Abstract

A theoretical model describing the dynamical behavior of dual-frequency solid-state lasers including a buffer reservoir (BR) is presented. It relies on the introduction of two additional coupled rate equations describing the interaction of the two laser modes with the BR. The relative intensity noise is derived by taking into account the fluctuations of both pump intensity and intra-cavity photons. This modelling approach accurately predicts the experimental noise spectra obtained with an Er,Yb:glass dual-frequency laser implemented in different cavity architecture configurations. The mode coupling strength in the BR is shown to rule the reduction efficiency of the excess noise lying at the in-phase and anti-phase frequencies.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. El Amili, G. Kervella, and M. Alouini, “Experimental evidence and theoretical modeling of two-photon absorption dynamics in the reduction of intensity noise of solid-state Er:Yb lasers,” Opt. Express 21(7), 8773–8780 (2013).
    [Crossref] [PubMed]
  2. A. El Amili, G. Loas, L. Pouget, and M. Alouini, “Buffer reservoir approach for cancellation of laser resonant noises,” Opt. Lett. 39(17), 5014–5017 (2014).
    [Crossref] [PubMed]
  3. A. El Amili and M. Alouini, “Noise reduction in solid-state lasers using a SHG-based buffer reservoir,” Opt. Lett. 40(7), 1149–1152 (2015).
    [Crossref] [PubMed]
  4. 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 Photonics Technol. Lett. 13(4), 367–369 (2001).
    [Crossref]
  5. M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
    [Crossref]
  6. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
    [Crossref] [PubMed]
  7. M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30(18), 2418–2420 (2005).
    [Crossref] [PubMed]
  8. A. E. Amili, K. Audo, and M. Alouini, “In-phase and antiphase self-intensity regulated dual-frequency laser using two-photon absorption,” Opt. Lett. 41(10), 2326–2329 (2016).
    [Crossref] [PubMed]
  9. E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
    [Crossref]
  10. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
    [Crossref]
  11. M. Alouini, “Theoretical and experimental study of Er3+ and Nd3+ solid-state lasers: application of dual-frequency lasers to optical and microwave telecommunications,” Ph.D. thesis, University of Rennes 1, Rennes (2001).
  12. V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
    [Crossref]
  13. W. E. Lamb, “Theory of an Optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
    [Crossref]
  14. G. Cardano, The Great Art (Ars Magna) or The Rules of Algebra (Dovers, 1993).
  15. S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
    [Crossref]
  16. M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett. 22(6), 384–386 (1997).
    [Crossref] [PubMed]
  17. S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
    [Crossref]
  18. M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
    [Crossref] [PubMed]

2016 (1)

2015 (2)

A. El Amili and M. Alouini, “Noise reduction in solid-state lasers using a SHG-based buffer reservoir,” Opt. Lett. 40(7), 1149–1152 (2015).
[Crossref] [PubMed]

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

2014 (1)

2013 (1)

2005 (1)

2004 (1)

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

2000 (1)

1998 (2)

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
[Crossref]

1997 (1)

1993 (1)

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

1992 (1)

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

1982 (1)

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

1964 (1)

W. E. Lamb, “Theory of an Optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Alouini, M.

A. E. Amili, K. Audo, and M. Alouini, “In-phase and antiphase self-intensity regulated dual-frequency laser using two-photon absorption,” Opt. Lett. 41(10), 2326–2329 (2016).
[Crossref] [PubMed]

A. El Amili and M. Alouini, “Noise reduction in solid-state lasers using a SHG-based buffer reservoir,” Opt. Lett. 40(7), 1149–1152 (2015).
[Crossref] [PubMed]

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

A. El Amili, G. Loas, L. Pouget, and M. Alouini, “Buffer reservoir approach for cancellation of laser resonant noises,” Opt. Lett. 39(17), 5014–5017 (2014).
[Crossref] [PubMed]

A. El Amili, G. Kervella, and M. Alouini, “Experimental evidence and theoretical modeling of two-photon absorption dynamics in the reduction of intensity noise of solid-state Er:Yb lasers,” Opt. Express 21(7), 8773–8780 (2013).
[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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

Amili, A. E.

