Abstract

Controlled frequency tuning of an optical parametric oscillator is accomplished through the application of a dc electric field that perturbs the index ellipsoids for the pump, the signal, and the idler beams by means of the linear electro-optic (Pockels) effect. The changes in the refractive indices induce a dispersion-compensating wavelength tuning of the optical parametric oscillator signal and idler beams to maintain the birefringent phase-matching condition. Broadband wavelength tuning by the electro-optic effect in a mid-infrared lithium niobate optical parametric oscillator is demonstrated. A linear dependence of the wavelength shift on applied voltage is observed with an idler tuning range of up to 90 nm achieved electro-optically. Tuning rates in excess of 5 cm-1/(kV/cm) are obtained. All observations, including the dispersion in the tuning rate, are quantitatively described by a simple theory that uses no adjustable parameters.

© 1997 Optical Society of America

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References

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  1. R. L. Byer, ed., “Optical parametric oscillators,” in Treatise in Quantum Electronics (Academic, New York, 1973).
  2. A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 447–450.
  3. R. C. Eckardt, C. D. Nabors, W. J. Kozlovsky, and R. L. Byer, “Optical parametric oscillator frequency tuning and control,” J. Opt. Soc. Am. B 8, 646 (1991).
    [Crossref]
  4. J. P. van der Ziel, “Electro-optic amplitude modulation of laser-generated second harmonics in KDP,” Appl. Phys. Lett. 5, 27 (1964).
    [Crossref]
  5. J. A. Giordmaine and R. C. Miller, “Tunable coherent parametric oscillation in LiNbO3 at optical frequencies,” Phys. Rev. Lett. 14, 973 (1965).
    [Crossref]
  6. L. B. Kreuzer, “Ruby-laser-pumped optical parametric oscillator with electro-optic effect tuning,” Appl. Phys. Lett. 10, 336 (1967).
    [Crossref]
  7. D. T. Hon, “Electro-optical compensation for self-heating in CD*A during SHG,” IEEE J. Quantum Electron. QE-12, 148 (1976).
    [Crossref]
  8. D. Lee and N. C. Wong, “Stabilization and tuning of a doubly resonant OPO,” J. Opt. Soc. Am. B 10, 1659 (1993).
    [Crossref]
  9. N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
    [Crossref]
  10. K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
    [Crossref]
  11. M. J. Weber, ed., “Optical materials. Part I,” in CRC Handbook of Laser Science and Technology (CRC, Boca Raton, Fla., 1986), p. 186.
  12. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), p. 75.
  13. D. F. Nelson, “General solution for the electro-optic effect,” J. Opt. Soc. Am. 65, 1144 (1975).
    [Crossref]
  14. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.
  15. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373 (1984).
    [Crossref]
  16. A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
    [Crossref]
  17. I. Biaggio, P. Kerkoc, L.-S. Wu, and P. Gunter, “Refractive indices of orthorhombic KNbO3: phase-matching configurations for NLO interactions,” J. Opt. Soc. Am. B 9, 507 (1992).
    [Crossref]
  18. W. R. Bosenberg and R. H. Jarman, “Type-II phase-matched KNbO3 optical parametric oscillator,” Opt. Lett. 18, 1323 (1993).
    [Crossref]
  19. D. E. Spence, S. Wielandy, C. L. Tang, and P. Gunter, “High-repetition-rate femtosecond optical parametric oscillator based on KNbO3,” Opt. Lett. 20, 680 (1995).
    [Crossref] [PubMed]

1995 (1)

1993 (2)

1992 (1)

1991 (1)

1990 (1)

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[Crossref]

1984 (2)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373 (1984).
[Crossref]

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

1979 (1)

N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
[Crossref]

1976 (1)

D. T. Hon, “Electro-optical compensation for self-heating in CD*A during SHG,” IEEE J. Quantum Electron. QE-12, 148 (1976).
[Crossref]

1975 (1)

1967 (1)

L. B. Kreuzer, “Ruby-laser-pumped optical parametric oscillator with electro-optic effect tuning,” Appl. Phys. Lett. 10, 336 (1967).
[Crossref]

1965 (1)

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

1964 (1)

J. P. van der Ziel, “Electro-optic amplitude modulation of laser-generated second harmonics in KDP,” Appl. Phys. Lett. 5, 27 (1964).
[Crossref]

Biaggio, I.

