Abstract

Optical parametric amplification in type I collinear and one-beam noncritical noncollinear phase-matching (PM) configurations has been investigated. The effects of absorption and walk-off of the interacting beams are fully taken into account, while their divergence, as well as the depletion of the pump, is assumed to be negligible. Numerical results with the organic crystal 3-methyl-4-nitropyridine-l-oxide show that, when the crystal thickness exceeds a certain value, one-beam noncritical noncollinear PM is more efficient than collinear PM owing to the different geometry of the interacting beams. Thus the applications of one-beam noncritical noncollinear type I PM in optical parametric amplification and oscillation experiments are expected to be even more interesting when the beams are focused.

© 1992 Optical Society of America

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  2. R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
    [CrossRef]
  3. See, for example, S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
    [CrossRef]
  4. G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
    [CrossRef]
  5. U. Sukowski and A. Seilmeier, “Intense tunable picosecond pulses generated by parametric amplification in β-BaB2O4,” Appl. Phys. B 50, 541–545 (1990).
    [CrossRef]
  6. S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. QE-15, 415–431 (1979).
    [CrossRef]
  7. R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, pp. 587–702.
  8. R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968).
    [CrossRef]
  9. D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
    [CrossRef]
  10. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  11. E. O. Ammann and P. C. Montgomery, “Threshold calculations for an optical parametric oscillator employing a hemispherical resonator,” J. Appl. Phys. 41, 5270–5274 (1970).
    [CrossRef]
  12. S. X. Dou, D. Josse, and J. Zyss, “Noncritical properties of noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-l-oxide,” J. Opt. Soc. Am. B 8, 1732–1739 (1991).
    [CrossRef]
  13. J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
    [CrossRef]
  14. J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
    [CrossRef]
  15. D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
    [CrossRef]
  16. See, for example, A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
  17. See, for example, G. A. Massey and J. C. Johnson, “Gain limitations in optical parametric amplifiers,” IEEE J. Quantum Electron. QE-15, 201–203 (1979).
    [CrossRef]
  18. S. X. Dou, D. Josse, R. Hierle, and J. Zyss, “Comparison between collinear and noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-1-oxide,” J. Opt. Soc. Am. B 9, 687 (1992).
    [CrossRef]
  19. G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
    [CrossRef]
  20. J. Falk and J. E. Murray, “Single-cavity noncollinear optical parametric oscillation,” Appl. Phys. Lett. 14, 245–247 (1969).
    [CrossRef]
  21. J. E. Bjorkholm, “Efficient optical parametric oscillation using doubly and singly resonant cavities,” Appl. Phys. Lett. 13, 53–56 (1968).
    [CrossRef]
  22. G. D. Boyd and 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]

1992 (1)

1991 (1)

1990 (1)

U. Sukowski and A. Seilmeier, “Intense tunable picosecond pulses generated by parametric amplification in β-BaB2O4,” Appl. Phys. B 50, 541–545 (1990).
[CrossRef]

1988 (1)

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
[CrossRef]

1985 (1)

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

1981 (1)

J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
[CrossRef]

1979 (3)

See, for example, G. A. Massey and J. C. Johnson, “Gain limitations in optical parametric amplifiers,” IEEE J. Quantum Electron. QE-15, 201–203 (1979).
[CrossRef]

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. QE-15, 415–431 (1979).
[CrossRef]

R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
[CrossRef]

1976 (1)

G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
[CrossRef]

1970 (1)

E. O. Ammann and P. C. Montgomery, “Threshold calculations for an optical parametric oscillator employing a hemispherical resonator,” J. Appl. Phys. 41, 5270–5274 (1970).
[CrossRef]

1969 (2)

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

J. Falk and J. E. Murray, “Single-cavity noncollinear optical parametric oscillation,” Appl. Phys. Lett. 14, 245–247 (1969).
[CrossRef]

1968 (4)

J. E. Bjorkholm, “Efficient optical parametric oscillation using doubly and singly resonant cavities,” Appl. Phys. Lett. 13, 53–56 (1968).
[CrossRef]

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968).
[CrossRef]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[CrossRef]

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

1966 (1)

G. D. Boyd and 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)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

1962 (1)

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

Ammann, E. O.

E. O. Ammann and P. C. Montgomery, “Threshold calculations for an optical parametric oscillator employing a hemispherical resonator,” J. Appl. Phys. 41, 5270–5274 (1970).
[CrossRef]

Armstrong, J. A.

