Abstract

We report on the theoretical analysis of an optical parametric oscillator in which a succession of parametric amplifications takes place to achieve more than 200% quantum efficiency at the wavelength of interest. The first interaction generates the desired radiation, which we call the signal, whatever its wavelength, and its complement, which we called the idler. When the idler is of no particular interest it is used as the pump in a second interaction to amplify the same signal, increasing the quantum efficiency for this radiation. The same type of process can be applied again until the maximum efficiency is reached.

© 1999 Optical Society of America

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References

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  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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
    [CrossRef]
  2. K. Koch, G. T. Moore, and E. C. Cheung, “Optical parametric oscillation with intracavity difference-frequency mixing,” J. Opt. Soc. Am. B, 2268–2273 (1995).
    [CrossRef]
  3. K. Koch, G. T. Moore, and E. C. Cheung, “Greater than 100% photon conversion efficiency from an optical parametric oscillator with intracavity difference-frequency mixing,” in Advanced Solid State Lasers, W. R. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), paper PD3.
  4. J. M. Fukumoto, H. Komine, W. H. Long, Jr., and E. A. Stappaerts, “Periodically poled LiNbO3 optical parametric oscillator with intracavity difference-frequency mixing,” in Advanced Solid State Lasers, W. R. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), paper PD4.
  5. 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]
  6. R. A. Baumgartner and R. L. Byer, “Optical parametric amplification,” IEEE J. Quantum Electron. QE-15, 432–444 (1979).
    [CrossRef]
  7. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, 2nd ed. (Springer, New York, 1971).
  8. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).
  9. S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
    [CrossRef]
  10. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21, 1336–1338 (1996).
    [CrossRef] [PubMed]
  11. See, for example, 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]
  12. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
    [CrossRef]
  13. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique (Hermann, Paris, 1973), Vol. I.
  14. E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
    [CrossRef]

1998 (1)

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[CrossRef]

1997 (2)

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

See, for example, 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 (1)

1979 (2)

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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
[CrossRef]

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

1969 (1)

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

Alexander, J. I.

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]

Baumgartner, R. A.

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

Becouarn, L.

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[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]

Bosenberg, W. R.

See, for example, 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]

W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21, 1336–1338 (1996).
[CrossRef] [PubMed]

Brévignon, M.

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[CrossRef]

Byer, R. L.

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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
[CrossRef]

Drobshoff, A.

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]

Harris, S. E.

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

Jundt, D. H.

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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
[CrossRef]

Lallier, E.

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
[CrossRef]

Lehoux, J.

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[CrossRef]

Myers, L. E.

See, for example, 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]

W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21, 1336–1338 (1996).
[CrossRef] [PubMed]

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]

Electron. Lett. (1)

E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Infrared difference frequency generation with quasi-phase-matched GaAs,” Electron. Lett. 34, 1609–1610 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

See, for example, 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]

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 50–200 kW,” Infrared Phys. 19, 263–271 (1979).
[CrossRef]

Opt. Lett. (2)

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]

Proc. IEEE (1)

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

Other (6)

P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, 2nd ed. (Springer, New York, 1971).

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).

K. Koch, G. T. Moore, and E. C. Cheung, “Optical parametric oscillation with intracavity difference-frequency mixing,” J. Opt. Soc. Am. B, 2268–2273 (1995).
[CrossRef]

K. Koch, G. T. Moore, and E. C. Cheung, “Greater than 100% photon conversion efficiency from an optical parametric oscillator with intracavity difference-frequency mixing,” in Advanced Solid State Lasers, W. R. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), paper PD3.

J. M. Fukumoto, H. Komine, W. H. Long, Jr., and E. A. Stappaerts, “Periodically poled LiNbO3 optical parametric oscillator with intracavity difference-frequency mixing,” in Advanced Solid State Lasers, W. R. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), paper PD4.

C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique (Hermann, Paris, 1973), Vol. I.

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Figures (6)

Fig. 1
Fig. 1

Energy diagram of n cascaded parametric interactions. The last interaction is represented at degeneracy.

Fig. 2
Fig. 2

Architecture for cw operation. To benefit from the cavity resonance for all interactions, the signal is the resonated wave.

Fig. 3
Fig. 3

Ratio of the length of the first interaction that achieves complete pump depletion to the length required for reaching threshold.

Fig. 4
Fig. 4

Functions (a) f(Wp1, Ws) and (b) f2(Wp1, Ws) expressed in millimeters. The condition of loosely focused Gaussian beams is satisfied when f0 or f20.

