Abstract

We exploit the coupled emission-states of a single-chip semiconductor InAs/GaAs quantum-dot laser emitting simultaneously on ground-state (λGS = 1245 nm) and excited-state (λES = 1175 nm) to demonstrate coupled-two-state self-mixing velocimetry for a moving diffuse reflector. A 13 Hz-narrow Doppler beat frequency signal at 317 Hz is obtained for a reflector velocity of 3 mm/s, which exemplifies a 66-fold improvement in width as compared to single-wavelength self-mixing velocimetry. Simulation results reveal the physical origin of this signal, the coupling of excited-state and ground-state photons via the carriers, which is unique for quantum-dot lasers and reproduce the experimental results with excellent agreement.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref]
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  15. U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).
  23. M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
    [Crossref]
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    [Crossref]
  25. F. M. Gardner, Phaselock Techniques, 3rd ed. (Wiley, 2005).
    [Crossref]
  26. R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
    [Crossref]
  27. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
    [Crossref]
  28. E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
    [Crossref]
  29. A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
    [Crossref]

2014 (1)

2013 (3)

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Donati and M. Norgia, “Self-Mixing Interferometry for Biomedical Signals Sensing,” IEEE J. Sel. Top. Quantum Electron. 20, 6900108 (2013).

M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
[Crossref]

2012 (2)

2011 (3)

K. Otsuka, “Self-Mixing Thin-Slice Solid-State Laser Metrology,” Sensors 11, 2195–2245 (2011).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

Y.-S. Juan and F.-Y. Lin, “Photonic Generation of Broadly Tunable Microwave Signals Utilizing a Dual-Beam Optically Injected Semiconductor Laser,” IEEE Photon. J. 3, 644–649 (2011).
[Crossref]

2010 (1)

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

2006 (1)

2005 (2)

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

2003 (1)

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

1999 (2)

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999).
[Crossref]

1998 (1)

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

1997 (1)

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
[Crossref]

1994 (1)

1992 (1)

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

1989 (1)

1964 (2)

D. M. Clunie and N. H. Rock, “The laser feedback interferometer,” Rev. Sci. Instr. 41, 489–492 (1964).
[Crossref]

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[Crossref]

Alferov, Zh. I.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Bardella, P.

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

Bedarev, D. A.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Bimberg, D.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).

Bjork, P. E.

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

Bowers, J. E.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Breuer, S.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Cheng, C.-H.

Clunie, D. M.

D. M. Clunie and N. H. Rock, “The laser feedback interferometer,” Rev. Sci. Instr. 41, 489–492 (1964).
[Crossref]

Coldren, L. A.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), Chap. 5.
[Crossref]

Corzine, S. W.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), Chap. 5.
[Crossref]

Cumming, H. Z.

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[Crossref]

Derickson, D. J.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Donati, S.

S. Donati and M. Norgia, “Self-Mixing Interferometry for Biomedical Signals Sensing,” IEEE J. Sel. Top. Quantum Electron. 20, 6900108 (2013).

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
[Crossref]

S. Donati, Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, 2004).

Drzewietzki, L.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Egorov, A. Yu.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Elsäßer, W.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Fiore, A.

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

Gardner, F. M.

F. M. Gardner, Phaselock Techniques, 3rd ed. (Wiley, 2005).
[Crossref]

Gauthier-Lafaye, O.

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

Gioannini, M.

M. Gioannini, “Ground-state power quenching in two-state lasing quantum dot lasers,” J. Appl. Phys. 111, 043108 (2012).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Giuliani, G.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
[Crossref]

Gliese, U.

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

Grundmann, M.

D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).

Helkey, R. J.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Hopkinson, M.

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Houlihan, J.

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Huang, K. F.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Huyet, G.

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Juan, Y.-S.

Y.-S. Juan and F.-Y. Lin, “Photonic Generation of Broadly Tunable Microwave Signals Utilizing a Dual-Beam Optically Injected Semiconductor Laser,” IEEE Photon. J. 3, 644–649 (2011).
[Crossref]

Ko, J.-Y.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

Kopev, P. S.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Kovsh, A. R.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Krakowski, M.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999).
[Crossref]

Ledentsov, N. N.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).

