Abstract

We present an experimental and theoretical study of the intensity noise correlation between the two orthogonally polarized modes in a dual frequency Vertical External Cavity Surface Emitting Laser (VECSEL). The dependence of the noise correlation spectra on the non-linear coupling between the two orthogonally polarized modes is put into evidence. Our results show that for small coupling the noise correlation amplitude and phase spectra remain nearly flat (around −6 dB and 0° respectively) within the frequency range of our interest (from 100 kHz to 100 MHz). But for higher values of the coupling constant the low frequency behaviors (below 1–2 MHz) of the correlation amplitude and phase spectra are drastically changed, whereas above this cut-off frequency (1–2 MHz) the correlation spectra are almost independent of coupling strength. The theoretical model is based on the assumptions that the only source of noise in the frequency range of our interest for the two modes are pump noises, which are white noises of equal amplitude but partially correlated.

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  1. M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
    [CrossRef]
  2. S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
    [CrossRef]
  3. G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dual frequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol.26, 2764–2773 (2008).
    [CrossRef]
  4. L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt.41, 5702–5712 (2002).
    [CrossRef] [PubMed]
  5. M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett.22, 384–386 (1997).
    [CrossRef] [PubMed]
  6. M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, “Dual tunable wavelength Er:Yb:Glass laser for terahertz beat frequency generation,” IEEE Photon. Technol. Lett.10, 1554–1556 (1998).
    [CrossRef]
  7. R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
    [CrossRef]
  8. F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
    [CrossRef]
  9. S. Taccheo, P. Laporta, O. Svelto, and G. de Geronimo, “Intensity noise reduction in a single-frequency ytterbium-codoped erbium laser,” Opt. Lett.21, 1747–1749 (1996).
    [CrossRef] [PubMed]
  10. G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett.34, 3421–3423 (2009).
    [CrossRef] [PubMed]
  11. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).
  12. M. M. Tehrani and L. Mandel, “Coherence theory of the ring laser,” Phys. Rev. A17, 677–693 (1978).
    [CrossRef]
  13. V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express18, 5008–5014 (2010).
    [CrossRef] [PubMed]
  14. M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995).
    [CrossRef] [PubMed]
  15. J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett.21, 351–353 (1996).
    [CrossRef] [PubMed]
  16. M. Travagnin, M. P. van Exter, and J. P. Woerdman, “Influence of carrier dynamics on the polarization stability and noise-induced polarization hopping in surface-emitting semiconductor lasers,” Phys. Rev. A56, 1497–1507 (1997).
    [CrossRef]
  17. G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol.26, 952–961 (2008).
    [CrossRef]
  18. A. Laurain, M. Myara, G. Beaudoin, I. Sagnes, and A. Garnache, “High power single–frequency continuously–tunable compact extended–cavity semiconductor laser,” Opt. Express17, 9503–9508 (2009).
    [CrossRef] [PubMed]
  19. G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett.32, 650–652 (2007).
    [CrossRef] [PubMed]
  20. G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” Europhys. Lett.87, 44005 (2009).
    [CrossRef]
  21. D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev.141, 306–322 (1966).
    [CrossRef]
  22. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
    [CrossRef] [PubMed]
  23. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18, 259–264 (1982).
    [CrossRef]
  24. C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave. Technol.4, 298–311 (1986).
    [CrossRef]

2010 (1)

2009 (3)

2008 (2)

2007 (1)

2006 (1)

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

2004 (1)

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

2002 (1)

2001 (1)

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

1998 (1)

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, “Dual tunable wavelength Er:Yb:Glass laser for terahertz beat frequency generation,” IEEE Photon. Technol. Lett.10, 1554–1556 (1998).
[CrossRef]

1997 (2)

M. Travagnin, M. P. van Exter, and J. P. Woerdman, “Influence of carrier dynamics on the polarization stability and noise-induced polarization hopping in surface-emitting semiconductor lasers,” Phys. Rev. A56, 1497–1507 (1997).
[CrossRef]

M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett.22, 384–386 (1997).
[CrossRef] [PubMed]

1996 (2)

1995 (1)

M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995).
[CrossRef] [PubMed]

1992 (1)

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

1986 (1)

C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave. Technol.4, 298–311 (1986).
[CrossRef]

1984 (1)

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
[CrossRef]

1982 (1)

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18, 259–264 (1982).
[CrossRef]

1978 (1)

M. M. Tehrani and L. Mandel, “Coherence theory of the ring laser,” Phys. Rev. A17, 677–693 (1978).
[CrossRef]

1966 (1)

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev.141, 306–322 (1966).
[CrossRef]

Abraham, N. B.

