Abstract

We show that it is possible to use backward optical parametric oscillation in GaSe to obtain tunable output in the 13–20-μm range with the minimum threshold intensity as low as a few 108 W/cm2. We may be able to use this configuration to achieve large amplification factors for a coherent weak beam in the far-infrared region. It is also possible to generate coherent far-infrared waves in the presence of pump and signal waves.

© 1998 Optical Society of America

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  1. S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
    [CrossRef]
  2. K. H. Yang, P. L. Richards, and Y. R. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO3,” Appl. Phys. Lett. 19, 320–323 (1971); D. S. Chemla and E. Batifol, “Optical backward parametric fluorescence in sodium nitrite,” Appl. Phys. Lett. 28, 135–137 (1976).
    [CrossRef]
  3. D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
    [CrossRef]
  4. Y. J. Ding and J. B. Khurgin, “Backward optical parametric oscillators and amplifiers,” IEEE J. Quantum Electron. 32, 1574–1582 (1996).
    [CrossRef]
  5. Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz waves in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998).
    [CrossRef]
  6. Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995); “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995); “Transversely-pumped counterpropagating optical parametric amplification and difference-frequency generation,” J. Opt. Soc. Am. B JOBPDE 14, 2161–2166 (1997).
    [CrossRef] [PubMed]
  7. K. L. Vodopyanov, “Parametric generation of tunable infrared radiation in ZnGeP2 and GaSe pumped at 3 μm,” J. Opt. Soc. Am. B 10, 1723–1729 (1993).
    [CrossRef]
  8. G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).
  9. J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
    [CrossRef]
  10. A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
    [CrossRef]
  11. K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
    [CrossRef]
  12. K. L. Vodopyanov and L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65–18 μm spectral region,” Opt. Commun. 118, 375–378 (1995).
    [CrossRef]

1998 (1)

Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz waves in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998).
[CrossRef]

1996 (1)

Y. J. Ding and J. B. Khurgin, “Backward optical parametric oscillators and amplifiers,” IEEE J. Quantum Electron. 32, 1574–1582 (1996).
[CrossRef]

1995 (1)

K. L. Vodopyanov and L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65–18 μm spectral region,” Opt. Commun. 118, 375–378 (1995).
[CrossRef]

1993 (1)

1991 (1)

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

1979 (1)

J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
[CrossRef]

1975 (1)

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

1974 (1)

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

1972 (1)

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

1966 (1)

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

Abdullaev, A. G.

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

Abdullaev, G. B.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Allakhverdiev, K. R.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

Batifol, E.

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

Byer, R. L.

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

Chemla, D. S.

J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
[CrossRef]

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

Ding, Y. J.

Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz waves in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998).
[CrossRef]

Y. J. Ding and J. B. Khurgin, “Backward optical parametric oscillators and amplifiers,” IEEE J. Quantum Electron. 32, 1574–1582 (1996).
[CrossRef]

Gribenyukov, A. I.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Harris, S. E.

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

Herbst, R. L.

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

Kerimov, T. A.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Khurgin, J. B.

Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz waves in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998).
[CrossRef]

Y. J. Ding and J. B. Khurgin, “Backward optical parametric oscillators and amplifiers,” IEEE J. Quantum Electron. 32, 1574–1582 (1996).
[CrossRef]

Kulevskii, L. A.

K. L. Vodopyanov and L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65–18 μm spectral region,” Opt. Commun. 118, 375–378 (1995).
[CrossRef]

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Kupecek, Ph. J.

J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
[CrossRef]

Oudar, J. L.

J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
[CrossRef]

Prokhorov, A. M.

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Salaev, E. Yu.

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Savel’ev, A. D.

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Smirnov, V. V.

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Vodopyanov, K. L.

K. L. Vodopyanov and L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65–18 μm spectral region,” Opt. Commun. 118, 375–378 (1995).
[CrossRef]

K. L. Vodopyanov, “Parametric generation of tunable infrared radiation in ZnGeP2 and GaSe pumped at 3 μm,” J. Opt. Soc. Am. B 10, 1723–1729 (1993).
[CrossRef]

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Voevodin, V. G.

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

S. E. Harris, “Proposed backward wave oscillation in the infrared,” Appl. Phys. Lett. 9, 114–116 (1966).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. J. Ding and J. B. Khurgin, “Backward optical parametric oscillators and amplifiers,” IEEE J. Quantum Electron. 32, 1574–1582 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

G. B. Abdullaev, L. A. Kulevskii, A. M. Prokhorov, A. D. Savel’ev, E. Yu. Salaev, and V. V. Smirnov, “GaSe, a new effective crystal for nonlinear optics,” JETP Lett. 16, 90–92 (1972).

