Abstract

We revisit both theoretically and experimentally the study of a two-crystal optical parametric oscillator (OPO) for which the signal and the idler beams are totally and exclusively output coupled after the first and the second crystals, respectively. This geometry, referred as cross-resonant OPO, is useful for applications that require the production of two beams that can be independently adjusted. A theoretical analysis is carried out by use of a plane-wave semianalytical rate-equation approach that completely includes pump depletion and reconstruction effects. We also report on an experimental investigation of a 1.064μm pump-pulsed KTP cross-resonant OPO whose performance is compared with that of a singly resonant OPO with a similar oscillation threshold. To illustrate the practical advantages of such a configuration, we performed difference-frequency generation in a CdSe crystal by mixing the signal and idler beams of the cross-resonant OPO to produce mid-infrared radiation over the 812μm range.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Giordmaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (1965).
    [Crossref]
  2. M. H. Dunn and M. Ebrahimzadeh, "Parametric generation of tunable light from continuous-wave to femtosecond pulses," Science 286, 1513-1517 (1999).
    [Crossref] [PubMed]
  3. D. R. Guyer and D. D. Lowenthal, "Novel cavity design for a high efficiency, high energy near infrared beta-BaB2O4 parametric generator," in Nonlinear Optics, R.A.Fisher and J.F.Reintjes, eds., Proc. SPIE 1220, 41-44 (1990).
  4. D. D. Lowenthal, "2-micron optical parametric sources," in Solid State Lasers IV, G.J.Quarles and M.A.WoodallII, eds., Proc. SPIE 1864, 190-199 (1993).
  5. G. T. Moore and K. Koch, "Efficient high-gain two-crystal optical parametric oscillator," IEEE J. Quantum Electron. 31, 761-768 (1995).
    [Crossref]
  6. D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
    [Crossref]
  7. D. Andreou, "16 µm tunable source using parametric processes in nonlinear crystals," Opt. Commun. 23, 37-43 (1977).
    [Crossref]
  8. P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (1979).
    [Crossref]
  9. S. Haidar and H. Ito, "Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR," Opt. Commun. 171, 171-176 (1999).
    [Crossref]
  10. A. Godard and E. Rosencher, "Energy yield of pulsed optical parametric oscillators: a rate-equation analysis," IEEE J. Quantum Electron. 40, 1527-1531 (2004).
    [Crossref]
  11. A. V. Smith, W. J. Alford, T. D. Raymond, and M. S. Bowers, "Comparison of a numerical model with measured performance of a seeded nanosecond KTP optical parametric oscillator," J. Opt. Soc. Am. B 12, 2253-2267 (1995).
    [Crossref]
  12. E. Rosencher and C. Fabre, "Oscillation characteristics of continuous-wave optical parametric oscillators: beyond the mean-field approximation," J. Opt. Soc. Am. B 19, 1107-1116 (2002).
    [Crossref]
  13. S. J. Brosnan and R. L. Byer, "Optical parametric oscillator threshold and linewidth studies," IEEE J. Quantum Electron. QE-15, 415-431 (1979).
    [Crossref]
  14. C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
    [Crossref]
  15. S. Schiller, K. Schneider, and J. Mlynek, "Theory of an optical parametric oscillator with resonant pump and signal," J. Opt. Soc. Am. B 16, 1512-1524 (1999).
    [Crossref]
  16. A. Fix and R. Wallenstein, "Spectral properties of pulsed nanosecond optical parametric oscillators: experimental investigation and numerical analysis," J. Opt. Soc. Am. B 13, 2484-2497 (1996).
    [Crossref]
  17. G. Arisholm, "Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators," J. Opt. Soc. Am. B 16, 117-127 (1999).
    [Crossref]
  18. A. V. Smith, J. G. Russell, and M. S. Bowers, "Numerical models of broad-bandwidth nanosecond optical parametric oscillators," J. Opt. Soc. Am. B 16, 609-619 (1999).
    [Crossref]
  19. C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
    [Crossref]
  20. A. V. Smith, D. J. Armstrong, M. C. Phillips, J. G. Russell, and G. Arisholm, "Degenerate type I nanosecond optical parametric oscillators," J. Opt. Soc. Am. B 20, 2319-2328 (2003).
    [Crossref]
  21. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  22. 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]
  23. R. A. Baumgartner and R. L. Byer, "Optical parametric amplification," IEEE J. Quantum Electron. QE-15, 432-444 (1979).
    [Crossref]
  24. N. P. Barnes, D. J. Gettemy, J. R. Hietanen, and R. A. Iannini, "Parametric amplification in AgGaSe2," Appl. Opt. 28, 5162-5168 (1989).
    [Crossref] [PubMed]