Lee, C.-W.

Lenstra, D.

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999).
[Crossref]

Lin, F.-Y.

Lin, L.-C.

Lin, T.-W.

Liu, J. M.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Makino, H.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

Maksimov, M. V.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Maleev, N. A.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Mandel, P.

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Mar, A.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Markus, A.

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

Mashanovitch, M. L.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), Chap. 5.
[Crossref]

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
[Crossref]

Mocker, H.W.

Montrosset, I.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Musikhin, Yu. G.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Nielsen, T. N.

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

Norgia, M.

S. Donati and M. Norgia, “Self-Mixing Interferometry for Biomedical Signals Sensing,” IEEE J. Sel. Top. Quantum Electron. 20, 6900108 (2013).

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

Norskov, S.

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

Ohtomo, T.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

Otsuka, K.

K. Otsuka, “Self-Mixing Thin-Slice Solid-State Laser Metrology,” Sensors 11, 2195–2245 (2011).
[Crossref]

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

K. Otsuka, “Ultrahigh sensitivity laser Doppler velocimetry with a microchip solid-state laser,” Appl. Opt. 33, 1111–1114 (1994).
[Crossref] [PubMed]

Panajotov, K.

M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
[Crossref]

Paranthoen, C.

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

Provost, J.

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

Rock, N. H.

D. M. Clunie and N. H. Rock, “The laser feedback interferometer,” Rev. Sci. Instr. 41, 489–492 (1964).
[Crossref]

Rossetti, M.

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

Rothberg, S.

Sciamanna, M.

M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
[Crossref]

Simpson, T. B.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Stubkjaer, K. E.

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

Sudo, S.

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

Suvorova, A. A.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Tai, K.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Tanguy, Y.

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Th, G. A.P.

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

Thornton, R. L.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Tsatsulnikov, A. F.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Ustinov, V. M.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Viktorov, E. A.

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Virte, M.

M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
[Crossref]

Volovik, B. V.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Wasserbauer, J. G.

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

Werner, P.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Wieczorek, S.

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999).
[Crossref]

Yeh, Y.

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[Crossref]

Zhukov, A. E.

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

K. Otsuka, T. Ohtomo, H. Makino, S. Sudo, and J.-Y. Ko, “Net motion of an ensemble of many Brownian particles captured with a self-mixing laser,” Appl. Phys. Lett. 94, 241117 (2005).
[Crossref]

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett. 4, 176–178 (1964).
[Crossref]

Appl. Phys. Lett., (1)

E. A. Viktorov, P. Mandel, Y. Tanguy, J. Houlihan, and G. Huyet, “Electron-hole asymmetry and two-state lasing in quantum dot lasers,” Appl. Phys. Lett., 87, 053113 (2005).
[Crossref]

Electron. Lett. (1)

R. J. Helkey, D. J. Derickson, A. Mar, J. G. Wasserbauer, J. E. Bowers, and R. L. Thornton, “Repetition Frequency Stabilisation of Passively Mode-Locked Semiconductor Lasers,” Electron. Lett. 28, 1920–1922 (1992).
[Crossref]

IEEE J. Quant. Electron. (3)

S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback interferometer for measurement of displacements without ambiguity,” IEEE J. Quant. Electron.,  31, 113–119, (1995).
[Crossref]

M. Virte, K. Panajotov, and M. Sciamanna, “Mode competition induced by optical feedback in two-color quantum dot lasers,” IEEE J. Quant. Electron. 49, 578–585 (2013).
[Crossref]

S. Breuer, M. Rossetti, L. Drzewietzki, P. Bardella, I. Montrosset, and W. Elsäßer, “Joint Experimental and Theoretical Investigations of Two-State Mode Locking in a Strongly Chirped Reverse-Biased Monolithic Quantum Dot Laser,” IEEE J. Quant. Electron. 47, 1320–1329 (2011).
[Crossref]

IEEE J. Sel. Top. Quant. Electron. (1)