Amon, A.

Audo, K.

Baili, G.

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

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 Photonics Technol. Lett. 13(4), 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. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

Blanc, S.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

Bouchoule, S.

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

Bretenaker, F.

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett. 22(6), 384–386 (1997).
[Crossref] [PubMed]

Brisset, J.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

Brunel, M.

M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30(18), 2418–2420 (2005).
[Crossref] [PubMed]

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

M. Brunel, F. Bretenaker, and A. Le Floch, “Tunable optical microwave source using spatially resolved laser eigenstates,” Opt. Lett. 22(6), 384–386 (1997).
[Crossref] [PubMed]

Crozatier, V.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

De, S.

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

Derozier, D.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

El Amili, A.

Gapontsev, V. P.

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

Geronimo, G.

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

Glorieux, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

Isineev, A. A.

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

Kervella, G.

Kravchenko, V. B.

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

Lamb, W. E.

W. E. Lamb, “Theory of an Optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Laporta, P.

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

Larat, C.

E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
[Crossref]

Le Floch, A.

Loas, G.

Longhi, S.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

Mandel, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

Matitsin, S. M.

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

Merlet, T.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

Otsuka, K.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

Pocholle, J.-P.

E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
[Crossref]

Poezevara, A.

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

Pouget, L.

Svelto, O.

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

Taccheo, S.

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

Tanguy, E.

E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
[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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

Vallet, M.

M. Brunel, A. Amon, and M. Vallet, “Dual-polarization microchip laser at 1.53 µm,” Opt. Lett. 30(18), 2418–2420 (2005).
[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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Alouini, F. Bretenaker, M. Brunel, A. Le Floch, M. Vallet, and P. Thony, “Existence of two coupling constants in microchip lasers,” Opt. Lett. 25(12), 896–898 (2000).
[Crossref] [PubMed]

Appl. Phys. B (1)

S. Taccheo, P. Laporta, O. Svelto, and G. Geronimo, “Theoretical and experimental analysis of noise in a codoped erbium-ytterbium glass laser,” Appl. Phys. B 66(1), 19–26 (1998).
[Crossref]

IEEE Photonics Technol. Lett. (2)

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 Photonics Technol. Lett. 13(4), 367–369 (2001).
[Crossref]

M. Brunel, F. Bretenaker, S. Blanc, V. Crozatier, J. Brisset, T. Merlet, and A. Poezevara, “High-Spectral Purity RF Beat Note Generated by a Two-Frequency Solid-State Laser in a Dual Thermooptic and Electrooptic Phase-Locked Loop,” IEEE Photonics Technol. Lett. 16(3), 870–872 (2004).
[Crossref]

Opt. Commun. (2)

E. Tanguy, C. Larat, and J.-P. Pocholle, “Modelling of the erbium-ytterbium laser,” Opt. Commun. 153(1-3), 172–183 (1998).
[Crossref]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Opt. Commun. 100(1-4), 311–321 (1993).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

V. P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14(4), 189–196 (1982).
[Crossref]

Opt. Lett. (6)

Phys. Rev. (1)

W. E. Lamb, “Theory of an Optical Maser,” Phys. Rev. 134(6A), A1429–A1450 (1964).
[Crossref]

Phys. Rev. A (2)

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46(3), 1692–1695 (1992).
[Crossref] [PubMed]

S. De, G. Baili, S. Bouchoule, M. Alouini, and F. Bretenaker, “Intensity- and phase-noise correlations in a dual-frequency vertical-external-cavity surface-emitting laser operating at telecom wavelength,” Phys. Rev. A 91(5), 053828 (2015).
[Crossref]

Other (2)

G. Cardano, The Great Art (Ars Magna) or The Rules of Algebra (Dovers, 1993).

M. Alouini, “Theoretical and experimental study of Er3+ and Nd3+ solid-state lasers: application of dual-frequency lasers to optical and microwave telecommunications,” Ph.D. thesis, University of Rennes 1, Rennes (2001).