2004 (1)

A. Godard and E. Rosencher, "Energy yield of pulsed optical parametric oscillators: a rate-equation analysis," IEEE J. Quantum Electron. 40, 1527-1531 (2004).
[Crossref]

2003 (1)

2002 (1)

2001 (1)

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

1999 (5)

1998 (1)

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

1996 (1)

1995 (2)

1989 (1)

1979 (3)

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

P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (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]

1977 (1)

D. Andreou, "16 µm tunable source using parametric processes in nonlinear crystals," Opt. Commun. 23, 37-43 (1977).
[Crossref]

1974 (1)

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

1965 (1)

J. A. Giordmaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (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]

Alford, W. J.

Andreou, D.

D. Andreou, "16 µm tunable source using parametric processes in nonlinear crystals," Opt. Commun. 23, 37-43 (1977).
[Crossref]

Arisholm, G.

Armstrong, D. J.

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]

Barnes, N. P.

Baumgartner, R. A.

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

Bowers, M. S.

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]

Cohadon, P. F.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Comte, M.

P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (1979).
[Crossref]

Drag, C.

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

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]

Dunn, M. H.

M. H. Dunn and M. Ebrahimzadeh, "Parametric generation of tunable light from continuous-wave to femtosecond pulses," Science 286, 1513-1517 (1999).
[Crossref] [PubMed]

Ebrahimzadeh, M.

M. H. Dunn and M. Ebrahimzadeh, "Parametric generation of tunable light from continuous-wave to femtosecond pulses," Science 286, 1513-1517 (1999).
[Crossref] [PubMed]

Fabre, C.

E. Rosencher and C. Fabre, "Oscillation characteristics of continuous-wave optical parametric oscillators: beyond the mean-field approximation," J. Opt. Soc. Am. B 19, 1107-1116 (2002).
[Crossref]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Fix, A.

Gatti, A.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Gettemy, D. J.

Giordmaine, J. A.

J. A. Giordmaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (1965).
[Crossref]

Godard, A.

A. Godard and E. Rosencher, "Energy yield of pulsed optical parametric oscillators: a rate-equation analysis," IEEE J. Quantum Electron. 40, 1527-1531 (2004).
[Crossref]

Guyer, D. R.

D. R. Guyer and D. D. Lowenthal, "Novel cavity design for a high efficiency, high energy near infrared beta-BaB2O4 parametric generator," in Nonlinear Optics, R.A.Fisher and J.F.Reintjes, eds., Proc. SPIE 1220, 41-44 (1990).

Haidar, S.

S. Haidar and H. Ito, "Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR," Opt. Commun. 171, 171-176 (1999).
[Crossref]

Hanna, D. C.

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

Hietanen, J. R.

Iannini, R. A.

Ito, H.

S. Haidar and H. Ito, "Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR," Opt. Commun. 171, 171-176 (1999).
[Crossref]

Jeandron, M.

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

Koch, K.

G. T. Moore and K. Koch, "Efficient high-gain two-crystal optical parametric oscillator," IEEE J. Quantum Electron. 31, 761-768 (1995).
[Crossref]

Kupecek, P.

P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (1979).
[Crossref]

Le Person, H.

P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (1979).
[Crossref]

Lefebvre, M.

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

Lowenthal, D. D.

D. R. Guyer and D. D. Lowenthal, "Novel cavity design for a high efficiency, high energy near infrared beta-BaB2O4 parametric generator," in Nonlinear Optics, R.A.Fisher and J.F.Reintjes, eds., Proc. SPIE 1220, 41-44 (1990).