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

Ashkin, A.

G. D. Boyd and 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]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

Baumgartner, R. A.

R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm, “Efficient optical parametric oscillation using doubly and singly resonant cavities,” Appl. Phys. Lett. 13, 53–56 (1968).
[CrossRef]

Bloembergen, N.

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

G. D. Boyd and 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]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

Brosnan, S. J.

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. QE-15, 415–431 (1979).
[CrossRef]

Byer, R. L.

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. QE-15, 415–431 (1979).
[CrossRef]

R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
[CrossRef]

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968).
[CrossRef]

R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, pp. 587–702.

Chemla, D. S.

J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
[CrossRef]

Dou, S. X.

Ducuing, J.

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

Dziedzic, J. M.

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

Elliott, R. A.

G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
[CrossRef]

Falk, J.

J. Falk and J. E. Murray, “Single-cavity noncollinear optical parametric oscillation,” Appl. Phys. Lett. 14, 245–247 (1969).
[CrossRef]

Harris, S. E.

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

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968).
[CrossRef]

Hierle, R.

S. X. Dou, D. Josse, R. Hierle, and J. Zyss, “Comparison between collinear and noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-1-oxide,” J. Opt. Soc. Am. B 9, 687 (1992).
[CrossRef]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
[CrossRef]

Hierle, R. B.

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

Johnson, J. C.

See, for example, G. A. Massey and J. C. Johnson, “Gain limitations in optical parametric amplifiers,” IEEE J. Quantum Electron. QE-15, 201–203 (1979).
[CrossRef]

G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
[CrossRef]

Josse, D.

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]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[CrossRef]

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

Ledoux, I.

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
[CrossRef]

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

Massey, G. A.

See, for example, G. A. Massey and J. C. Johnson, “Gain limitations in optical parametric amplifiers,” IEEE J. Quantum Electron. QE-15, 201–203 (1979).
[CrossRef]

G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
[CrossRef]

Montgomery, P. C.

E. O. Ammann and P. C. Montgomery, “Threshold calculations for an optical parametric oscillator employing a hemispherical resonator,” J. Appl. Phys. 41, 5270–5274 (1970).
[CrossRef]

Murray, J. E.

J. Falk and J. E. Murray, “Single-cavity noncollinear optical parametric oscillation,” Appl. Phys. Lett. 14, 245–247 (1969).
[CrossRef]

Nicoud, J. F.

J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
[CrossRef]

Oudar, J. L.

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

Pershan, P. S.

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

Raj, R. K.

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

Seilmeier, A.

U. Sukowski and A. Seilmeier, “Intense tunable picosecond pulses generated by parametric amplification in β-BaB2O4,” Appl. Phys. B 50, 541–545 (1990).
[CrossRef]

Sukowski, U.

U. Sukowski and A. Seilmeier, “Intense tunable picosecond pulses generated by parametric amplification in β-BaB2O4,” Appl. Phys. B 50, 541–545 (1990).
[CrossRef]

Yariv, A.

See, for example, A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

Zyss, J.

S. X. Dou, D. Josse, R. Hierle, and J. Zyss, “Comparison between collinear and noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-1-oxide,” J. Opt. Soc. Am. B 9, 687 (1992).
[CrossRef]

S. X. Dou, D. Josse, and J. Zyss, “Noncritical properties of noncollinear phase-matched second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-l-oxide,” J. Opt. Soc. Am. B 8, 1732–1739 (1991).
[CrossRef]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
[CrossRef]

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
[CrossRef]

Appl. Phys. B (1)

U. Sukowski and A. Seilmeier, “Intense tunable picosecond pulses generated by parametric amplification in β-BaB2O4,” Appl. Phys. B 50, 541–545 (1990).
[CrossRef]

Appl. Phys. Lett. (3)

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, “Highly efficient second-harmonic generation of picosecond pulses at 1.32 μm in 3-methyl-4-nitropyridine-1-oxide,” Appl. Phys. Lett. 53, 2251–2253 (1988).
[CrossRef]

J. Falk and J. E. Murray, “Single-cavity noncollinear optical parametric oscillation,” Appl. Phys. Lett. 14, 245–247 (1969).
[CrossRef]

J. E. Bjorkholm, “Efficient optical parametric oscillation using doubly and singly resonant cavities,” Appl. Phys. Lett. 13, 53–56 (1968).
[CrossRef]