S. Breuer, M. Rossetti, L. Drzewietzki, I. Montrosset, M. Krakowski, and W. Elsäßer, “Dual-State Absorber-Photocurrent Characteristics and Bistability of Two-Section Quantum-Dot Lasers,” IEEE J. Sel. Top. Quant. Electron. 19, 1901609 (2013).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

A. Markus, O. Gauthier-Lafaye, J. Provost, C. Paranthoen, and A. Fiore, “Impact of intraband relaxation on the performance of a quantum-dot laser,” IEEE J. Sel. Top. Quantum Electron. 9, 1308–1314, (2003).
[Crossref]

S. Donati and M. Norgia, “Self-Mixing Interferometry for Biomedical Signals Sensing,” IEEE J. Sel. Top. Quantum Electron. 20, 6900108 (2013).

IEEE Photon. J. (1)

Y.-S. Juan and F.-Y. Lin, “Photonic Generation of Broadly Tunable Microwave Signals Utilizing a Dual-Beam Optically Injected Semiconductor Laser,” IEEE Photon. J. 3, 644–649 (2011).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

U. Gliese, T. N. Nielsen, S. Norskov, and K. E. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” IEEE Trans. Microw. Theory Tech. 46, 458–468 (1998).
[Crossref]

J. Appl. Phys. (1)

M. Gioannini, “Ground-state power quenching in two-state lasing quantum dot lasers,” J. Appl. Phys. 111, 043108 (2012).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, 283–294 (2002).
[Crossref]

J. Semicond. (1)

B. V. Volovik, A. F. Tsatsulnikov, D. A. Bedarev, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, N. N. Ledentsov, M. V. Maksimov, N. A. Maleev, Yu. G. Musikhin, A. A. Suvorova, V. M. Ustinov, P. S. Kopev, Zh. I. Alferov, D. Bimberg, and P. Werner, “Long-wavelength emission in structures with quantum dots formed in the stimulated decomposition of a solid solution at strained islands,” J. Semicond. 33, 901–905 (1999).
[Crossref]

Opt. Commun. (2)

L. Drzewietzki, G. A.P. Th, M. Gioannini, S. Breuer, I. Montrosset, W. Elsäßer, M. Hopkinson, and M. Krakowski, “Theoretical and experimental investigations of the temperature dependent continuous wave lasing characteristics and the switch-on dynamics of an InAs/InGaAs quantum-dot semiconductor laser,” Opt. Commun. 283, 5092–5098 (2010).
[Crossref]

S. Wieczorek, B. Krauskopf, and D. Lenstra, “A unifying view of bifurcations in a semiconductor laser subject to optical injection,” Opt. Commun. 172, 279–295 (1999).
[Crossref]

Opt. Express (2)

Quantum Semiclass. Opt. (1)

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Rev. Sci. Instr. (1)

D. M. Clunie and N. H. Rock, “The laser feedback interferometer,” Rev. Sci. Instr. 41, 489–492 (1964).
[Crossref]

Sensors (1)

K. Otsuka, “Self-Mixing Thin-Slice Solid-State Laser Metrology,” Sensors 11, 2195–2245 (2011).
[Crossref]

Other (4)

D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), Chap. 5.
[Crossref]

F. M. Gardner, Phaselock Techniques, 3rd ed. (Wiley, 2005).
[Crossref]

S. Donati, Electro-Optical Instrumentation: Sensing and Measuring with Lasers (Prentice Hall, 2004).

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Figures (7)