Alouini, M.

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express18, 5008–5014 (2010).
[CrossRef] [PubMed]

G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett.34, 3421–3423 (2009).
[CrossRef] [PubMed]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” Europhys. Lett.87, 44005 (2009).
[CrossRef]

G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol.26, 952–961 (2008).
[CrossRef]

G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett.32, 650–652 (2007).
[CrossRef] [PubMed]

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, “Dual tunable wavelength Er:Yb:Glass laser for terahertz beat frequency generation,” IEEE Photon. Technol. Lett.10, 1554–1556 (1998).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
[CrossRef]

Baili, G.

Beaudoin, G.

Benazet, B.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

Bielawski, S.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

Bretenaker, F.

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express18, 5008–5014 (2010).
[CrossRef] [PubMed]

G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett.34, 3421–3423 (2009).
[CrossRef] [PubMed]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” Europhys. Lett.87, 44005 (2009).
[CrossRef]

G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol.26, 952–961 (2008).
[CrossRef]

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dual frequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol.26, 2764–2773 (2008).
[CrossRef]

G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett.32, 650–652 (2007).
[CrossRef] [PubMed]

L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt.41, 5702–5712 (2002).
[CrossRef] [PubMed]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, “Dual tunable wavelength Er:Yb:Glass laser for terahertz beat frequency generation,” IEEE Photon. Technol. Lett.10, 1554–1556 (1998).
[CrossRef]

M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett.22, 384–386 (1997).
[CrossRef] [PubMed]

Brunel, M.

Chazelas, J.

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

Czarny, R.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

de Geronimo, G.

Derozier, D.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

Di Bin, P.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

Dolfi, D.

V. Pal, P. Trofimoff, B.-X. Miranda, G. Baili, M. Alouini, L. Morvan, D. Dolfi, F. Goldfarb, I. Sagnes, R. Ghosh, and F. Bretenaker, “Measurement of the coupling constant in a two-frequency VECSEL,” Opt. Express18, 5008–5014 (2010).
[CrossRef] [PubMed]

G. Baili, L. Morvan, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Experimental demonstration of a tunable dual-frequency semiconductor laser free of relaxation oscillations,” Opt. Lett.34, 3421–3423 (2009).
[CrossRef] [PubMed]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” Europhys. Lett.87, 44005 (2009).
[CrossRef]

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dual frequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol.26, 2764–2773 (2008).
[CrossRef]

G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol.26, 952–961 (2008).
[CrossRef]

G. Baili, M. Alouini, D. Dolfi, F. Bretenaker, I. Sagnes, and A. Garnache, “Shot-noise-limited operation of a monomode high-cavity-finesse semiconductor laser for microwave photonics applications,” Opt. Lett.32, 650–652 (2007).
[CrossRef] [PubMed]

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

L. Morvan, N. D. Lai, D. Dolfi, J.-P. Huignard, M. Brunel, F. Bretenaker, and A. Le Floch, “Building blocks for a two-frequency laser lidar-radar: a preliminary study,” Appl. Opt.41, 5702–5712 (2002).
[CrossRef] [PubMed]

Feng, Q.

M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995).
[CrossRef] [PubMed]

Formont, S.

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

Garnache, A.

Ghosh, R.

Glorieux, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

Goldfarb, F.

Henry, C. H.

C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave. Technol.4, 298–311 (1986).
[CrossRef]

C. H. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron.18, 259–264 (1982).
[CrossRef]

Huignard, J.-P.

Krakowski, M.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

Lai, N. D.

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Laporta, P.

Larat, C.

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2 laser for continuous wave THz generation through photomixing,” Electron. Lett.40, 942–943 (2004).
[CrossRef]

Laurain, A.

Le Floch, A.

Lippi, G. L.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
[CrossRef]

Malherbe, T.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” Europhys. Lett.87, 44005 (2009).
[CrossRef]

Mandel, L.

M. M. Tehrani and L. Mandel, “Coherence theory of the ring laser,” Phys. Rev. A17, 677–693 (1978).
[CrossRef]

Mandel, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

Martin-Regalado, J.

McCumber, D. E.

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev.141, 306–322 (1966).
[CrossRef]

Miranda, B.-X.

Moloney, J. V.

