Abstract

We present numerical modeling and laboratory studies of degenerate type I nanosecond optical parametric oscillators. Because the signal and idler waves are identical and parametric gain is phase sensitive, their round-trip phase is a critical parameter. We show that signal spectrum, transverse mode, and conversion efficiency are all strongly influenced by this phase. We also examine the influence of signal-wave injection seeding and phase-velocity mismatch.

© 2003 Optical Society of America

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References

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  1. S. Longhi, “Hydrodynamic equation model for degenerate optical parametric oscillators,” J. Mod. Opt. 43, 1089–1094 (1996).
  2. G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
    [CrossRef] [PubMed]
  3. M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
    [CrossRef]
  4. M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
    [CrossRef]
  5. L. I. Plimak and D. F. Walls, “Dynamical restrictions to squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 50, 2627–2641 (1994).
    [CrossRef] [PubMed]
  6. S. Prasad, “Quantum-noise and squeezing in an optical parametric oscillator with arbitrary output-mirror coupling. 3. Effect of pump amplitude and phase fluctuations,” Phys. Rev. A 49, 1406–1426 (1994).
    [CrossRef] [PubMed]
  7. H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
    [CrossRef] [PubMed]
  8. S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
    [CrossRef]
  9. 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, 646–667 (1991).
    [CrossRef]
  10. A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
    [CrossRef]
  11. K. Staliunas, “Three-dimensional structures and spatial solitons in optical parametric oscillators,” Phys. Rev. Lett. 81, 81–84 (1998).
    [CrossRef]
  12. W. J. Alford, R. J. Gehr, R. L. Schmitt, A. V. Smith, and G. Arisholm, “Beam tilt and angular dispersion in broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 1525–1532 (1999).
    [CrossRef]
  13. G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
    [CrossRef]
  14. 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]
  15. 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]
  16. D. J. Armstrong and A. V. Smith, “Tendency of nanosecond optical parametric oscillators to produce purely phase-modulated light,” Opt. Lett. 21, 1634–1636 (1996).
    [CrossRef] [PubMed]

2002 (1)

S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
[CrossRef]

2001 (1)

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

1999 (4)

1998 (2)

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[CrossRef]

K. Staliunas, “Three-dimensional structures and spatial solitons in optical parametric oscillators,” Phys. Rev. Lett. 81, 81–84 (1998).
[CrossRef]

1996 (2)

S. Longhi, “Hydrodynamic equation model for degenerate optical parametric oscillators,” J. Mod. Opt. 43, 1089–1094 (1996).

D. J. Armstrong and A. V. Smith, “Tendency of nanosecond optical parametric oscillators to produce purely phase-modulated light,” Opt. Lett. 21, 1634–1636 (1996).
[CrossRef] [PubMed]

1995 (2)

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. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

1994 (3)

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[CrossRef] [PubMed]

L. I. Plimak and D. F. Walls, “Dynamical restrictions to squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 50, 2627–2641 (1994).
[CrossRef] [PubMed]

S. Prasad, “Quantum-noise and squeezing in an optical parametric oscillator with arbitrary output-mirror coupling. 3. Effect of pump amplitude and phase fluctuations,” Phys. Rev. A 49, 1406–1426 (1994).
[CrossRef] [PubMed]

1991 (1)

Alford, W. J.

Arisholm, G.

Armstrong, D. J.

Bowers, M. S.

Brambilla, M.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[CrossRef] [PubMed]

Byer, R. L.

Chaturvedi, S.

S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
[CrossRef]

Colet, P.

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
[CrossRef]

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[CrossRef]

Colville, F. G.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Dechoum, K.

S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
[CrossRef]

Deng, H.

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

Drummond, P. D.

S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
[CrossRef]

Dunn, M. H.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Eckardt, R. C.

Erenso, D.

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

Gehr, R. J.

Henderson, A. J.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Kozlovsky, W. J.

Longhi, S.

