Abstract

We show that thermal effects can lead to periodic mode hopping in cw optical parametric oscillators (OPOs). This mode hopping may occur as soon as two modes have different intensities at the point where they exchange their stability; this condition is easily fulfilled in OPOs that are triply resonant, or doubly resonant with a weakly resonant pump. We have observed such oscillations experimentally in a type  II OPO in both configurations. A simple thermo-optic multimode model reproduces well the experimental regimes. We expect that multimode instabilities based on this mechanism can be observed with various aspects in many experimental setups at high pumping rate.

© 2001 Optical Society of America

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References

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  1. C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).
  2. R. Smith, IEEE J. Quantum Electron. QE-9, 530 (1973).
    [CrossRef]
  3. G. Agarwal and S. Gupta, J. Opt. Soc. Am. B 14, 2174 (1997).
    [CrossRef]
  4. P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
    [CrossRef]
  5. A. Douillet, J.-J. Zondy, A. Yelisseyev, S. Lobanov, and L. Isaenko, J. Opt. Soc. Am. B 16, 1481 (1999).
    [CrossRef]
  6. C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
    [CrossRef]
  7. L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
    [CrossRef]
  8. C. Richy, K. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, J. Opt. Soc. Am. B 12, 456 (1995).
    [CrossRef]

2000 (1)

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

1999 (1)

1998 (1)

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

1997 (2)

C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).

G. Agarwal and S. Gupta, J. Opt. Soc. Am. B 14, 2174 (1997).
[CrossRef]

1995 (1)

1988 (1)

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

1973 (1)

R. Smith, IEEE J. Quantum Electron. QE-9, 530 (1973).
[CrossRef]

Agarwal, G.

Bielawski, S.

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

Cohadon, P.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

Cohadon, P. F.

C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).

Derozier, D.

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

Douillet, A.

Fabre, C.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).

C. Richy, K. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, J. Opt. Soc. Am. B 12, 456 (1995).
[CrossRef]

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Gatti, A.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

Giacobino, E.

C. Richy, K. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, J. Opt. Soc. Am. B 12, 456 (1995).
[CrossRef]

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Gupta, S.

Horowicz, R.

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Isaenko, L.

Lefranc, M.

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

Lobanov, S.

Lugiato, L.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

C. Richy, K. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, J. Opt. Soc. Am. B 12, 456 (1995).
[CrossRef]

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Marte, M.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

Oldano, C.

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Petsas, K.

Richy, C.

Ritsch, H.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

Schwob, C.

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).

Smith, R.

R. Smith, IEEE J. Quantum Electron. QE-9, 530 (1973).
[CrossRef]

Suret, P.

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

Yelisseyev, A.

Zemmouri, J.

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

Zondy, J.-J.

Appl. Phys. B (1)

C. Schwob, P. Cohadon, C. Fabre, M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, Appl. Phys. B 66, 685 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Smith, IEEE J. Quantum Electron. QE-9, 530 (1973).
[CrossRef]

J. Opt. B (1)

C. Fabre, P. F. Cohadon, and C. Schwob, J. Opt. B 9, 165 (1997).

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

Nuovo Cimento D (1)

L. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. Horowicz, Nuovo Cimento D 10, 959 (1988).
[CrossRef]

Phys. Rev. A (1)

P. Suret, D. Derozier, M. Lefranc, J. Zemmouri, and S. Bielawski, Phys. Rev. A 61, 021805(R) (2000).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental self-pulsing regimes: (a) signal and (b) pump intensity in a TRO (lc=7 mm, Ppump=1.5 W) and (c) signal and (d) pump intensity in a DRO (lc=15 mm, Ppump=3.6 W).

Fig. 2
Fig. 2

Spectral analysis: (a) output of the Fabry–Perot analyzer as its length is swept over one free spectral range (10  GHz); (b), (c) details of the resonance of mode  1. (b) Signal intensity fed to the Fabry–Perot analyzer, (c) output of the Fabry–Perot analyzer.

Fig. 3
Fig. 3

Numerical integration of Eqs.  (1)–(4). (a) A12 (solid line) and A22 (dashed line), (b) Ap2. E=6, Δp=-3, Δ1=4, Δ2=5.3, α=2, β=0.7, γ=10, ϵ=3×10-4, and η=10-40. One time unit corresponds to 70  ns.

Fig. 4
Fig. 4

Phase portrait θ,A12+A22. Thick box, trajectory associated with the regime of Fig.  3. Solid (dashed) curves, stable (unstable) stationary states of model (1)–(4). The stable solution for θ<θc θ>θe is mode  1 (mode  2).

Equations (4)

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A˙p=γ-1+iσpθAp-A12-A22+E,
A˙1=-1+iσ1θA1+ApA1*+η,
A˙2=-1+iσ2θA2+ApA2*+η,
θ˙=ϵ-θ+αAp2+βA12+A22,

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