Abstract

We present a model of quasi-phase-matched continuous-wave optical parametric oscillators that accounts for self-induced heating of the photorefractive crystal and modal interaction through pump depletion. The model allows the temperature and therefore the refractive index of the nonlinear medium to vary in the radial and longitudinal dimensions as a result of local absorption of the optical power. We consider the effect of this nonuniform index on single-mode and multimode operation. For a single signal–idler pair we observe thermal lensing, bulk tuning, and modal distortion. For multiple pairs of signal and idler we demonstrate and discuss other phenomena, including spatially dependent modal competition.

© 2002 Optical Society of America

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  1. B. A. Richman, K. W. Aniolek, T. J. Kulp, and S. E. Bisson, “Continuously tunable, single-longitudinal-mode, pulsed mid-infrared optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 17, 1233–1239 (2000).
    [CrossRef]
  2. F. K. Hopkins, “Military laser applications: providing focus to nonlinear optics R & D,” Opt. Photon. News, February, 1998, pp. 32–38.
  3. Y. X. Fan and R. L. Byer, “Progress in optical parametric oscillators,” in New Lasers for Analytical and Industrial Chemistry, A. Bernhardt, ed., Proc. SPIE 461, 27–32 (1984).
    [CrossRef]
  4. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
    [CrossRef]
  5. N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. 24, 1750–1752 (1999).
    [CrossRef]
  6. P. E. Powers, T. J. Kulp, and S. E. Bisson, “Continuous tuning of a continuous-wave periodically poled lithium niobate optical parametric oscillator by use of a fan-out grating design,” Opt. Lett. 23, 159–161 (1998).
    [CrossRef]
  7. L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, and R. L. Byer, “Quasi-phase-matched 1.064-μm-pumped optical parametric oscillator in bulk periodically poled LiNbO3,” Opt. Lett. 20, 52–54 (1995).
    [CrossRef] [PubMed]
  8. V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
    [CrossRef]
  9. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “Continuous-wave singly resonant optical parametric oscillator based on periodically poled LiNbO3,” Opt. Lett. 21, 713–715 (1996).
    [CrossRef] [PubMed]
  10. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1997).
    [CrossRef]
  11. W. R. Bosenberg, J. I. Alexander, L. E. Myers, and R. W. Wallace, “2.5-W, continuous-wave, 629-nm solid-state laser source,” Opt. Lett. 23, 207–209 (1998).
    [CrossRef]
  12. D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34, 1356–1366 (1998).
    [CrossRef]
  13. M. A. Dreger and J. K. McIver, “Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion,” J. Opt. Soc. Am. B 7, 776–784 (1990).
    [CrossRef]
  14. S. Severini, C. Sibilia, and M. Bertolotti, “Transverse effects in a parametric down-conversion process in three dimensions,” J. Opt. Soc. Am. B 17, 580–585 (2000).
    [CrossRef]
  15. P. Kerkoc, S. Horinouchi, K. Sasaki, Y. Nagae, and D. Pugh, “Thermal effects on second-harmonic generation in biaxial molecular crystals,” J. Opt. Soc. Am. B 16, 1686–1691 (1999).
    [CrossRef]
  16. G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rosanov, ed., Proc. SPIE 3685, 86–97 (1999).
  17. S. E. Bisson, Sandia National Laboratories, 7011 East Ave., MS 9051, Livermore, Calif. (personal communication, 2000).
  18. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, “Progress in quasi-phasematched optical parametric oscillators using periodically poled LiNbO3,” in Nonlinear Frequency Generation and Conversion, 2700, 216–226 (1996).
  19. L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
    [CrossRef]
  20. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  21. 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]
  22. 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]
  23. G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14, 2543–2549 (1997).
    [CrossRef]
  24. M. D. Feit and J. J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
    [CrossRef] [PubMed]
  25. L. Yu, M. C. Huang, M. Z. Chen, W. Z. Chen, W. D. Huang, and Z. Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23, 409–411 (1998).
    [CrossRef]
  26. R. O. Moore, “A study of optical devices with parametric gain,” Ph.D. dissertation (Northwestern University, Evanston, Ill., 2001).
  27. A. V. Smith, R. J. Gehr, and M. S. Bowers, “Numerical models of broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 609–619 (1999).
    [CrossRef]
  28. Almaz Optics, Inc., “Lithium niobate, LiNbO3,” http://www.almazoptics.com/homepage/LiNbO3.htm.
  29. S. Longhi, “Spatio-temporal instabilities and threshold condition in a broad-area optical parametric oscillator,” Opt. Commun. 153, 90–94 (1998).
    [CrossRef]
  30. C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
    [CrossRef]

2000

1999

1998

1997

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14, 2543–2549 (1997).
[CrossRef]

C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
[CrossRef]

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

1996

1995

1990

1984

Y. X. Fan and R. L. Byer, “Progress in optical parametric oscillators,” in New Lasers for Analytical and Industrial Chemistry, A. Bernhardt, ed., Proc. SPIE 461, 27–32 (1984).
[CrossRef]

1978

Alexander, J. I.

Alford, W. J.

Aniolek, K. W.