S. Longhi, “Hydrodynamic equation model for degenerate optical parametric oscillators,” J. Mod. Opt. 43, 1089–1094 (1996).

Lugiato, L. A.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[CrossRef] [PubMed]

Nabors, C. D.

Oppo, G.-L.

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[CrossRef] [PubMed]

Padgett, M. J.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Plimak, L. I.

L. I. Plimak and D. F. Walls, “Dynamical restrictions to squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 50, 2627–2641 (1994).
[CrossRef] [PubMed]

Prasad, S.

S. Prasad, “Quantum-noise and squeezing in an optical parametric oscillator with arbitrary output-mirror coupling. 3. Effect of pump amplitude and phase fluctuations,” Phys. Rev. A 49, 1406–1426 (1994).
[CrossRef] [PubMed]

Raymond, T. D.

San Miguel, M.

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
[CrossRef]

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[CrossRef]

Santagiustina, M.

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
[CrossRef]

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[CrossRef]

Schmitt, R. L.

Singh, S.

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

Smith, A. V.

Staliunas, K.

K. Staliunas, “Three-dimensional structures and spatial solitons in optical parametric oscillators,” Phys. Rev. Lett. 81, 81–84 (1998).
[CrossRef]

Vyas, R.

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

Walgraef, D.

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
[CrossRef]

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[CrossRef]

Walls, D. F.

L. I. Plimak and D. F. Walls, “Dynamical restrictions to squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 50, 2627–2641 (1994).
[CrossRef] [PubMed]

Zhang, J.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

J. Mod. Opt. (1)

S. Longhi, “Hydrodynamic equation model for degenerate optical parametric oscillators,” J. Mod. Opt. 43, 1089–1094 (1996).

J. Opt. B (1)

M. Santagiustina, P. Colet, M. San Miguel, and D. Walgraef, “Space inversion symmetry breaking and pattern selection in nonlinear optics,” J. Opt. B 1, 191–197 (1999).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

S. Chaturvedi, K. Dechoum, and P. D. Drummond, “Limits to squeezing in the degenerate optical parametric oscillator,” Phys. Rev. A 65, 033805 (2002).
[CrossRef]

G.-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A 49, 2028–2032 (1994).
[CrossRef] [PubMed]

L. I. Plimak and D. F. Walls, “Dynamical restrictions to squeezing in a degenerate optical parametric oscillator,” Phys. Rev. A 50, 2627–2641 (1994).
[CrossRef] [PubMed]

S. Prasad, “Quantum-noise and squeezing in an optical parametric oscillator with arbitrary output-mirror coupling. 3. Effect of pump amplitude and phase fluctuations,” Phys. Rev. A 49, 1406–1426 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

H. Deng, D. Erenso, R. Vyas, and S. Singh, “Entanglement, interference, and measurement in a degenerate parametric oscillator,” Phys. Rev. Lett. 86, 2770–2773 (2001).
[CrossRef] [PubMed]

K. Staliunas, “Three-dimensional structures and spatial solitons in optical parametric oscillators,” Phys. Rev. Lett. 81, 81–84 (1998).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the experimental apparatus for the BBO OPO: BS, beam splitter that reflects 532-nm light and transmits 1064-nm light; CG, colored glass filter that removes residual 532-nm light while transmitting 1064-nm light; OPO, degenerate OPO; PZT; piezoelectric transducer. The LiNbO3 OPO experiment was similar, except no seed light was used.

Fig. 2
Fig. 2

Round-trip spectral reflectivity of the BBO OPO cavity mirrors near 1064 nm.

Fig. 3
Fig. 3

Spectrum computed from the broadband, plane-wave OPO model for the parameters listed in Table 1, with the OPO cavity tuned to exact resonance (δ=0). This is an average over 40 model runs, each with a different starting noise field. A simulated spectral resolution of 5 cm-1 averages over the individual longitudinal modes.

