J. Quantum Electron. QE-29, 2334–2341 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

K. Fiedler, S. Schiller, R. Paschotta, P. Kürz, and J. Mlynek, “Highly efficient frequency doubling with a doubly resonant monolithic total-internal-reflection ring resonator,” Opt. Lett. 18, 1786–1788 (1993).
[CrossRef] [PubMed]

Z. Y. Ou and H. J. Kimble, “Enhanced conversion efficiency for harmonic generation with double resonance,” Opt. Lett. 18, 1053–1055 (1993).
[CrossRef] [PubMed]

1992 (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1991 (2)

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

E. S. Polzik and H. J. Kimble, “Frequency doubling with KNbO3 in an external cavity,” Opt. Lett. 16, 1400–1402 (1991).
[CrossRef] [PubMed]

1990 (1)

G. T. Maker and A. I. Ferguson, “Efficient frequency doubling of a diode-laser-pumped Nd:YAG laser using an external resonant cavity,” Opt. Commun. 76, 369–375 (1990).
[CrossRef]

1988 (1)

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
[CrossRef]

1987 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

1970 (1)

R. Asby, “Theory of optical parametric amplification from a focused Gaussian beam,” Phys. Rev. B 2, 4273–4282 (1970).
[CrossRef]

1969 (1)

R. Asby, “Optical-mode interaction in nonlinear media,” Phys. Rev. 187, 1062–1069 (1969).
[CrossRef]

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[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, 109–123 (1966).
[CrossRef]

1964 (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Asby, R.

R. Asby, “Theory of optical parametric amplification from a focused Gaussian beam,” Phys. Rev. B 2, 4273–4282 (1970).
[CrossRef]

R. Asby, “Optical-mode interaction in nonlinear media,” Phys. Rev. 187, 1062–1069 (1969).
[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, 109–123 (1966).
[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]

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

Byer, R. L.

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12, 1014–1016 (1987).
[CrossRef] [PubMed]

Cheung, E. C.

G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
[CrossRef]

Dearborn, M. E.

K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Drühl, K.

K. Drühl, “Dispersion-induced generation of higher order transversal modes in singly-resonant optical parametric oscillators,” Opt. Commun. 145, 5–8 (1998).
[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, 109–123 (1966).
[CrossRef]

Fejer, M. M.

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Ferguson, A. I.

G. T. Maker and A. I. Ferguson, “Efficient frequency doubling of a diode-laser-pumped Nd:YAG laser using an external resonant cavity,” Opt. Commun. 76, 369–375 (1990).
[CrossRef]

Fiedler, K.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Hayasaka, K.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Imajo, H.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Jundt, D. H.

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
[CrossRef]

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Kimble, H. J.

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]

Knittel, J.

J. Knittel and A. H. Kung, “39.5% conversion of low-power Q-switched Nd:YAG laser radiation of 266 nm by use of a resonant ring cavity,” Opt. Lett. 22, 366–368 (1997).
[CrossRef] [PubMed]

J. Knittel and A. H. Kung, “Fourth harmonic generation in a resonant ring cavity,” IEEE J. Quantum Electron. QE-33, 2021–2028 (1997).
[CrossRef]

Koch, K.

K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
[CrossRef]

G. T. Moore and K. Koch, “The tandem optical parametric oscillator,” IEEE J. Quantum Electron. QE-32, 2085–2094 (1996).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
[CrossRef]

G. T. Moore and K. Koch, “Optical parametric oscillation with detuned intracavity sum-frequency generation,” IEEE J. Quantum Electron. QE-29, 2334–2341 (1993).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Kozlovsky, W. J.

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12, 1014–1016 (1987).
[CrossRef] [PubMed]

Kung, A. H.

J. Knittel and A. H. Kung, “39.5% conversion of low-power Q-switched Nd:YAG laser radiation of 266 nm by use of a resonant ring cavity,” Opt. Lett. 22, 366–368 (1997).
[CrossRef] [PubMed]

J. Knittel and A. H. Kung, “Fourth harmonic generation in a resonant ring cavity,” IEEE J. Quantum Electron. QE-33, 2021–2028 (1997).
[CrossRef]

Kürz, P.

Magel, G. A.

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

Maker, G. T.