Fig. 5
Fig. 5

Quantum efficiency for the signal versus pump intensity for three cascaded interactions. Note the existence of a hysteresis cycle. Dotted curve, the efficiency obtained by decreasing the pump intensity after the OPO has turned on.

Fig. 6
Fig. 6

Stability parameter of the three-interaction cavity with complete pump depletion versus amount of noise with α=δs1(0)/ρs1(0). A stability parameter less than 1 is a sufficient condition to yield a stable oscillator as far as the output power is concerned.

Tables (1)

Tables Icon

Table 1 Optimized Configuration for a Pump Power Density of 5 MW/cm2a

Equations (58)

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ηe=ηqλp/λs.
P1:ωpyieldsωsandωi,1(ωs+ωi,1=ωp),
P2:ωi,1yieldsωsandωi,2(ωs+ωi,2=ωi,1).
P1:ωpωs+ωi,1(ωp=ωs+ωi,1),
P2:ωi,1ωs+ωi,2(ωi,1=ωs+ωi,2),
.
Pn:ωi,n-1ωs+ωi,n(ωi,n-1=ωs+ωi,n),
dEsjdzj=idjcωsjnsjEpjEij*,
dEijdzj=idjcωijnijEpjEsj*,
dEpjdzj=idjcωpjnpjEsjEij,
dρsjdzj=κjρpjρsj,
dρijdzj=κjρpjρsj,
dρpjdzi=-κjρsjρij,
κj=djcωpjωsωijnpjnsnij1/2.
msj2=ρsj2+ρpj2=ρsj2(0)+ρpj2(0),
mij2=ρij2+ρpj2=ρpj2(0).
ρpj2(zj)=ρpj2(0)sn2(Zj, γj),
ρsj2(zj)=ρsj2(0)+ρpj2(0)[1-sn2(Zj, γj)],
ρij2(zj)=ρpj2(0)[1-sn2(Zj, γj)],
γj=mijmsj,
Zj=K(γj)-κjmsjzj.
Lj=(1-2kj)K(γj)κjmsj=(1-2kj)K(γj)γjκjρpj(0).
Lj=K(γj)γjκjρpj(0).
ρsj+12(0)=ρsj2(Lj)=ρs12(0)+jρp12(0).
ρpj2(0)=ρij-12(Lj-1)=ρpj-12(0)=ρp12(0).
ρs12(0)=rρsn2(Ln),
ρs12(0)ρp12(0)=nr1-r.
ηq=(1-Ro)ρsn2(Ln)ρp12(0).
ηq=1-Ro1-rn.
γj2=11+ρsj2(0)ρpj2(0)=11+ρs12(0)+(j-1)ρp12(0)ρp12(0),
γj2=1-rj+(n-j)r,
ρp1(0)=2Ip1(0)0cωp11/2.
cosh[κ1ρp1(0)Lth]=1r.
Lth=arccosh1r1κ1ρp1(0).
L1Lth=K(γ1)γ1arccosh(1/r),
γ1=1-r1+(n-1)r1/2.
S=rδsn(Ln)δs1(0).
δZj=δγjddγjK(γj)-κjδmsjLj.
δγj=γjρsj2(0)+ρpj2(0)pj(0)γj2-pj(0)-sj(0),
δmsj=pj(0)+sj(0)msj.
sn(Zj+δZj, γj+δγj)δZj.
δsj+1(0)=δsj(Lj)=1[ρsj2(0)+ρpj2]1/2[pj(0)+sj(0)-½ρpj2(0)δZj2].
δpj+1(0)=δij(Lj)=δpj(0)-½ρpj(0)δZj2.
gsgi=4Wp2M2,
M=WsWiWpWs2Wi2+Ws2Wp2+Wi2Wp2,
1Wi2=1Ws2+1Wp2,
gsgi=Wp2Ws2+Wp2.
1Wpj2=1Wpj-12+1Ws2.
Wpj2=Wp12Ws2Ws2+(j-1)Wp12,
gsgij=Wp12Ws2+jWp12.
lj=Ljgsgij.
f(Wp1, Ws)=2npn+1πWpp+12λpn+1-j=1nlj0.
1.06µm1.44µm2.26µm5.2µm+4.0µm+4.0µm+4.0µm.
zr(λpn)zr(λs)=Wpn2Ws2λsλpn=Wp12Ws2+(n-1)Wp12λs-(n-1)λp1λp1,
zr(λpn)zr(λs)<1n-1λs-(n-1)λp1λp1;
λsλp12(n-1) zr(λpn)zr(λs)<1.
f2(Wp1, Ws)=2npnπWpn2λpn-j=1nlj0.
Ppj=1npjλpj-nsλs-nijλij.

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