D. D. Lowenthal, "2-micron optical parametric sources," in Solid State Lasers IV, G.J.Quarles and M.A.WoodallII, eds., Proc. SPIE 1864, 190-199 (1993).

Lugiato, L.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Luther-Davies, B.

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

Marte, M. A.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Miller, R. C.

J. A. Giordmaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (1965).
[Crossref]

Mlynek, J.

Moore, G. T.

G. T. Moore and K. Koch, "Efficient high-gain two-crystal optical parametric oscillator," IEEE J. Quantum Electron. 31, 761-768 (1995).
[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]

Phillips, M. C.

Raymond, T. D.

Ribet, I.

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

Ritsch, H.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Rosencher, E.

A. Godard and E. Rosencher, "Energy yield of pulsed optical parametric oscillators: a rate-equation analysis," IEEE J. Quantum Electron. 40, 1527-1531 (2004).
[Crossref]

E. Rosencher and C. Fabre, "Oscillation characteristics of continuous-wave optical parametric oscillators: beyond the mean-field approximation," J. Opt. Soc. Am. B 19, 1107-1116 (2002).
[Crossref]

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

Russell, J. G.

Schiller, S.

Schneider, K.

Schwob, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Smith, A. V.

Smith, R. C.

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

Wallenstein, R.

Wyatt, R.

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (2)

C. Drag, I. Ribet, M. Jeandron, M. Lefebvre, and E. Rosencher, "Temporal behavior of a high repetition rate infrared optical parametric oscillator based on periodically poled materials," Appl. Phys. B 73, 195-200 (2001).
[Crossref]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, "Transverse effects and mode couplings in OPOs," Appl. Phys. B 66, 685-699 (1998).
[Crossref]

Appl. Phys. Lett. (1)

D. C. Hanna, B. Luther-Davies, R. C. Smith, and R. Wyatt, "CdSe down-converter tuned from 9.5 to 24 µm," Appl. Phys. Lett. 25, 127-172 (1974).
[Crossref]

IEEE J. Quantum Electron. (4)

A. Godard and E. Rosencher, "Energy yield of pulsed optical parametric oscillators: a rate-equation analysis," IEEE J. Quantum Electron. 40, 1527-1531 (2004).
[Crossref]

G. T. Moore and K. Koch, "Efficient high-gain two-crystal optical parametric oscillator," IEEE J. Quantum Electron. 31, 761-768 (1995).
[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]

Infrared Phys. (1)

P. Kupecek, H. Le Person, and M. Comte, "A multipurpose efficient tunable infrared coherent source with tuning range from 0.8 to 25 µm and peak powers in the range 50-20 kW," Infrared Phys. 19, 263-271 (1979).
[Crossref]

J. Opt. Soc. Am. B (7)

Opt. Commun. (2)

S. Haidar and H. Ito, "Injection-seeded optical parametric oscillator for efficient difference frequency generation in mid-IR," Opt. Commun. 171, 171-176 (1999).
[Crossref]

D. Andreou, "16 µm tunable source using parametric processes in nonlinear crystals," Opt. Commun. 23, 37-43 (1977).
[Crossref]

Phys. Rev. (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]

Phys. Rev. Lett. (1)

J. A. Giordmaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (1965).
[Crossref]

Science (1)

M. H. Dunn and M. Ebrahimzadeh, "Parametric generation of tunable light from continuous-wave to femtosecond pulses," Science 286, 1513-1517 (1999).
[Crossref] [PubMed]

Other (3)

D. R. Guyer and D. D. Lowenthal, "Novel cavity design for a high efficiency, high energy near infrared beta-BaB2O4 parametric generator," in Nonlinear Optics, R.A.Fisher and J.F.Reintjes, eds., Proc. SPIE 1220, 41-44 (1990).

D. D. Lowenthal, "2-micron optical parametric sources," in Solid State Lasers IV, G.J.Quarles and M.A.WoodallII, eds., Proc. SPIE 1864, 190-199 (1993).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Cited By

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

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Schematic diagrams of (a) the cross-resonant OPO cavity and (b) the power axial distribution of signal and idler, with the notation used in this paper.

Fig. 2
Fig. 2

Schematic diagram of the singly resonant OPO with the notation used in this paper.