Fig. 1
Fig. 1 Schematic of the experimental coupled two-state self-mixing velocimetry set-up realized by a two-state QD laser. Emission diagnosis equipment is not shown.
Fig. 2
Fig. 2 Experimentally obtained two-state emission: (a) Optical spectrum and (b) time domain signal of state-resolved ES-self-mixing velocimetry.
Fig. 3
Fig. 3 Experimentally obtained two-state self-mixing velocimetry signals. The reflector velocity is 3 mm/s. (a) Two-state self-mixing velocimetry and low-pass filtered two-state self-mixing velocimetry time-signal. (b) Radio-frequency spectrum measured simultaneously with the time-signal of Fig. 3(a) and Fourier transform of time domain signal.
Fig. 4
Fig. 4 Experimentally obtained electrical spectra of the coupled two-state self-mixing velocimetry for increasing reflector velocity displayed as a contour plot.
Fig. 5
Fig. 5 (a) Simplified set-up considered in the modelling. (b) Simulated photon density versus current characteristic of the laser without external cavity feedback. GS photon density (red), ES photon density (blue) and total photon density (black) are calculated with the model presented in [16].
Fig. 6
Fig. 6 (a,c) Simulation results of total normalized photon density (sGS + sES) versus time and (b,d) corresponding Fourier transform. The red line is the low frequency component obtained by low pass filtering the time-domain traces. The results in (a) and (b) are obtained by the two-state emitting laser, whereas in (c) and (d) they are obtained by two independent lasers emitting from the GS and ES, respectively. Letters A and B in (a) indicate time frames discussed in the following and in Fig. 7. In (b) also the Fourier transform from the experimental result of Fig. 3(a) is included.
Fig. 7
Fig. 7 (a,b) Simulation results of the equivalent GS (blue) and ES (red) facet reflectivity calculated according to Eq. (2). The dashed line is the equivalent reflectivity with Δ R GS , ES eq = 0 . (c,d) Normalized photon density (black line) and filtered low frequency component (red line). The time frames of (a,c) and (b,d) correspond to the ones indicated with letter A/B in Fig. 6(a).

Equations (11)

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

| r 2 , GS , ES eff | 2 = | r 2 + t 2 2 η F r 3 exp ( j Φ GS , ES ) | 2 r 2 2 + δ R 2 , GS , ES eff .
δ R 2 , GS , ES eff = 2 r 2 η F r 3 t 2 2 cos ( Φ 0 , GS , ES + 2 v refl c ω GS , ES ( T T 0 ) )
d s GS , ES d t = β sp R sp , GS , ES + ρ GS , ES e + ρ GS , ES h 1 τ g , GS , ES s GS , ES s GS , ES τ p , GS , ES eff .
1 τ p , GS , ES eff = v g L a log ( 1 r 1 | r 2 , GS , ES eff | ) + v g α i .
n 0 , ES e + μ ES δ ρ ES e τ r , GS e ( 1 ρ 0 , GS δ ρ GS e ) = s 0 , GS + δ s GS τ p , GS ( 1 δ τ p , GS eff τ p , GS ) n 0 , W L e + δ n W L e τ c , ES e ( 1 ρ 0 , ES δ ρ ES e ) n 0 , ES e + μ ES δ ρ ES e τ r , GS e ( 1 ρ 0 , GS δ ρ GS e ) = s 0 , ES + δ s ES τ p , ES ( 1 δ τ p , ES eff τ p , ES )
δ s tot = δ s GS + δ s ES = s 0 , GS a GS δ τ p , GS eff τ p , GS + s 0 , ES a ES δ τ p , ES eff τ p , ES + ( τ p , ES a ES τ p , GS a GS ) n 0 , ES e δ ρ GS e + μ ES δ ρ ES e δ ρ GS e μ ES δ ρ ES e ( 1 ρ 0 , GS ) τ r , GS e
δ s tot s 0 , GS δ τ p , GS e f f τ p + s 0 , ES δ τ p , ES e f f τ p + δ τ p , ES e f f δ τ p , GS e f f τ p , GS e n 0 , ES e δ ρ GS e .
δ ρ GS e = τ g , GS τ p 2 δ τ p , GS eff
δ τ p , GS , ES eff = τ p 2 2 r 2 2 v g L a δ R 2 , GS , ES eff .
δ s coupling n 0 , ES e τ r , GS e ( δ τ p , ES eff δ τ p , GS eff ) δ τ p , GS eff τ g , GS τ p 2 .
δ R 2 , GS eff δ R 2 , ES eff = η F r 2 r 3 t 2 2 { cos ( Φ 0 , GS Φ 0 , ES + 2 v refl c ( ω ES ω GS ) ( T T 0 ) ) } .

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