M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995).
[CrossRef] [PubMed]

Monsterleet, A.

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

Morvan, L.

Myara, M.

Otsuka, K.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A46, 1692–1695 (1992).
[CrossRef] [PubMed]

Pal, V.

Pillet, G.

Prati, F.

Puccioni, G. P.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
[CrossRef]

Sagnes, I.

San Miguel, M.

J. Martin-Regalado, M. San Miguel, N. B. Abraham, and F. Prati, “Polarization switching in quantum-well vertical-cavity surface-emitting lasers,” Opt. Lett.21, 351–353 (1996).
[CrossRef] [PubMed]

M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995).
[CrossRef] [PubMed]

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

Svelto, O.

Taccheo, S.

Tehrani, M. M.

M. M. Tehrani and L. Mandel, “Coherence theory of the ring laser,” Phys. Rev. A17, 677–693 (1978).
[CrossRef]

Thony, P.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

Tonda-Goldstein, S.

S. Tonda-Goldstein, D. Dolfi, A. Monsterleet, S. Formont, J. Chazelas, and J.-P. Huignard, “Optical signal processing in radar systems,” IEEE Trans. Microwave Theory and Techniques54, 847–853 (2006).
[CrossRef]

Travagnin, M.

M. Travagnin, M. P. van Exter, and J. P. Woerdman, “Influence of carrier dynamics on the polarization stability and noise-induced polarization hopping in surface-emitting semiconductor lasers,” Phys. Rev. A56, 1497–1507 (1997).
[CrossRef]

Tredicce, J. R.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and J. R. Tredicce, “Deterministic chaos in laser with injected signal,” Opt. Commun.51, 308–314 (1984).
[CrossRef]

Trofimoff, P.

Vallet, M.

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dual frequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol.26, 2764–2773 (2008).
[CrossRef]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, “Offset phase locking of Er:Yb:Glass laser eigenstates for RF photonics applications,” IEEE Photon. Technol. Lett.13, 367–369 (2001).
[CrossRef]

M. Alouini, M. Brunel, F. Bretenaker, M. Vallet, and A. Le Floch, “Dual tunable wavelength Er:Yb:Glass laser for terahertz beat frequency generation,” IEEE Photon. Technol. Lett.10, 1554–1556 (1998).
[CrossRef]

van Exter, M. P.

M. Travagnin, M. P. van Exter, and J. P. Woerdman, “Influence of carrier dynamics on the polarization stability and noise-induced polarization hopping in surface-emitting semiconductor lasers,” Phys. Rev. A56, 1497–1507 (1997).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of the considered two-frequency laser. The ordinary (o) and extraordinary (e) polarized modes are partially spatially separated in the active medium thanks to the birefringent crystal BC.

Fig. 2
Fig. 2

Experimental setup used to study the intensity noise spectra and correlations. BC: birefringent crystal; R: radius of curvature of output coupler; T: transmittance of the output coupler; L: lens; BS: beam splitter; OI: optical isolator used to prevent unwanted feedback to the laser; FPI: Fabry-Perot interferometer; D: photodiode; PBS: polarization beam splitter; RFA: radio frequency amplifier. d represents the spatial separation between the two modes on the gain structure.

Fig. 3
Fig. 3

Results for 1-mm thick crystal, which corresponds to a spatial separation d = 100 μm between the modes. Relative intensity noise (RIN) spectra for the two oscillating modes: (a) experimental and (b) theoretical. Intensity noise correlation amplitude spectrum: (c) experimental and (d) theoretical. Intensity noise correlation phase spectrum: (e) experimental and (f) theoretical. Parameter values used for simulation: C = ξ12ξ21 = 0.1; r1 = 1.3, r2 = 1.4; τ1 ≈ 5 ns, τ2 ≈ 7 ns; τ = 3 ns; RINpump = −135 dB/Hz and η = 0.85.

Fig. 4
Fig. 4

Results for 0.5-mm thick crystal, which corresponds to a spatial separation d = 50 μm between the modes. Relative intensity noise (RIN) spectra for the two oscillating modes: (a) experimental and (b) theoretical. Intensity noise correlation amplitude spectrum: (c) experimental and (d) theoretical. Intensity noise correlation phase spectrum: (e) experimental and (f) theoretical. Parameter values used for simulation: C = ξ12ξ21 = 0.35; r1 = 1.4, r2 = 1.48; τ1 ≈ 5 ns, τ2 ≈ 7 ns; τ = 3 ns; RINpump = −135 dB/Hz and η = 0.85.