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Figures (9)

Fig. 1
Fig. 1 Energy levels of the Er:Yb active medium.
Fig. 2
Fig. 2 Dual-frequency laser setup with the measurement bench. The laser is composed by an Er,Yb:glass laser. A polarizer at the output of the laser allows studying each mode. The measurement bench is composed by two arms. The first arm is dedicated for RIN spectrum measurement. It is composed by an InGaAs photodiode, an electrical amplifier and an electrical spectrum analyzer (ESA). The second arm is used to ensure that the laser remains single mode during measurements using a Fabry-Perot analyzer.
Fig. 3
Fig. 3 a) Experimental RIN spectra for the x- (1) and the y- polarized (2) mode (RBW: 100 Hz, Iphd = 1 mA). b) RIN spectrum of the pump laser (RBW: 100 Hz, Iphd = 1mA).
Fig. 4
Fig. 4 a) Theoretical RIN spectra for the two modes. b) Comparison of experimental and theoretical RIN spectra.
Fig. 5
Fig. 5 a) Theoretical RIN spectra where only the pump noise (1) and the photon fluctuations (2) are considered as a noise source. b) Transfer function of the Yb3+ excited state population.
Fig. 6
Fig. 6 Dual-frequency laser with the Si plate bringing the TPA in the laser dynamics. a) In this first configuration, the Si plate is placed between the YVO4 and the output coupler. b) In the second configuration the Si plate is placed between the active medium and the YVO4.
Fig. 7
Fig. 7 a) Experimental RIN spectra for the x- (1) and the y- (2) polarized mode (RBW: 100 Hz, Iphd = 1 mA) and theoretical RIN spectrum (3). b) Evolution of the RIN spectrum for different TPA efficiencies.
Fig. 8
Fig. 8 a) Experimental RIN spectra for the x- (1) and the y- (2) polarized mode (RBW: 100 Hz, Iphd = 1 mA) and theoretical RIN spectrum (3). b) Evolution of the RIN spectrum for different TPA efficiencies.
Fig. 9
Fig. 9 Evolution of the RIN spectrum for different TPA efficiencies a) when the coupling strength in the NLA is reduced to 0.25 as compared to Fig. 8(b) and b) when the recombination lifetime is reduced to 3 ns.

Tables (1)

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Table 1 Values of the parameters used for the computation of the RIN spectra

Equations (42)