Arisholm, G.

G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rosanov, ed., Proc. SPIE 3685, 86–97 (1999).

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14, 2543–2549 (1997).
[CrossRef]

Bertolotti, M.

Bisson, S. E.

Bosenberg, W. R.

Bowers, M. S.

Byer, R. L.

Chen, M. Z.

Chen, W. Z.

Cohadon, P. F.

C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
[CrossRef]

Dominic, V.

Dreger, M. A.

Drobshoff, A.

Eckardt, R. C.

Fabre, C.

C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
[CrossRef]

Fan, Y. X.

Y. X. Fan and R. L. Byer, “Progress in optical parametric oscillators,” in New Lasers for Analytical and Industrial Chemistry, A. Bernhardt, ed., Proc. SPIE 461, 27–32 (1984).
[CrossRef]

Feit, M. D.

Fejer, M. M.

Fix, A.

Fleck, J. J. A.

Gehr, R. J.

Hanna, D. C.

V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
[CrossRef]

Horinouchi, S.

Huang, M. C.

Huang, W. D.

Kerkoc, P.

Kulp, T. J.

Longhi, S.

S. Longhi, “Spatio-temporal instabilities and threshold condition in a broad-area optical parametric oscillator,” Opt. Commun. 153, 90–94 (1998).
[CrossRef]

Lowenthal, D. D.

D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34, 1356–1366 (1998).
[CrossRef]

McIver, J. K.

Miller, G. D.

Missey, M.

Myers, L. E.

Nagae, Y.

O’Brien, N.

Pierce, J. W.

Powers, P.

Powers, P. E.

Pruneri, V.

V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
[CrossRef]

Pugh, D.

Raymond, T. D.

Richman, B. A.

Russell, P. S.

V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
[CrossRef]

Sasaki, K.

Schepler, K. L.

Schwob, C.

C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
[CrossRef]

Severini, S.

Sibilia, C.

Smith, A. V.

Wallace, R. W.

Wallenstein, R.

Webjorn, J.

V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
[CrossRef]

Yu, L.

Zhu, Z. Z.

Appl. Opt.

Appl. Phys. Lett.

V. Pruneri, J. Webjorn, P. S. Russell, and D. C. Hanna, “532 nm pumped optical parametric oscillator in bulk periodically poled lithium-niobate,” Appl. Phys. Lett. 67, 2126–2128 (1995).
[CrossRef]

IEEE J. Quantum Electron.

D. D. Lowenthal, “CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption,” IEEE J. Quantum Electron. 34, 1356–1366 (1998).
[CrossRef]

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663–1672 (1997).
[CrossRef]

J. Opt. Soc. Am. B

S. Severini, C. Sibilia, and M. Bertolotti, “Transverse effects in a parametric down-conversion process in three dimensions,” J. Opt. Soc. Am. B 17, 580–585 (2000).
[CrossRef]

M. A. Dreger and J. K. McIver, “Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion,” J. Opt. Soc. Am. B 7, 776–784 (1990).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

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]

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]

B. A. Richman, K. W. Aniolek, T. J. Kulp, and S. E. Bisson, “Continuously tunable, single-longitudinal-mode, pulsed mid-infrared optical parametric oscillator based on periodically poled lithium niobate,” J. Opt. Soc. Am. B 17, 1233–1239 (2000).
[CrossRef]

G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14, 2543–2549 (1997).
[CrossRef]

A. V. Smith, R. J. Gehr, and M. S. Bowers, “Numerical models of broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 609–619 (1999).
[CrossRef]

P. Kerkoc, S. Horinouchi, K. Sasaki, Y. Nagae, and D. Pugh, “Thermal effects on second-harmonic generation in biaxial molecular crystals,” J. Opt. Soc. Am. B 16, 1686–1691 (1999).
[CrossRef]

Opt. Commun.

S. Longhi, “Spatio-temporal instabilities and threshold condition in a broad-area optical parametric oscillator,” Opt. Commun. 153, 90–94 (1998).
[CrossRef]

Opt. Lett.

Proc. SPIE

G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rosanov, ed., Proc. SPIE 3685, 86–97 (1999).

Y. X. Fan and R. L. Byer, “Progress in optical parametric oscillators,” in New Lasers for Analytical and Industrial Chemistry, A. Bernhardt, ed., Proc. SPIE 461, 27–32 (1984).
[CrossRef]

Quantum Semiclassic. Opt.

C. Fabre, P. F. Cohadon, and C. Schwob, “CW optical parametric oscillators: single mode operation and frequency tuning properties,” Quantum Semiclassic. Opt. 9, 165–172 (1997).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

R. O. Moore, “A study of optical devices with parametric gain,” Ph.D. dissertation (Northwestern University, Evanston, Ill., 2001).

Almaz Optics, Inc., “Lithium niobate, LiNbO3,” http://www.almazoptics.com/homepage/LiNbO3.htm.