IEEE J. Quantum Electron. (5)

See, for example, G. A. Massey and J. C. Johnson, “Gain limitations in optical parametric amplifiers,” IEEE J. Quantum Electron. QE-15, 201–203 (1979).
[CrossRef]

J. Zyss, I. Ledoux, R. B. Hierle, R. K. Raj, and J. L. Oudar, “Optical parametric interactions in 3-methyl-4-nitropyridine-1-oxide (POM) single crystals,” IEEE J. Quantum Electron. QE-21, 1286–1295 (1985).
[CrossRef]

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. QE-15, 415–431 (1979).
[CrossRef]

R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
[CrossRef]

G. A. Massey, J. C. Johnson, and R. A. Elliott, “Generation of frequency-controlled nanosecond and picosecond optical pulses by high-gain parametric amplification,” IEEE J. Quantum Electron. QE-12, 143–147 (1976).
[CrossRef]

J. Appl. Phys. (2)

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

E. O. Ammann and P. C. Montgomery, “Threshold calculations for an optical parametric oscillator employing a hemispherical resonator,” J. Appl. Phys. 41, 5270–5274 (1970).
[CrossRef]

J. Chem. Phys. (1)

J. Zyss, D. S. Chemla, and J. F. Nicoud, “Demonstration of efficient nonlinear optical crystals with vanishing molecular adipole moment: second harmonic generation in 3-methyl-4-nitropyridine-l-oxide,” J. Chem. Phys. 74, 4800–4811 (1981).
[CrossRef]

J. Opt. Soc. Am. B (2)

Phys. Rev. (5)

G. D. Boyd, A. Ashkin, J. M. Dziedzic, and D. A. Kleinman, “Second-harmonic generation of light with double refraction,” Phys. Rev. 137, 1305–1320 (1965).
[CrossRef]

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

R. L. Byer and S. E. Harris, “Power and bandwidth of spontaneous parametric emission,” Phys. Rev. 168, 1064–1068 (1968).
[CrossRef]

D. A. Kleinman, “Theory of optical parametric noise,” Phys. Rev. 174, 1027–1041 (1968).
[CrossRef]

G. D. Boyd and 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]

Proc. IEEE (1)

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

Other (2)

R. L. Byer, “Optical parametric oscillators,” in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, pp. 587–702.

See, for example, A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).

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Figures (6)

Fig. 1
Fig. 1

Propagation of the interacting beams in collinear OPA. Ks is the wave vector of the signal beam.

Fig. 2
Fig. 2

Propagation of the interacting beams in OBNC noncollinear OPA. θs (θi) is the noncollinear PM angle between the signal (idler) and the pump.

Fig. 3
Fig. 3

Logarithm of gain as a function of the crystal length l at different beam radii of the signal and the pump in collinear and OBNC noncollinear OPA. The pump intensity at its beam axis is (a) 50 MW/cm2 and (b) 100 MW/cm2.

Fig. 4
Fig. 4

Logarithm of gain as a function of the crystal length l with different crystal parameters in collinear and OBNC noncollinear OPA. α and ρ refer to absorption and walk-off, respectively. α ≠ 0 and ρ ≠ 0 means that they take the actual values for POM.

Fig. 5
Fig. 5

Power distribution of the output signal and idler beams along the directon of x. D(xl) is defined as, where xl = 0 corresponds to the beam center of the output signal at the output surface of the crystal when there is no pump, i.e., xl = xl − (x0 + l tan ρ) = xl − (1/2)l tan ρ in the collinear case and xl = xl in the OBNC noncollinear case, (a) Collinear OPA; (b) noncollinear OPA. In the collinear case the power distribution of the idler is the same as that of the signal. In the noncollinear case the relative peak value of the curve for the idler with respect to that of the curve for the signal corresponds to the calculated result.

Fig. 6
Fig. 6

Logarithm of gain as a function of the beam radii ω0 of the pump and the signal at fixed pump power in collinear and OBNC noncollinear OPA. The pump power corresponds to an intensity of 50 MW/cm2 at beam axis when ω0 = 1.0 mm.