Fig. 3
Fig. 3

Signal output and depleted pump of an ideal CRO ( R = 1 ) and a SRO with 50% output coupler ( R sro = 0.5 ) as functions of input pump power in CW operation. The intensities are normalized relative to the threshold power.

Fig. 4
Fig. 4

Spatial distribution of intracavity photon flux normalized to threshold power for (a), (c), (e) an ideal CRO ( R = 1 ) and (b), (d), (f) a 50% output coupler SRO ( R sro = 0.5 ) . Values of normalized input pump power X are shown. The axial position is normalized to crystal length L.

Fig. 5
Fig. 5

Temporal profiles of input pump, depleted-pump, output signal, and output idler pulses for a Gaussian input pump pulse. The FWHM duration of the incoming pulse is N = 15 in normalized units for (a), (c), (f) the ideal CRO ( R = 1 ) and (e), (h) the so-called long-cavity SRO with a a 50% output coupler ( R sro = 0.5 ) . This corresponds to a duration of N = 60 for (b), (d), (g) the so-called short-cavity SRO with a a 50% output coupler ( R sro = 0.5 ) . Power is expressed in terms of photons normalized to the CW threshold power. Various peak powers are considered: (a), (b) X peak = 1.9 ; (c)–(e) X peak = 3.2 ; (f)–(h) X peak = 5 .

Fig. 6
Fig. 6

Signal output of an ideal CRO ( R = 1 ) and of so-called short- and long-cavity SRO’s with a 50% output coupler ( R sro = 0.5 ) as a function of input pump power in pulsed operation. The intensities are normalized relative to the CW threshold power and expressed in terms of photon numbers. The FWHM duration of the incoming Gaussian pulse is N = 15 in normalized units for the CRO and the long-cavity SRO, which corresponds to N = 60 for the short-cavity SRO.

Fig. 7
Fig. 7

Total output energy as a function of input pump energy for (a) the cross-resonant OPO and (b) the 25 mm singly resonant OPO cavity. Insets, temporal profiles of input pump, depleted pump, and OPO output.

Fig. 8
Fig. 8

(a) Transverse profile of the emitted beam. (b) Long-term stability of the CRO and its laser pump.

Fig. 9
Fig. 9

(a) DFG and (b) OPA setups.

Fig. 10
Fig. 10

Temporal profiles of (a) the 1.97 μm signal wave (before and after depletion), (b) the 2.43 μ m idler wave (before and after amplification), and (c) the generated 12 μ m difference-frequency wave, normalized to the incoming signal’s intensity.

Fig. 11
Fig. 11

(a) DFG energy as a function of total incoming energy, measurements, and theoretical calculations in the general and undepleted cases. (b) Parametric gain at 2.34 μ m versus pump energy at 1.97 μ m for the CdSe nonlinear crystal; measurements and theoretical calculations.

Equations (68)