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d N 2 , Y b d t = σ Y b I p ( N Y b 2 N 2 , Y b ) γ Y b N 2 , Y b k T R N E r N 2 , Y b ,
d N d t = 2 σ I N γ ( N E r + N ) + k T R N 2 , Y b ( N E r N ) ,
d I d t = c 2 L 2 e σ N I γ c I   γ P I ,
d P N L d t = ψ N L I γ N L P N L   ,
d N 2 , Y b d t = σ Y b I p ( N Y b 2 N 2 , Y b ) γ Y b N 2 , Y b k T R N E r N 2 Y b ,
d N x d t = 2 σ ( I x + κ I y ) N x γ ( N E r , x + N x ) + k T R N 2 , Y b ( N E r , x N x ) ,
d N y d t = 2 σ ( I y + κ I x ) N y γ ( N E r , y + N y ) + k T R N 2 , Y b ( N E r , y N y ) ,
d I x d t = c 2 L 2 e σ N x I x γ c , x I x   γ p , x I x ,
d I y d t = c 2 L 2 e σ N y I y γ c , y I y γ p , y I y ,
d P N L , x d t = ψ N L , x ( I x + ψ N L , y ψ N L , x η I y ) γ N L P N L , x   ,
d P N L , y d t = ψ N L , y ( I y + ψ N L , x ψ N L , y η I x ) γ N L P N L , y .
N i t h = γ c , i 2 e σ 2 L c ,
N 2 , Y b s t a t = σ Y b I p N Y b 2 σ Y b I p + γ Y b + k T R N E r ,
N i s t a t = γ c , i s t a t + γ p , i s t a t 2 e σ c / 2 L .
P N L , i s t a t = ψ N L , i I i s t a t + ψ N L , j η I j s t a t γ N L ,
I i = I s a t 1 κ 2 [ ( N o , i N i s t a t 1 ) κ ( N o , j N j s t a t 1 ) ] ,
N x s t a t N x t h A x y ( N 0 , x N x s t a t 1 ) B x y ( N 0 , y N y s t a t 1 )   = 0 ,
N y s t a t N y t h A y x ( N 0 , y N y s t a t 1 ) B y x ( N 0 , x N x s t a t 1 )   = 0 ,
RIN( ω ) = | H pump | 2 ( S pump I p 2 ) + | H photon | 2 ( S photon γ c 2 ) ,
δ I x D x ( ω ) = T x ( ω ) δ I y + δ γ c , x I x s t a t ,
δ I y D y ( ω ) = T y ( ω ) δ I x + δ γ c , y I y s t a t ,
D i ( ω ) =   i ω +   γ c , i s t a t + ψ N L , i I i s t a t γ N L c 2 L   ( 1 + γ N L i ω + γ N L + η ψ N L , j I j s t a t ψ N L , i I i s t a t ) 2 e σ c 2 L [ N i s t a t + A i I i s t a t ] ,
T i ( ω ) = c 2 L [ 2 e σ κ A i η ψ N L , j i ω + γ N L ] I i s t a t ,
A i ( ω ) = 2 σ N i s t a t i ω + 2 σ ( I i s t a t +   κ I j s t a t + I s a t ) .
δ I i = T i δ γ c , j I j s t a t + D j δ γ c , i I i s t a t D x D y T x T y .
| δ I s p , x | 2 = | δ I s p , x | 2 = | δ I s p | 2 ,
δ I s p , x δ I s p , y * = 0 .
| H photon,x ( ω ) | 2 = | δ I x I x s t a t δ γ c , x γ c , x s t a t | 2 = ( γ c , x s t a t ) 2 | T x | 2 + | D y | 2 | D x D y T x T y | 2 ,
| H photon,y ( ω ) | 2 = | δ I y I y s t a t δ γ c , y γ c , y s t a t | 2 = ( γ c , y s t a t ) 2 | T y | 2 + | D x | 2 | D x D y T x T y | 2 .
δ I x D x ( ω ) = T x ( ω ) δ I y + J x ( ω ) δ I p ,
δ I y D y ( ω ) = T y ( ω ) δ I x + J y ( ω ) δ I p ,
J i ( ω ) = c 2 L 2 e σ A i k T R β 2 σ ( N E r , i N i s t a t 1 ) I i ,
δ N 2 , Y b = σ Y b ( N Y b 2 N 2 , Y b s t a t ) i ω + 2 σ Y b I p s t a t + γ Y b + k T R N E r δ I p = β δ I p .
| δ I p , x | 2 = | δ I p , y | 2 = | δ I p | 2 ,
δ I p , x δ I p , y * = ξ | δ I p | 2 e i φ ,
| H p u m p , x ( ω ) | 2 = | δ I x I x s t a t δ I p I p s t a t | 2 = ( I p s t a t I x s t a t ) 2 | T x J y | 2 + | D y J x | 2 + ξ ( T x J y D y * J x * + T x * J y * D y J x ) | D x D y T x T y | 2 ,
| H p u m p , y ( ω ) | 2 = | δ I y I y s t a t δ I p I p s t a t | 2 = ( I p s t a t I y s t a t ) 2 | T y J x | 2 + | D x J y | 2 + ξ ( T y J x D x * J y * + T y * J x * D x J y ) | D x D y T x T y | 2 ,
f I N = 1 2 π c 2 L 4 e σ 2 N s t a t I s t a t ( 1 + κ ) ,
f A N = 1 2 π c 2 L 4 e σ 2 N s t a t I s t a t ( 1 κ ) .
C = [ 1 ( f A N f I N ) 2 1 + ( f A N f I N ) 2 ] 2 .
δ N 2 , Y b δ I p = σ Y b ( N Y b 2 N 2 , Y b s t a t ) i ω + 2 σ Y b I p + γ Y b + k T R N E r .
R = I 1 ( x , y ) I 2 ( x , y ) d x d y I 1 2 ( x , y ) d x d y I 2 2 ( x , y ) d x d y = e d 2 w 2 .

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