Abstract

A theoretical and experimental investigation of the intensity noise reduction induced by two-photon absorption in a Er,Yb:Glass laser is reported. The time response of the two-photon absorption mechanism is shown to play an important role on the behavior of the intensity noise spectrum of the laser. A model including an additional rate equation for the two-photon-absorption losses is developed and allows the experimental observations to be predicted.

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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. Tech. Lett.13, 367–369 (2001).
    [CrossRef]
  2. D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev.141, 306–322 (1966).
    [CrossRef]
  3. 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]
  4. J. Zhang, H. Ma, C. Xie, and K. Peng, “Suppression of intensity noise of a laser-diode-pumped single-frequency Nd:YVO4 laser by optoelectronic control,” Appl. Opt.42, 1068–1074 (2003).
    [CrossRef] [PubMed]
  5. 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]
  6. M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
    [CrossRef]
  7. H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
    [CrossRef]
  8. J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967).
    [CrossRef]
  9. R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).
  10. P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
    [CrossRef]
  11. R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.
  12. S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
    [CrossRef]
  13. J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982).
    [CrossRef]
  14. R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987).
    [CrossRef]
  15. J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987).
    [CrossRef]

2009

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

2007

2003

2001

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

1998

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

1996

1993

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

1987

R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987).
[CrossRef]

J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987).
[CrossRef]

1982

J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982).
[CrossRef]

1967

J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967).
[CrossRef]

1966

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

1965

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
[CrossRef]

Alouini, M.

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]

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Baili, 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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.

Bretenaker, F.

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]

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Brunel, M.

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

De Geronimo, G.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

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]

del Alamo, J. A.

J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987).
[CrossRef]

deMars, G. A.

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
[CrossRef]

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Dolfi, D.

Esterowitz, L.

J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967).
[CrossRef]

Feng, M.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

Fossum, J. G.

J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982).
[CrossRef]

Garnache, A.

Ghosh, C.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

Holonyak, N.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

James, A.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

Laporta, P.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

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]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

Le Floch, A.

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Lee, D. S.

J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982).
[CrossRef]

Longhi, S.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

Ma, H.

McCumber, D. E.

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

Mertens, R. P.

R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987).
[CrossRef]

Peng, K.

Pinto, J. F.

J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967).
[CrossRef]

Sagnes, I.

Statz, H.

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
[CrossRef]

Svelto, O.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

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]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

Swanson, R. M.

J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987).
[CrossRef]

Taccheo, S.

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

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]

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

Tang, C. L.

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
[CrossRef]

Then, H. W.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

Vallet, M.

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

van Leeuwen, R.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

Van Overstraeten, R. J.

R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987).
[CrossRef]

Walter, G.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

Wang, Q.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

Watkins, L. S.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

Xie, C.

Xu, B.

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

Zhang, J.

Appl. Opt.

Appl. Phys. B

S. Taccheo, P. Laporta, O. Svelto, and G. De Geronimo, “Theoretical and experimental analysis of intensity noise in a co doped erbium-ytterbium glass laser,” Appl. Phys. B66, 19–26 (1998).
[CrossRef]

Appl. Phys. Lett.

M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett.95, 033509 (2009).
[CrossRef]

IEEE Photon. Tech. Lett.

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. Tech. Lett.13, 367–369 (2001).
[CrossRef]

IEEE. J. Quant. Elec.

J. F. Pinto and L. Esterowitz, “Suppression of spiking behavior in flash-pumped 2–μm lasers,” IEEE. J. Quant. Elec.30, 167–169 (1967).
[CrossRef]

J. Appl. Phys.

H. Statz, G. A. deMars, and C. L. Tang, “Problem of spike elimination in lasers,” J. Appl. Phys.36, 1510–1514 (1965).
[CrossRef]

Opt. Lett.

Optics Comm.

P. Laporta, S. Longhi, S. Taccheo, and O. Svelto, “Analysis and modelling of the erbium-ytterbium glass laser,” Optics Comm.100, 311–321 (1993).
[CrossRef]

Phys. Rev.

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

Solid-State Electron.

J. G. Fossum and D. S. Lee, “A physical model for the dependence of carrier lifetime on doping density in nondegenerate silicon,” Solid-State Electron.25, 741–747 (1982).
[CrossRef]

R. J. Van Overstraeten and R. P. Mertens, “Heavy doping effects in Si,” Solid-State Electron.30, 1077–1087 (1987).
[CrossRef]

J. A. del Alamo and R. M. Swanson, “Modelling of minority-carrier transport in heavily doped silicon emitters,” Solid-State Electron.30, 1127–1136 (1987).
[CrossRef]

Other

R. van Leeuwen, B. Xu, L. S. Watkins, Q. Wang, and C. Ghosh, “Low noise high power ultra-stable diode pumped Er-Yb phosphate glass laser,” Proc. SPIE 6975, Enabling Photonics Technologies for Defense, Security, and Aerospace Applications IV, 69750K (March24, 2008).

R. W. Boyd, Nonlinear Optics (Academic Press, 2008), pp. 16.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. O.I: optical isolator; BS: beam splitter. The arrow shows the direction of displacement of the two-photon absorber in order to change the effective cross-section of the TPA.

Fig. 2
Fig. 2

RIN spectra of the laser without and with an intracavity two-photon absorber (Si plate). In this example, the insertion of the Si plate leads to a 33 dB reduction of the intensity noise at the relaxation oscillation frequency. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

Fig. 3
Fig. 3

RIN spectra of the laser with a Si plate. Each spectrum is recorded for different positions z from the active medium of the TPA plate. The full lines in red are the theoretical transfer functions. The numerical values of the laser parameters used in the calculation are: NE = 1.08 × 1020 cm−3; γ = 154 s−1; e = 0.15 cm; L = 5 cm; σ = 6 × 10−21 cm2; γc = 2.2 × 108 s−1; α(z1)ψ = 6.4 × 10−22 cm2; α(z2)ψ = 2.7 × 10−22 cm2; α(z3)ψ = 1.7×10−22 cm2; α(z4)ψ = 6.9×10−23 cm2; α(z5)ψ = 6.7×10−23 cm2. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

Fig. 4
Fig. 4

RIN spectra of the laser with a GaAs plate. Each spectrum is recorded for different positions z from the active medium of the TPA plate. The full lines in red are the theoretical transfer functions. The numerical values of the laser parameters used are the same as those in Fig. 3 except γc = 1.56 × 108 s−1; α(z1)ψ = 1.7 × 10−19 cm2; α(z2)ψ = 7.5 × 10−20 cm2; α(z3)ψ = 5.5 × 10−20 cm2. ESA resolution bandwidth: 100 Hz; video bandwidth: 100 Hz.

Equations (7)

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d N d t = 2 σ I N ( w p + γ ) N + ( w p γ ) N E ,
d I d t = c 2 L 2 e σ I N γ c I γ T P A I ,
d P T P A d t = α ψ I γ P P T P A ,
H δ γ c ( ω ) = δ I / I ¯ δ γ c / γ ¯ c = γ ¯ c i ω + γ ¯ c ( 1 N ¯ N th ) + γ T P A ( 1 γ P i ω + γ P ) + γ ¯ c N ¯ N th 2 σ I ¯ i ω + 2 σ ( I ¯ + I sat ) ,
N ¯ = 1 2 ( α ψ I sat 2 e σ γ T P A + N t h + ( α ψ I sat 2 e σ γ T P A N th ) 2 + 4 α ψ I sat 2 e σ γ T P A N 0 ) ,
I ¯ = I sat ( N 0 N 1 ) ,
P ¯ T P A = α ψ γ P I ¯ ,

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