G. T. Maker and A. I. Ferguson, “Efficient frequency doubling of a diode-laser-pumped Nd:YAG laser using an external resonant cavity,” Opt. Commun. 76, 369–375 (1990).
[CrossRef]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Mlynek, J.

Moore, G. T.

K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
[CrossRef]

G. T. Moore and K. Koch, “The tandem optical parametric oscillator,” IEEE J. Quantum Electron. QE-32, 2085–2094 (1996).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
[CrossRef]

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
[CrossRef]

G. T. Moore and K. Koch, “Optical parametric oscillation with detuned intracavity sum-frequency generation,” IEEE J. Quantum Electron. QE-29, 2334–2341 (1993).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Nabors, C. D.

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Second-harmonic generation of a continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity,” Opt. Lett. 12, 1014–1016 (1987).
[CrossRef] [PubMed]

Ou, Z. Y.

Paschotta, R.

Polzik, E. S.

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Schiller, S.

Urabe, S.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Watanabe, M.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B: Photophys. Laser Chem. 31, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, “Periodically poled LiNbO3 for high-efficiency second-harmonic generation,” Appl. Phys. Lett. 59, 2657–2659 (1991).
[CrossRef]

IEEE J. Quantum Electron. (7)

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. QE-2, 109–123 (1966).
[CrossRef]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient 2nd harmonic-generation of a diode-laser-pumped cw Nd-YAG laser using monolithic MgO-LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. QE-24, 913–919 (1988).
[CrossRef]

J. Knittel and A. H. Kung, “Fourth harmonic generation in a resonant ring cavity,” IEEE J. Quantum Electron. QE-33, 2021–2028 (1997).
[CrossRef]

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

G. T. Moore and K. Koch, “The tandem optical parametric oscillator,” IEEE J. Quantum Electron. QE-32, 2085–2094 (1996).
[CrossRef]

G. T. Moore and K. Koch, “Optical parametric oscillation with detuned intracavity sum-frequency generation,” IEEE J. Quantum Electron. QE-29, 2334–2341 (1993).
[CrossRef]

K. Koch, G. T. Moore, and M. E. Dearborn, “Raman oscillation with intracavity second-harmonic generation,” IEEE J. Quantum Electron. QE-33, 1743–1748 (1997).
[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]

Opt. Commun. (4)

G. T. Moore, K. Koch, and E. C. Cheung, “Optical parametric oscillation with intracavity second-harmonic generation,” Opt. Commun. 113, 463–470 (1995).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, “Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity,” Opt. Commun. 97, 225–227 (1993).
[CrossRef]

G. T. Maker and A. I. Ferguson, “Efficient frequency doubling of a diode-laser-pumped Nd:YAG laser using an external resonant cavity,” Opt. Commun. 76, 369–375 (1990).
[CrossRef]

K. Drühl, “Dispersion-induced generation of higher order transversal modes in singly-resonant optical parametric oscillators,” Opt. Commun. 145, 5–8 (1998).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. (1)

R. Asby, “Optical-mode interaction in nonlinear media,” Phys. Rev. 187, 1062–1069 (1969).
[CrossRef]

Phys. Rev. B (1)

R. Asby, “Theory of optical parametric amplification from a focused Gaussian beam,” Phys. Rev. B 2, 4273–4282 (1970).
[CrossRef]

Proc. SPIE (1)

G. T. Moore, K. Koch, and E. C. Cheung, “Theory of multi-stage intracavity frequency conversion in optical parametric oscillators,” in Solid State Lasers and Nonlinear Crystals, G. J. Quarles, L. Esterowitz, and L. K. Cheng, eds., Proc. SPIE 2379, 84–94 (1995).
[CrossRef]

Other (2)

G. T. Moore and K. Koch, “Efficient frequency conversion at low power using periodic refocusing,” J. Opt. Soc. Am. B (to be published).

Notation and properties of elliptic integrals and Jacobi elliptic functions taken from M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chaps. 16–17, pp. 576–626.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of a singly resonant cavity-enhanced frequency tripler. The cavity resonates the fundamental frequency ω1. The cavity has an input coupler with intensity reflectivity R and intracavity attenuation R0. The SHG and the SFG interactions are followed by a reflector that outcouples all the second- and third-harmonic waves, ω2=2ω1 and ω3=3ω1, respectively.