Fig. 5
Fig. 5

Results for 0.2-mm thick crystal, which corresponds to a spatial separation d = 20 μm between the modes. Relative intensity noise (RIN) spectra for the two oscillating modes: (a) experimental and (b) theoretical. Intensity noise correlation amplitude spectrum: (c) experimental and (d) theoretical. Intensity noise correlation phase spectrum: (e) experimental and (f) theoretical. Parameter values used for simulation: C = ξ12ξ21 = 0.65; r1 = 1.45, r2 = 1.5; τ1 ≈ 5 ns, τ2 ≈ 6 ns; τ = 3 ns; RINpump = −135 dB/Hz and η = 0.85.

Fig. 6
Fig. 6

The theoretical normalized transfer function for both in-phase and anti-phase relaxation mechanism for three different values of coupling (a) C = 0.1, (b) C = 0.65 and (c) C = 0.35. The other parameters used for the simulation: r1 = r2 = 1.5; photon lifetimes for the two modes inside the cavity: τ1 = τ2 = 5 ns; population inversion lifetime: τ = 3 ns; pump noise correlation factor: η = 0.85.

Equations (24)

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d F 1 ( t ) dt = F 1 τ 1 + κ N 1 F 1 ,
d F 2 ( t ) dt = F 2 τ 2 + κ N 2 F 2 ,
d N 1 ( t ) dt = 1 τ ( N 01 N 1 ) κ N 1 ( F 1 + ξ 12 F 2 ) ,
d N 2 ( t ) dt = 1 τ ( N 02 N 2 ) κ N 2 ( F 2 + ξ 21 F 1 ) ,
C = ξ 12 ξ 21
N 1 N th 1 = 1 κ τ 1 ,
N 2 N th 2 = 1 κ τ 2 ,
F 1 F 10 = F sat ( r 1 1 ) ξ 12 ( r 2 1 ) 1 C ,
F 2 F 20 = F sat ( r 2 1 ) ξ 21 ( r 1 1 ) 1 C ,
N 01 ( t ) = N 01 ¯ + δ N 01 ( t ) ,
N 02 ( t ) = N 02 ¯ + δ N 02 ( t ) .
F 1 ( t ) = F 10 + δ F 1 ( t ) ,
F 2 ( t ) = F 20 + δ F 2 ( t ) ,
N 1 ( t ) = N th 1 + δ N 1 ( t ) ,
N 2 ( t ) = N th 2 + δ N 2 ( t ) .
δ F ˜ 1 ( f ) = 1 τ [ 1 / τ 2 2 i π f κ F 20 ( r 2 / τ 2 i π f ) ] δ N ˜ 01 ( f ) ξ 12 δ N ˜ 02 ( f ) / τ 1 [ 1 / τ 1 2 i π f κ F 10 ( r 1 / τ 2 i π f ) ] [ 1 / τ 2 2 i π f κ F 20 ( r 2 / τ 2 i π f ) ] C / τ 1 τ 2 ,
δ F ˜ 2 ( f ) = 1 τ [ 1 / τ 1 2 i π f κ F 10 ( r 1 / τ 2 i π f ) ] δ N ˜ 02 ( f ) ξ 21 δ N ˜ 01 ( f ) / τ 2 [ 1 / τ 2 2 i π f κ F 20 ( r 2 / τ 2 i π f ) ] [ 1 / τ 1 2 i π f κ F 10 ( r 1 / τ 2 i π f ) ] C / τ 1 τ 2 .
| δ N ˜ 01 ( f ) | 2 = | δ N ˜ 02 ( f ) | 2 = | δ N ˜ 0 | 2 ,
δ N ˜ 01 ( f ) δ N ˜ 02 * ( f ) = η | δ N ˜ 0 | 2 e i ψ .
RIN pump 1 = | δ N ˜ 0 ( f ) | 2 N 01 ¯ 2 ,
RIN pump 2 = | δ N ˜ 0 ( f ) | 2 N 02 ¯ 2 .
RIN 1 ( f ) = | δ F ˜ 1 ( f ) | 2 F 10 2 ,
RIN 2 ( f ) = | δ F ˜ 2 ( f ) | 2 F 20 2 .
Θ ( f ) = δ F ˜ 1 ( f ) δ F ˜ 2 * ( f ) | δ F ˜ 1 ( f ) | 2 | δ F ˜ 2 ( f ) | 2 .

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