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

A m ( z ) = u m ( z ) exp [ i φ m ( z ) ]
E m ( z ) = ( ω m n m ) 1 2 A m ( z ) exp ( i k m z ) ,
d d z u s ( z ) = κ u i ( z ) u p ( z ) ,
d d z u i ( z ) = κ u s ( z ) u p ( z ) ,
d d z u p ( z ) = κ u s ( z ) u i ( z ) ,
κ = χ ( 2 ) 2 c ( ω s ω i ω p n s n i n p ) 1 2 ,
p s 1 = p s 0 cosh 2 ( κ L p in ) ,
p i 1 = p s 0 sinh 2 ( κ L p in ) ,
p s 3 = R sinh 4 ( κ L p in ) p s 0 ,
p i 3 = R sinh 2 ( κ L p in ) cosh 2 ( κ L p in ) p s 0 ,
p th cw = [ sinh 1 ( 1 R ) κ L ] 2 .
p th , sro cw = [ cosh 1 ( 1 R sro ) κ L ] 2 .
τ d d t p s ( t ) p s 0 ( n + 1 ) p s 0 ( n ) = { R 2 sinh 4 [ sinh 1 ( 1 R ) p in p th cw ] 1 } p s 0 ( n ) ,
τ cro = τ R 2 sinh 4 [ sinh 1 ( 1 R ) p in p th cw ] 1 .
τ sro = τ R sro cosh 2 [ cosh 1 ( 1 R sro ) p in p th , sro cw ] 1 .
τ sro τ cro = 2 cosh 2 [ cosh 1 ( 2 ) p in p th cw ] .
Δ ϕ = 2 m π ,
Δ ϕ = ω s c ( n s L + L ) ω i c ( n i L + L ) + θ ,
ω s 0 ( n s L + L ) ω i 0 ( n i L + L ) + θ c = 2 m π c ,
( ω s 0 + Δ ω ) ( n s L + L ) ( ω i 0 Δ ω ) ( n i L + L ) + θ c = 2 ( m + 1 ) π c .
Δ ω = 2 π c ( n s + n i ) L + 2 L .
p s 1 = p s 0 cn 2 [ i κ L p in ( p s 0 p in ) ] ,
p i 1 = p s 0 sn 2 [ i κ L p in ( p s 0 p in ) ] ,
p p 1 = p in + p s 0 sn 2 [ i κ L p in ( p s 0 p in ) ] ,
a 0 x d t [ ( a 2 t 2 ) ( b 2 t 2 ) ] 1 2 = sn 1 ( x b b 2 a 2 ) ,
p s 3 = R H ( p in , p s 0 ) p s 0 sn 2 { i κ L [ p in p s 0 H ( p in , p s 0 ) ] 1 2 R H ( p in , p s 0 ) p s 0 p in p s 0 H ( p in , p s 0 ) } ,
p i 3 = R H ( p in , p s 0 ) p s 0 cn 2 { i κ L [ p in p s 0 H ( p in , p s 0 ) ] 1 2 R H ( p in , p s 0 ) p s 0 p in p s 0 H ( p in , p s 0 ) } ,
p p 3 = p in H ( p in , p s 0 ) p s 0 + R H ( p in , p s 0 ) p s 0 sn 2 { i κ L [ p in p s 0 H ( p in , p s 0 ) ] 1 2 R H ( p in , p s 0 ) p s 0 p in p s 0 H ( p in , p s 0 ) } ,
H ( p in , p s 0 ) = sn 2 ( i κ L p in p s 0 p in ) .
p s 0 ( n + 1 ) = R 2 H [ p in ( n ) , p s 0 ( n ) ] p s 0 ( n ) sn 2 ( i κ L { p in ( n ) p s 0 ( n ) H [ p in ( n ) , p s 0 ( n ) ] } 1 2 R H [ p in ( n ) , p s 0 ( n ) ] p s 0 ( n ) p in ( n ) p s 0 ( n ) H [ p in ( n ) , p s 0 ( n ) ] ) .
H ( p in , p s 0 ) sn 2 { i κ L [ p in p s 0 H ( p in , p s 0 ) ] 1 2 R H ( p in , p s 0 ) p s 0 p in p s 0 H ( p in , p s 0 ) } = 1 R 2 .
H ( X , Y ) sn 2 { i sinh 1 ( 1 R ) [ X H ( X , Y ) Y ] 1 2 R H ( X , Y ) Y X H ( X , Y ) Y } = 1 R 2 ,
H ( X , Y ) = sn 2 [ i sinh 1 ( 1 R ) X Y X ] .
Y out = Y [ 1 + H ( X , Y ) ] .