Fig. 2
Fig. 2

Ratio of nonlinear couplings gb/ga as a function of SHG nonlinear coupling ga. The solid curves represent the ratios for complete second-harmonic depletion in the SFG interaction and unconstrained SHG. The dashed curves are the optimum ratios for frequency tripling 1319 nm in PPLN with first- and third-order SFG QPM and with the total interaction length limited to 5 cm. The curves are calculated assuming that the input-coupler intensity reflectivity R varies to maintain impedance matching of the cavity and that R0=99%.

Fig. 3
Fig. 3

Contours of third-harmonic power-conversion efficiency in the (ga, gb) plane. The calculated efficiency assumes the optimum input coupler was used at each point in the plane R=R0TaTb and R0=99%. Contour curves are drawn for η3=10%90% in steps of 10%. The thick solid curve is where CSHD occurs. The thick dashed curve represents the best device performance for unconstrained SHG interaction length. The straight dashed device lines correspond to constraints on the total interaction length for the resonant tripler discussed in Section 5. The device lines with first-order SFG QPM have three times the slope of those with third-order SFG QPM. Optimum design points lie between the two thick curves.

Fig. 4
Fig. 4

Contours of optimum input-coupler intensity reflectivity R=R0TaTb in the (ga, gb) plane. We assume R0=99%. Contour curves are drawn for R=98%77% in steps of 1%. The heavy solid curve is where CSHD occurs. The thick dashed curve represents the best device performance for unconstrained SHG interaction length. The straight dashed device lines correspond to constraints on the total interaction length for the resonant tripler discussed in Section 5.

Fig. 5
Fig. 5

Nonlinear couplings ga and gb as a function of SHG interaction length La under the condition La+Lb=5 cm. The gb values shown should be one-third as large for third-order SFG QPM.

Fig. 6
Fig. 6

Contours of third-harmonic power-conversion efficiency as a function of SHG and SFG nonlinear couplings ga and gb for fixed input coupler R=92%. The intracavity attenuation is assumed to be R0=99%. Contour curves are plotted from 3η3=80%10% in steps of 10%. The solid line through the origin represents the operating line of the device as the incident pump power is varied. The dashed line represents the device line for choosing the optimum SHG interaction length.

Fig. 7
Fig. 7

Calculated dependence of PPLN resonant tripler steady-state third-harmonic power-conversion efficiency 3η3 on SHG grating length, with the total interaction length La+Lb=5 cm kept constant. Fixed parameters are R=92% for first-order SFG QPM and R=97% for third-order SFG QPM, R0=99%, and P1=350 mW.

Fig. 8
Fig. 8

Power dependence of third-harmonic power-conversion efficiency of PPLN resonant tripler for La=1.89 cm and R=92% (first-order SFG QPM) and La=0.85 cm and R=97% (third-order SFG QPM). The intracavity attenuation is R0=99%.

Fig. 9
Fig. 9

Dependence of PPLN resonant tripler third-harmonic power-conversion efficiency 3η3 on input-coupler reflectivity R. The input pump power is P1=350 mW, whereas R0 and La have the same values as in Fig. 7.

Fig. 10
Fig. 10

Dependence of PPLN resonant-tripler third-harmonic power-conversion efficiency 3η3 on intracavity attenuation R0. The input pump power is P1=350 mW, whereas R and La have the same values as in Fig. 7.

Fig. 11
Fig. 11

Third-harmonic power-conversion efficiency 3η3 as a function of SHG phase-mismatch Qa for first- and third-order SFG QPM. The circles and squares represent results from three-dimensional numerical simulations for first- and third-order SFG QPM, respectively, and the curves are obtained from the MPW model.

Fig. 12
Fig. 12

Third-harmonic power-conversion efficiency 3η3 as a function of SFG phase mismatch Qb for first- and third-order SFG QPM. The circles and squares represent results from three-dimensional numerical simulations for first- and third-order SFG QPM, respectively, and the curves are obtained from the MPW model.