Bosenberg, W. R.

Buritskii, K. S.

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

Byer, R. L.

Chernykh, V. A.

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

Chirakadze, A.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[Crossref]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), p. 75.

Eckardt, R. C.

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373 (1984).
[Crossref]

Giordmaine, J. A.

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

Gunter, P.

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), p. 75.

Hon, D. T.

D. T. Hon, “Electro-optical compensation for self-heating in CD*A during SHG,” IEEE J. Quantum Electron. QE-12, 148 (1976).
[Crossref]

Hvitia, B.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[Crossref]

Jarman, R. H.

Kaikoku, K.

N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
[Crossref]

Kerkoc, P.

Kozlovsky, W. J.

Kreuzer, L. B.

L. B. Kreuzer, “Ruby-laser-pumped optical parametric oscillator with electro-optic effect tuning,” Appl. Phys. Lett. 10, 336 (1967).
[Crossref]

Kubota, K.

N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
[Crossref]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373 (1984).
[Crossref]

Lee, D.

Machavariani, S.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[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 (1965).
[Crossref]

Nabors, C. D.

Natsvlishvili, A.

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[Crossref]

Nelson, D. F.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), p. 75.

Prokhorov, A. M.

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

Spence, D. E.

Tang, C. L.

Uesugi, N.

N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
[Crossref]

van der Ziel, J. P.

J. P. van der Ziel, “Electro-optic amplitude modulation of laser-generated second harmonics in KDP,” Appl. Phys. Lett. 5, 27 (1964).
[Crossref]

Wielandy, S.

Wong, N. C.

Wu, L.-S.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 447–450.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

Zolotov, E. M.

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

Appl. Phys. Lett. (3)

J. P. van der Ziel, “Electro-optic amplitude modulation of laser-generated second harmonics in KDP,” Appl. Phys. Lett. 5, 27 (1964).
[Crossref]

N. Uesugi, K. Kaikoku, and K. Kubota, “Electric field tuning of SHG in a 3-dimensional LiNbO3 optical waveguide,” Appl. Phys. Lett. 34, 60 (1979).
[Crossref]

L. B. Kreuzer, “Ruby-laser-pumped optical parametric oscillator with electro-optic effect tuning,” Appl. Phys. Lett. 10, 336 (1967).
[Crossref]

IEEE J. Quantum Electron. (1)

D. T. Hon, “Electro-optical compensation for self-heating in CD*A during SHG,” IEEE J. Quantum Electron. QE-12, 148 (1976).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

J. Phys. D (1)

A. Chirakadze, S. Machavariani, A. Natsvlishvili, and B. Hvitia, “Dispersion of the linear electro-optic effect in lithium niobate,” J. Phys. D 23, 1216 (1990).
[Crossref]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373 (1984).
[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 (1965).
[Crossref]

Sov. J. Quantum Electron. (1)

K. S. Buritskii, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Calculation of the conditions for parametric generation of light in LiNbO3:Ti channel waveguides,” Sov. J. Quantum Electron. 14, 972 (1984).
[Crossref]

Other (5)

M. J. Weber, ed., “Optical materials. Part I,” in CRC Handbook of Laser Science and Technology (CRC, Boca Raton, Fla., 1986), p. 186.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991), p. 75.

R. L. Byer, ed., “Optical parametric oscillators,” in Treatise in Quantum Electronics (Academic, New York, 1973).

A. Yariv, Quantum Electronics (Wiley, New York, 1975), pp. 447–450.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

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Figures (7)

Fig. 1
Fig. 1

Mid-infrared OPO in which LiNbO3 is used with transverse electrodes for electro-optic tuning. The collinear geometry has a propagation direction of θ45° and ϕ-30° with respect to crystal axes , ŷ, and , whereas the polarization directions are extraordinary for the pump beam (at frequency ω p) and ordinary for the signal and the idler beams (at frequencies ω s and ω i, respectively). The electric-field vector is perpendicular to the propagation direction and in a plane containing the optic () axis in each LiNbO3 crystal (i.e., parallel to the pump beam polarization).

