Abstract

We describe a spontaneous symmetry-breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type II harmonic generation. It is based on a triply resonant cavity containing a type II χ2 crystal pumped at fundamental frequency ω0. The pump beam generates a second-harmonic mode at frequency 2ω0 that acts as a pump for frequency-degenerate type II parametric downconversion. Under operating conditions symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we show a breaking of the symmetry of the intensities of these two waves.

© 2005 Optical Society of America

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  1. L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, Il Nuovo Cimento 10D, 959 (1988).
    [CrossRef]
  2. A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
    [CrossRef]
  3. A. Eschmann and M. D. Reid, Phys. Rev. A 49, 2881 (1993).
    [CrossRef]
  4. Z. Y. Ou, Phys. Rev. A 49, 4902 (1994).
    [CrossRef] [PubMed]
  5. M. A. M. Marte, J. Opt. Soc. Am. B 12, 2296 (1995).
    [CrossRef]
  6. M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
    [CrossRef] [PubMed]
  7. U. Peschel, C. Etrich, and F. Lederer, Opt. Lett. 23, 500 (1998).
    [CrossRef]
  8. C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
    [CrossRef]
  9. M. A. Marte, Phys. Rev. Lett. 74, 4815 (1995).
    [CrossRef] [PubMed]
  10. A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
    [CrossRef]
  11. S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
    [CrossRef]
  12. T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, J. Opt. Soc. Am. B 10, 1668 (1993).
    [CrossRef]
  13. C. Richy, K. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, J. Opt. Soc. Am. B 12, 456 (1995).
    [CrossRef]

2004 (1)

A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
[CrossRef]

1998 (1)

1997 (3)

C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
[CrossRef]

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
[CrossRef]

1996 (1)

M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
[CrossRef] [PubMed]

1995 (3)

1994 (1)

Z. Y. Ou, Phys. Rev. A 49, 4902 (1994).
[CrossRef] [PubMed]

1993 (2)

1988 (1)

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

Amon, A.

A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
[CrossRef]

Bachor, H.-A.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

Bruckmeier, R.

S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
[CrossRef]

Cohadon, P. F.

C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
[CrossRef]

Collett, M. J.

M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
[CrossRef] [PubMed]

Debuisschert, T.

Eschmann, A.

A. Eschmann and M. D. Reid, Phys. Rev. A 49, 2881 (1993).
[CrossRef]

Etrich, C.

Fabre, C.

C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
[CrossRef]

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

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, J. Opt. Soc. Am. B 10, 1668 (1993).
[CrossRef]

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

Giacobino, E.

Horowicz, R. J.

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

Jack, M. W.

M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
[CrossRef] [PubMed]

Lam, P. K.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

Lederer, F.

Lefranc, M.

A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
[CrossRef]

Lugiato, L.

Lugiato, L. A.

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

Marte, M. A.

M. A. Marte, Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef] [PubMed]

Marte, M. A. M.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

M. A. M. Marte, J. Opt. Soc. Am. B 12, 2296 (1995).
[CrossRef]

McClelland, D. E.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

Oldano, C.

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

Ou, Z. Y.

Z. Y. Ou, Phys. Rev. A 49, 4902 (1994).
[CrossRef] [PubMed]

Peschel, U.

Petsas, K.

Reid, M. D.

A. Eschmann and M. D. Reid, Phys. Rev. A 49, 2881 (1993).
[CrossRef]

Richy, C.

Schiller, S.

S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
[CrossRef]

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

Schwob, C.

C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
[CrossRef]

Sizmann, A.

Taubman, M. S.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

Walls, D. F.

M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
[CrossRef] [PubMed]

White, A. G.

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
[CrossRef]

Il Nuovo Cimento (1)

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

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

Opt. Commun. (1)

S. Schiller, R. Bruckmeier, and A. G. White, Opt. Commun. 138, 158 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

M. W. Jack, M. J. Collett, and D. F. Walls, Phys. Rev. A 53, 1801 (1996).
[CrossRef] [PubMed]

A. G. White, P. K. Lam, M. S. Taubman, M. A. M. Marte, S. Schiller, D. E. McClelland, and H.-A. Bachor, Phys. Rev. A 55, 4511 (1997).
[CrossRef]

A. Eschmann and M. D. Reid, Phys. Rev. A 49, 2881 (1993).
[CrossRef]

Z. Y. Ou, Phys. Rev. A 49, 4902 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. Amon and M. Lefranc, Phys. Rev. Lett. 92, 094101 (2004).
[CrossRef]

M. A. Marte, Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef] [PubMed]

Quantum Semiclassic Opt. (1)

C. Fabre, P. F. Cohadon, and C. Schwob, Quantum Semiclassic Opt. 9, 165 (1997).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme of the ring cavity. M1, pump coupling mirror; M2,3, highly reflective mirrors at ω0 and 2ω0. Inset, input polarization (IP) and downconverted polarization (DP) with crystal neutral axes (1) and (2).

Fig. 2
Fig. 2

Top, normalized intensities of the fundamental frequency as a function of Iin with Δ=0. Bottom, normalized intensities of the extraordinary and ordinary fundamental frequency (solid curve) and harmonic frequency fields (dashed curve) as a function of Δ with Iin=0.001. The other parameters are γ0=0.06, γ=γ=0.11, and Δ0=0.

Fig. 3
Fig. 3

Principle of the dual cavity. DM, dichroic mirror; PBS, polarizing beam splitter; PZT, piezoelectric ceramic. A.R., antireflection; Rmax, high-reflection coating.

Fig. 4
Fig. 4

Experimental recordings of the intracavity intensities as a function of the cavity length scanned in time.

Tables (1)

Tables Icon

Table 1 Intensity Reflection Coefficients

Equations (10)

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

Δ1,2=ω0cn1,2l+L2π,    Δ0=2ω0cn0l+L2π,
γ-iΔ1A1=A0A2*+2γAin2,
γ-iΔ2A2=A0A1*+2γAin2,
γ0-iΔ0A0=-A1A2,
Δ1=Δ2=Δ.
γ2+Δ2-1γ02+Δ02I1I2I1-I2=0,
γ2+Δ2+I2γ02+Δ02+2γγ0-ΔΔ0γ02+Δ02II=γAin2.
I1I2=γ02+Δ02γ2+Δ2,
I1+I2=γAin2γ2+Δ2-2γγ0-ΔΔ0.
Iin<Ithreshold=2γ2+Δ2γ×γ02+Δ02γ2+Δ21/2+γγ0-ΔΔ0,

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