Fig. 13
Fig. 13

Second- and third-harmonic powers P2 (open squares) and P3 (filled circles) generated by the LBO resonant tripler in steady state were calculated with three-dimensional simulations for a series of pump powers. The upper curve (open circles) shows the input pump power P1(t), assuming a Gaussian time dependence 2.6 kW exp(-t2) typical of a cw mode-locked laser. The higher-harmonic power is fitted by the curves P2(t)=0.314 kW exp(-0.7t2-0.04t4) and P3(t)=1.716 kW exp(-1.2t2-0.2t4). Also shown are the power Pl(t) (filled squares) going into cavity loss, fitted by Pl(t)=0.57 kW exp(-0.55t2-0.04t4), and the power Pr(t) (diamonds) leaving the exit port of the input coupler.

Equations (44)

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ρ2(z2)=12ρ1(z1)tanh(Λa),
ρ1(z2)=ρ1(z1)sech(Λa),
κa=dacna12ω13na21/2
Ca=(1/2)ρ12+ρ22=(1/2)ρ12(z1)
ρ3(z3)=[ρ1(z2)ρ2(z2)mb]1/2sn(Λb|mb),
ρ2(z3)=[ρ22(z2)-ρ1(z2)ρ2(z2)mbsn2(Λb|mb)]1/2,
ρ1(z3)=[ρ12(z2)-ρ1(z2)ρ2(z2)mbsn2(Λb|mb)]1/2,
κb=dbc6ω13nb3nb2nb11/2,
D1=ρ12+ρ32=ρ12(z2),
D2=ρ22+ρ32=ρ22(z2),
mb=2sinh2(Λa),0Ta13,
mb=sinh2(Λa)2,13Ta1,
Ta=sech2(Λa)
ρ1(z1)exp[iϕ1(z1)]=(1-R)1/2ρ1(z0)+Rρ1(zf)exp[iϕ1(zf)].
ρ1(zf)exp[iϕ1(zf)]=R0ρ1(z1)×exp(ik1Lc)exp[iϕ1(z1)],
ρ1(z1)exp[iϕ1(z1)]=(1-R)1/21-(RR0)1/2 exp(iψ)ρ1(z0),
Qρ12(z1)ρ12(z0)=(1-R)|1-(RR0)1/2 exp(iψ)|2.
ρ1(zf)exp[iϕ1(zf)]=R0ρ1(z2)exp[ik1Lc+iϕ1(z2)].
ρ1(z2)=ρ1(z1)Ta.
ρ1(z1)exp[iϕ1(z1)]=(1-R)1/2ρ1(z0)1-(RR0Ta)1/2 exp(iψ),
Q=(1-R)|1-(RR0Ta)1/2 exp(iψ)|2,
ga2=2Λa2Q.
η2aρ22(z2)/ρ12(z0)=(1-Ta)2Q.
ρ1(zf)exp[iϕ1(zf)]=R0ρ1(z3)exp[ik1Lc+iϕ1(z3)].
ρ1(z3)=ρ1(z1)TaTb,
Tb=1-n sn2(Λb|mb)
n=1,0Ta,
n=mb,Ta1.
ρ1(z1)exp[iϕ1(z1)]=(1-R)1/2ρ1(z0)1-(RR0TaTb)1/2 exp(iψ),
Q=1-R|1-(RR0TaTb)1/2 exp(iψ)|2,
η3=Ta(1-Tb)Q.
η2b=1-(3-2Tb)Ta2Q.
ga2=2Λa2Q.
gb2=mbΛb2nTaQ.
D2D<=sn2(Λb|mb)=nmb.
Λb=K(mb),
gbgaCSHD=mb2nTa1/2 K(mb)Λa.
ρ12(z1, n)=|(1-R)1/2ρ1(z0, n)+(RR0)1/2ρ1(z3, n-1)×exp{i[k1Lc+ϕ1(z3, n-1)]}|2.
I=8π z1z2dz exp(iqz)S(z),
ga=gˆa1+δa21/2 1Laz1z2dz exp(iqaz)1-iz/Z,
gb=gˆb1+δb21/2 1Lbz2z3dz exp(iqbz)1-iz/Z.
dσ1dz=i43π1/2 κbw1exp(iqbz)1-iz/Zσ3σ2*,
dσ2dz=i43π1/2 κbw1exp(iqbz)1-iz/Zσ3σ1*,
dσ3dz=i43π1/2 κbw1exp(-iqbz)1+iz/Zσ1σ2.

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