Fig. 4
Fig. 4

Short-time slices of a signal wave calculated from the broadband, plane-wave OPO model for the parameters listed in Table 1, with the OPO cavity tuned to exact resonance (δ=0) (a) early in the signal pulse and (b) late in the signal pulse. Solid curves, signal phases; dashed curves, normalized signal irradiances.

Fig. 5
Fig. 5

Spectra computed from the broadband, plane-wave OPO model for parameters listed in Table 1 (a) with the OPO cavity shortened from resonance so δ=-0.1π and (b) with the OPO cavity lengthened from resonance so δ=+0.1π. These are averages over 40 model runs, each with a different starting noise field. A simulated spectral resolution of 5 cm-1 averages over the individual longitudinal modes.

Fig. 6
Fig. 6

Short-time slice of a signal wave calculated from the broadband, plane-wave OPO model for parameters listed in Table 1 with the OPO cavity shortened such that δ=-0.1π: (a) early in the signal pulse, (b) late in the signal pulse. Solid curves, signal phases; dashed curves, normalized signal irradiances.

Fig. 7
Fig. 7

Far-field signal fluence profile computed from the diffractive, monochromatic OPO model for δ=0.25π.

Fig. 8
Fig. 8

Vertically centered horizontal (critical plane) slice of the computed signal irradiance (dashed curve) and phase (solid curve) at the crystal’s exit face at the peak of the signal pulse.

Fig. 9
Fig. 9

Left, measured BBO OPO unseeded signal spectra and right, far-field beam profiles for cavity detunings of δ-0.15π (top row), δ0.0π (middle row), and δ0.25π (bottom row).

Fig. 10
Fig. 10

Measured BBO OPO unseeded-signal energy as the length of the OPO cavity is scanned over 1.5 signal wavelengths. The error bars represent the experimental pulse-to-pulse variation in signal energy. Split spectra and ring modes are individually present in the separate zones indicated by hatching.

Fig. 11
Fig. 11

Measured LiNbO3 OPO unseeded-signal energy as the length of the OPO cavity is scanned over 1.5 signal wavelengths. The error bars represent the experimental pulse-to-pulse variation in signal energy. In the zones labeled I the spectrum is split and the far-field transverse mode is a ring. In the zones labeled II spectral splitting and ring modes are not evident within the available spectral and spatial resolution of the experiment.

Fig. 12
Fig. 12

Measured signal energy versus pump energy for seeded and unseeded BBO OPOs pumped by a seeded Nd:YAG laser and for an unseeded BBO OPO pumped by an unseeded Nd:YAG laser. The cavity is tuned to δ=0 when the pump laser is injection seeded.

Tables (1)

Tables Icon

Table 1 Parameters for Model and Laboratory OPOs

Equations (21)

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z-i2kj t2+tan ρjx+1vjt+iβj2t2
×j(x, y, z, t)=Pj(x, y, z, t)exp(±iΔkz),
Ps=ideffωscns ps*,
Pp=ideffωpcnp ss.
1vj=dkjdωω=ωj,
βj=-12vj2dvjdωω=ωj.
Δωbw=πLcrystalβs1/2.
d(ϕ++ϕ-)=Lcrystal(dk++dk-)
=Lcrystaldk0dω Δω+12d2k0dω2 Δω2-dk0dω Δω+12d2k0dω2 Δω2
=Lcrystald2k0dω2 Δω2.
d(ϕ++ϕ-)=-2LcrystalΔω2βs.
2δ=-2LcrystalΔω2βs.
Δω=-δLcrystalβs1/2,
z=-iβs2t2.
=0sin(Δωt)
2t2=-Δω2,
z=iβsΔω2.
ϕ=LcrystalβsΔω2.
Δω=-δLcrystalβs1/2,
ϕtilt=-θ22 ks(Lcrystal/ns+Lcavity-Lcrystal).
θ={2δ/ks[Lcavity+Lcrystal(ns-1-1)]}1/2.

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