Opt. Commun. (5)

J. L. Oudar, Ph. J. Kupecek, and D. S. Chemla, “Medium infrared in gallium selenide,” Opt. Commun. 29, 119–122 (1979).
[CrossRef]

Y. J. Ding and J. B. Khurgin, “A new scheme for efficient generation of coherent and incoherent submillimeter to THz waves in periodically-poled lithium niobate,” Opt. Commun. 148, 105–109 (1998).
[CrossRef]

K. L. Vodopyanov, L. A. Kulevskii, V. G. Voevodin, A. I. Gribenyukov, K. R. Allakhverdiev, and T. A. Kerimov, “High efficiency middle IR parametric superradiance in ZnGeP2 and GaSe crystals pumped by an erbium laser,” Opt. Commun. 83, 322–326 (1991).
[CrossRef]

K. L. Vodopyanov and L. A. Kulevskii, “New dispersion relationships for GaSe in the 0.65–18 μm spectral region,” Opt. Commun. 118, 375–378 (1995).
[CrossRef]

D. S. Chemla, E. Batifol, R. L. Byer, and R. L. Herbst, “Optical backward mixing in sodium nitrite,” Opt. Commun. 11, 57–61 (1974).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. G. Abdullaev, K. R. Allakhverdiev, L. A. Kulevskii, A. M. Prokhorov, E. Yu. Salaev, and V. V. Smirnov, “Parametric conversion of infrared radiation in a GaSe crystal,” Sov. J. Quantum Electron. 5, 665–668 (1975).
[CrossRef]

Other (2)

Y. J. Ding, S. J. Lee, and J. B. Khurgin, “Transversely-pumped counterpropagating optical parametric oscillation and amplification,” Phys. Rev. Lett. 75, 429–432 (1995); “Transversely-pumped counterpropagating optical parametric oscillators and amplifiers: conversion efficiencies and tuning ranges,” IEEE J. Quantum Electron. 31, 1648–1658 (1995); “Transversely-pumped counterpropagating optical parametric amplification and difference-frequency generation,” J. Opt. Soc. Am. B JOBPDE 14, 2161–2166 (1997).
[CrossRef] [PubMed]

K. H. Yang, P. L. Richards, and Y. R. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO3,” Appl. Phys. Lett. 19, 320–323 (1971); D. S. Chemla and E. Batifol, “Optical backward parametric fluorescence in sodium nitrite,” Appl. Phys. Lett. 28, 135–137 (1976).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Wave-propagation configuration for backward OPO in GaSe. Since GaSe is a negative uniaxial crystal, a pump wave with wavelength λp should be an extraordinary wave in GaSe with θ and ϕ angles between the propagation direction and its projection upon the xy plane, and the optic axis (z axis) and x axis, respectively. The signal and idler waves with the respective wavelengths λs and λi (λs<λi) are the ordinary waves in GaSe.

Fig. 2
Fig. 2

Cutoff idler wavelength versus pump wavelength.

Fig. 3
Fig. 3

Signal (dashed curve) and idler (solid curve) wavelengths versus angle for λp7270 Å.

Fig. 4
Fig. 4

Threshold intensity versus idler wavelength for backward OPO.

Fig. 5
Fig. 5

For generating coherent waves at 17 μm, the threshold intensity (solid curve) and crystal angle (dashed curve) are plotted versus pump wavelength.

Fig. 6
Fig. 6

Conversion efficiency in terms of intensities for the idler wave versus normalized pump intensity.

Fig. 7
Fig. 7

Amplification factor for the idler wave versus normalized input intensity for λp7270 Å and λi17 μm. It is obvious that this amplifier is especially effective for a very weak wave in the far-infrared domain.

Equations (10)

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

ne(λp, θ)λp=no(λs)λs-no(λi)λi,
1λp=1λs+1λi,
1ne2(λp,θ)=cos2 θno2(λp)+sin2 θne2(λp)
ne2(λp)=5.76+0.3879λp2-0.2288λp4+0.1223λp6+1.855λp2λp2-1780,
no2(λp,s,i)=7.443+0.405λp,s,i2+0.0186λp,s,i4+0.0061λp,s,i6+3.1485λp, s, i2λp,s,i2-2194.
deff=d22 cos θ sin(3ϕ),
Ith=λsλine(λp, θ)no(λs)no(λi)2η0L2deff2,
ηi=λpλi η,
0π/2 dθ1-η sin2 θ=π2 IpIth.
IinIth8π λpλi G-3/2.

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