Fig. 2
Fig. 2

Phase-matching curve for angle wavelength tuning in a LiNbO3 OPO.

Fig. 3
Fig. 3

Schematic of ring OPO configuration used in electro-optic tuning experiments. The extraordinary-polarized (ext) pump beam enters the OPO ring cavity through dichroic beam splitter BS1 and undergoes nonlinear interaction in a pair of LiNbO3 crystals with axes directed in an alternating fashion. The transverse electrodes on the two LiNbO3 crystals are connected to dc voltage sources for electro-optic tuning control. The depleted pump beam and the ordinary-polarized (ord) idler beam are transmitted through trichoic beam splitter BS2 to emerge from the ring cavity. Only the ordinary-polarized signal beam is resonated around the ring cavity by beam splitter BS2, mirror M, thin-film polarizing beam splitter PBS, and beam splitter BS1. A variable portion of this signal beam is coupled out of the ring cavity by the half-wave plate λ/2 and polarizing beam splitter PBS to limit backconversion.

Fig. 4
Fig. 4

Photograph of ring OPO setup used in electro-optic tuning experiments.

Fig. 5
Fig. 5

Wavelength tuning for signal and idler beams as a function of applied dc voltage in an OPO with two LiNbO3 crystals (each 10 mm in length, with 4.43-mm electrospacing) pumped at a wavelength of 1.064 µm.

Fig. 6
Fig. 6

Signal wavelength tuning as a function of applied dc voltage for a series of zero-field wavelengths set by mechanical angle tuning of the pair of LiNbO3 crystals; this OPO was again pumped at a wavelength of 1.064 µm, but now the LiNbO3 crystals were 20 mm long, with electrode spacings of 4.09 mm.

Fig. 7
Fig. 7

Dependence of signal (or idler) tuning rate on signal beam wave number. The open circles represent the slopes from Fig. 6, whereas the filled circle denotes the slope from Fig. 5. The curve indicates the theoretical prediction from Eq. 9 (or Eq. 11) obtained by use of the Sellmeier equations and the electro-optic coefficients for LiNbO3; no adjustable fitting parameters were employed.

Tables (1)

Tables Icon

Table 1 Electro-optic Tuning Rate (i.e., Slope from Fig. 5 or 6) and Linear Correlation Coefficient R for Each Zero-Field Wavelength

Equations (23)

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

ωp=ωs+ωi,
npωp=nsωs+niωi,
θ=sin-1nepnop/λpns/λs+ni/λi2-nep2nop2-nep21/2,
reffe=-(r22+r13+r33+2r51)/(22)40pm/V,
reffo=(r22-r13)/22.6pm/V,
δn=-neff3reffE3/2,
ωpωp,
npnp0+Δnp,
ωsωs0+Δω,
nsns0+Δns,
ωiωi0-Δω,
nini0+Δni,
Δnp=npEdE=δnp,
Δns=nsEdE+nsωdω=δns+n˙s|ωs0Δω,
Δni=niEdE+niωdω=δni+n˙i|ωi0Δω,
Δωωi0(δns-δni)-ωp(δns-δnp)(ns0-ni0)-ωi0n˙i|ωi0+ωs0n˙s|ωs0.
Δω2(n˙i|ωi0+n˙s|ωs0)+Δω(ni0-ns0+δnp-δns
+ωi0n˙i|ωi0-ωs0n˙s|ωs0)
+(ωi0δni+ωs0δns-ωpδnp)=0,
Δλiλi0(δns-δni)-(λi0/λp)(δns-δnp)(ns0-ni0)+λi0n˙i|λi0-λs0n˙s|λs0,
Δλi2[n˙i|λi0+(λs0/λi0)2n˙s|λs0]+Δλi(ni0-ns0+δni
-δns-λi0n˙i|λi0+λs0n˙s|λs0)
+[λi02(δnp/λp-δni/λi0-δns/λs0)]=0,

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