Tables (1)

Tables Icon

Table 1 Parameters of POM Related to OPA in Type I Collinear and OBNC Noncollinear PM Configurationsa

Equations (26)

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

d A s d z = α 2 cos ρ s A s j κ / ( cos 2 ρ s ) A i * A p ,
d A i * d z = α 2 cos ρ i A i * + j κ / ( cos 2 ρ i ) A s A p ,
κ = ( 1 / 2 ) 0 d eff ( μ 0 ω s ω i ω p 0 n s n i n p ) 1 / 2 ,
A p ( x l , y l , z ) = A p ( 0 , 0 , 0 ) × exp { [ x l ( l z ) ( tan ρ ) ] 2 + y l 2 ω 0 p 2 α p z 2 } ,
A s ( x l , y l , w ) = A s ( x l , y l , z ) exp ( α z / 2 cos ρ ) ,
A i ( x l , y l , w ) = A i ( x l , y l , z ) exp ( α z / 2 cos ρ ) ,
d w = A p ( x l , y l , z ) d z
d A s d w = j ( κ cos 2 ρ ) A i * ,
d A i * d w = + j ( κ cos 2 ρ ) A s .
A s ( x l , y l , w ) = A s ( x l , y l , 0 ) cosh [ ( κ / cos 2 ρ ) w ] ,
A i * ( x l , y l , w ) = j A s ( x l , y l , 0 ) sinh [ ( κ / cos 2 ρ ) w ] ,
A s ( x l , y l , l ) = A s ( x l , y l , 0 ) cosh [ ( κ / cos 2 ρ ) w ( x l , y l , l ) ] × exp ( α l / 2 cos ρ ) ,
A l * ( x l , y l , l ) = j A s ( x l , y l , 0 ) sinh [ ( κ / cos 2 ρ ) w ( x l , y l , l ) ] × exp ( α l / 2 cos ρ ) ,
w ( x l , y l , l ) = 0 l A p ( x l , y l , z ) d z .
A s ( x l , y l , 0 ) = A s ( x 0 , 0 , 0 ) × exp { [ x l ( l tan ρ + x 0 ) ] 2 + y l 2 ω 0 s 2 } ,
P s ( l ) = + + 1 2 ( 0 μ 0 ) 1 / 2 ω s | A s ( x l , y l , l ) | 2 d x l d y l = P s ( 0 ) π ω 0 s 2 / 2 exp ( α l cos ρ ) + + | A s ( x l , y l , 0 ) A s ( x 0 , 0 , 0 ) | 2 × cosh 2 [ Γ 0 L ( x l , y l , l ) ] d x l d y l ,
P s ( 0 ) = ( 1 2 π ω 0 s 2 ) 1 2 ( 0 μ 0 ) 1 / 2 ω s | A s ( x 0 , 0 , 0 ) | 2 , Γ 0 = ( κ cos 2 ρ ) A p ( 0 , 0 , 0 ) = ( κ cos 2 ρ ) [ I p ( 0 , 0 , 0 ) ( 1 / 2 ) ( 0 / μ 0 ) 1 / 2 ω p ] 1 / 2 , L ( x l , y l , l ) = w ( x l , y l , l ) A p ( 0 , 0 , 0 ) ,
L ( x l , y l , l ) = ( 2 / α p ) [ 1 exp ( α p l / 2 ) ] ,
P s ( l ) = P s ( 0 ) cosh 2 ( Γ 0 l ) ,
d A s d z = ( α s 2 ) A s j ( κ cos ρ s ) A i * A p ,
d A i * d z = ( α i 2 cos β ) A i * + j ( κ cos ρ i cos β ) A s A p ,
A i * ( x , y , z ) = + j ( κ cos ρ i cos β ) × 0 z exp [ α i ( z u ) 2 cos β ] A s ( x , y , u ) A p ( x , y , u ) d u ,
A s ( x l , y l , l ) A s ( x , y , l ) = ( κ 2 cos ρ s cos ρ i cos β ) × 0 l exp [ α s ( l z ) 2 ] A p ( x , y , z ) × 0 z exp [ α i ( z u ) 2 cos β ] × A s ( x , y , u ) A p ( x , y , u ) d u d z .
Γ 0 = κ ( cos ρ s cos ρ i cos β ) 1 / 2 A p ( 0 , 0 , 0 ) = κ ( cos ρ s cos ρ i cos β ) 1 / 2 [ I p ( 0 , 0 , 0 ) ( 1 / 2 ) ( 0 / μ 0 ) 1 / 2 ω p ] 1 / 2 ,
l s = 2 π 1 / 2 ω 0 / tan ρ .
d eff ( d 14 POM )

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