F. K. Hopkins, “Military laser applications: providing focus to nonlinear optics R & D,” Opt. Photon. News, February, 1998, pp. 32–38.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1997).
[CrossRef]

S. E. Bisson, Sandia National Laboratories, 7011 East Ave., MS 9051, Livermore, Calif. (personal communication, 2000).

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, “Progress in quasi-phasematched optical parametric oscillators using periodically poled LiNbO3,” in Nonlinear Frequency Generation and Conversion, 2700, 216–226 (1996).

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Figures (13)

Fig. 1
Fig. 1

SRO with linear cavity. Dashed arrow indicates the option of seeded or unseeded signal.

Fig. 2
Fig. 2

Flow chart and schematic of the field evolution and temperature deposit–diffusion algorithm.

Fig. 3
Fig. 3

Signal field run to steady state, with self-induced heating.

Fig. 4
Fig. 4

Steady-state temperature in crystal with a single signal–idler pair.

Fig. 5
Fig. 5

Tuning curve of signal output power versus signal wavelength, without (solid curve) and with (dashed curve) a self-induced nonuniform temperature profile. Input pump power, 13 W.

Fig. 6
Fig. 6

Output signal (squares) and idler (filled circles) power versus input pump power, without (solid curves) and with (dashed curves) a self-induced nonuniform temperature profile. Signal wavelength, 1.57 µm.

Fig. 7
Fig. 7

Longitudinal (z) and radial (r) variation in the crystal temperature.

Fig. 8
Fig. 8

Thermal lensing experienced by a signal and a pump passing through a crystal with a nonuniform temperature profile. Shown are the beam radii for the signal with a uniform temperature profile (dotted curve) and with a nonuniform temperature profile (solid curve) and for the pump with a uniform temperature profile (dashed curve) and with a nonuniform temperature profile (dashed–dotted curve). Nonlinear mixing was turned off in these runs.

Fig. 9
Fig. 9

Two signal beams, at 1.570 µm (top) and 1.576 µm (bottom), with no heating effects included. Note that, in the absence of temperature effects, the beams reach steady state very quickly.

Fig. 10
Fig. 10

Two signal beams, at 1.570 µm (top) and 1.576 µm (bottom), with heating effects included.

Fig. 11
Fig. 11

Transient temperature profile (at t=0.2 ms) accompanying Fig. 10.

Fig. 12
Fig. 12

Two signals separated by the free spectral range of an etalon (wavelengths, 1.570 and 1.569 µm). The first signal is perfectly phase matched at zero initial temperature buildup.

Fig. 13
Fig. 13

Two signals separated by the free spectral range of an etalon (wavelengths, 1.570 and 1.571 µm). The first signal is perfectly phase matched at zero initial temperature buildup.

Tables (2)

Tables Icon

Table 1 Wavelength-Dependent OPO Parameters

Tables Icon

Table 2 Output Powers of OPO with Uniform Crystal Temperatures Adjusted to Effect Perfect Quasi Phase Matching, Adjusted to 0.5 °C above Perfect Phase Matching, and with a Nonuniform Crystal Temperature Generated from Previous Runs with a Maximum Slightly Less Than 0.5 °Ca

Equations (23)

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

2E-2t2 1c2 E+μ0P=0.
E=j=p,s,i 12{exp[i(kjz-ωjt)]Ej(r, t)+c.c.}cˆ,
P=j=p,s,i 12[exp(-iωjt)Pj(r, t)+c.c.]cˆ,
Pp=0{χ(1)(T, ωp)Ep exp(ikpz)+χ(2)(ωp, ωs, ωi)EsEi exp[i(ks+ki)z]},
Ps=0{χ(1)(T, ωs)Es exp(iksz)+χ(2)(ωs, ωp,-ωi)EpEi* exp[i(kp-ki)z]},
Pi=0{χ(1)(T, ωi)Ei exp(ikiz)+χ(2)(ωi, ωp,-ωs)EpEs* exp[i(kp-ks)z]}.
kj=n(Tamb, ωj)ωjcnjωjc,
Δnj=Δn(r, ωj)n[T(r), ωj]-nj.
Epz-i2kp2Ep-2πiλpΔnpEp+αp2Ep
=2πinpλpdeff EsEi exp(-iΔkz),
Esz-i2ks2Es-2πiλsΔnsEs+αs2Es
=2πinsλsdeff EpEi* exp(iΔkz),
Eiz-i2ki2Ei-2πiλiΔniEi+αi2Ei
=2πiniλideff EpEs* exp(iΔkz),
Es2z-i2ks22Es2-2πiλs2Δns2Es2+αs22Es2
=2πins2λs2deff EpEi2* exp(iΔk2z),
Ei2z-i2ki22Ei2-2πiλi2Δni2Ei2+αi22Ei2
=2πini2λi2deff EpEs2* exp(iΔk2z).
Epz-i2kp2Ep-2πiλpΔnpEp+αp2Ep
=2πinpλpdeff [Es1Ei1 exp(-iΔk1z)
+Es2Ei2 exp(-iΔk2z)],
Tt=Dh2T+0c2ρcp(αs1ns1|Es1|2+αi1ni1|Ei1|2+αs2ns2|Es2|2+αi2ni2|Ei2|2+αpnp|Ep|2),
κ Tz=-h(T-Tamb),

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