Z out = R H ( X , Y ) Y cn 2 { i sinh 1 ( 1 R ) [ X H ( X , Y ) Y ] 1 2 R H ( X , Y ) Y X H ( X , Y ) Y } ,
X out = X H ( X , Y ) Y ( 1 R sn 2 { i sinh 1 ( 1 R ) [ X H ( X , Y ) Y ] 1 2 R H ( X , Y ) Y X H ( X , Y ) Y } ) .
Z out = R Y out + ( 1 R 2 ) Y R ,
X out = X Y out ( 1 R ) Y R .
Y ( n + 1 ) Y ( n ) = R 2 H [ X ( n ) , Y ( n ) ] Y ( n ) sn 2 ( i sinh 1 ( 1 R ) { X ( n ) Y ( n ) H [ X ( n ) , Y ( n ) ] } 1 2 R H [ X ( n ) , Y ( n ) ] Y ( n ) X ( n ) Y ( n ) H [ X ( n ) , Y ( n ) ] ) Y ( n ) τ d Y d t ,
d Y d T + Y = R 2 Y F ( X , Y ) ,
F ( X , Y ) = H ( X , Y ) sn 2 { i sinh 1 ( 1 R ) [ X Y H [ X , Y ] ] 1 2 R H [ X , Y ] Y X Y H [ X , Y ] } ,
d Y sro d T + ( 1 R sro ) Y sro = R sro Y sro F sro ( X sro , Y sro ) ,
F sro ( X sro , Y sro ) = sn 2 [ i cosh 1 ( 1 R sro ) X sro Y sro X sro ] .
E dfg = ω dfg ω i E i { 0 ψ ( ρ , t ) sn 2 [ i Γ ( ρ , t ) L ω s w i E i E s ] 2 π ρ d ρ } d t ,
ψ ( ρ , t ) = 4 ln 2 π 3 2 w 2 τ exp ( 4 ln 2 t 2 τ 2 ) exp ( 2 ρ 2 w 2 ) ,
Γ ( ρ , t ) = [ 2 Z 0 ω dfg ω i d eff 2 c 2 n s n i n dfg E s ψ ( ρ , t ) ] 1 2 .
E dfg undep = 2 Z 0 ω dfg 2 d eff 2 c 2 n s n i n dfg L 2 E s E i 2 ln 2 π 3 2 w 2 τ .
G = [ 0 ψ ( ρ , t ) cosh 2 [ Γ ( ρ , t ) L ] 2 π ρ d ρ ] d t .
sinh ( κ 1 L 1 p th cw ) sinh ( κ 2 L 2 p th cw ) = 1 R .
sinh ( 2 1 + γ κ L p th cw ) sinh ( 2 γ 1 + γ κ L p th cw ) = 1 R .
d d γ [ sinh ( 2 1 + γ κ L p th cw ) sinh ( 2 γ 1 + γ κ L p th cw ) ] = 2 κ L p th cw ( 1 + γ ) 2 sinh ( 2 κ L p th cw 1 γ 1 + γ ) .
d d z A s ( z ) = i κ A i * ( z ) A p ( z ) ,
d d z A i ( z ) = i κ A s * ( z ) A p ( z ) ,
E i 1 = i n s ω i n i ω s sinh ( A p 0 κ L ) A s 0 * exp ( i n i ω i c L ) .
A s 2 = 0 ,
A i 2 = i R n s ω i n i ω s sinh ( A p 0 κ L ) A s 0 * exp [ i ω i c ( n i L + L 12 ) + i θ i ] ,
A p 2 = A p 0 exp [ i ω p c ( n p L + L 12 ) + i θ p ] = A p 0 exp ( i θ p ) ,
E s 3 = R sinh 2 ( A p 0 κ L ) A s 0 exp [ i ( n s ω s c n i ω i c ) L i ω i c L 12 i ( θ i + ϕ p ) ] .
Δ ϕ = ( n s ω s c n i ω i c ) L + ω s c L 30 ω i c L 12 + θ ,
θ = θ s θ i ϕ p ,
Δ ϕ = ω s c ( n s L + L ) ω i c ( n i L + L ) + θ .
cn 2 [ i cosh 1 ( 1 R sro ) X sro Y sro X sro ] = 1 R sro ,
Y out , sro = ( 1 R sro ) Y sro cn 2 [ i cosh 1 ( 1 R sro ) X sro Y sro X sro ] ,
Z out , sro = Y sro sn 2 [ i cosh 1 ( 1 R sro ) X sro Y sro X sro ] ,
X out , sro = X sro + Y sro sn 2 [ i cosh 1 ( 1 R sro ) X sro Y sro X sro ] ,
Y out , sro = ( 1 R sro ) Y sro R sro ,
Z out , sro = ( 1 R sro ) Y sro R sro ,
X out , sro = X sro ( 1 R sro ) Y sro R sro .

Metrics