Abstract

We present a simple analytical model that describes the injection current and temperature dependence of optical feedback interferometry signal strength for a single-mode laser diode. The model is derived from the Lang and Kobayashi rate equations, and is developed both for signals acquired from the monitoring photodiode (proportional to the variations in optical power) and for those obtained by amplification of the corresponding variations in laser voltage. The model shows that both the photodiode and the voltage signal strengths are dependent on the laser slope efficiency, which itself is a function of the injection current and the temperature. Moreover, the model predicts that the photodiode and voltage signal strengths depend differently on injection current and temperature. This important model prediction was proven experimentally for a near-infrared distributed feedback laser by measuring both types of signals over a wide range of injection currents and temperatures. Therefore, this simple model provides important insight into the radically different biasing strategies required to achieve optimal sensor sensitivity for both interferometric signal acquisition schemes.

© 2015 Optical Society of America

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References

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  1. T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).
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    [Crossref]
  4. Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
    [Crossref]
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    [Crossref]
  7. Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. 17, 1216–1225 (1981).
    [Crossref]
  8. S. Donati, “Responsivity and noise of self-mixing photodetection schemes,” IEEE J. Quantum Electron. 47, 1428–1433 (2011).
    [Crossref]
  9. M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
    [Crossref]
  10. K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (4)

2013 (2)

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

S. Donati and R.-H. Horng, “The diagram of feedback regimes revisited,” IEEE J. Sel. Top. Quantum Electron. 19, 1500309 (2013).
[Crossref]

2012 (1)

2011 (3)

R. S. Matharu, J. Perchoux, R. Kliese, Y. L. Lim, and A. D. Rakić, “Maintaining maximum signal-to-noise ratio in uncooled vertical-cavity surface-emitting laser-based self-mixing sensors,” Opt. Lett. 36, 3690–3692 (2011).
[Crossref]

S. Donati, “Responsivity and noise of self-mixing photodetection schemes,” IEEE J. Quantum Electron. 47, 1428–1433 (2011).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

2006 (1)

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).

1995 (1)

1994 (1)

1984 (1)

G. Acket, D. Lenstra, A. den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[Crossref]

1981 (2)

J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “The intrinsic electrical equivalent-circuit of a laser diode,” IEEE J. Quantum Electron. 17, 4–7 (1981).
[Crossref]

Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. 17, 1216–1225 (1981).
[Crossref]

1980 (2)

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Acket, G.

G. Acket, D. Lenstra, A. den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[Crossref]

Barbieri, S.

Bertling, K.

Bes, C.

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).

Bosch, T.

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).

Choi, D.

Citrin, D. S.

Coldren, L. A.

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

Corzine, S. W.

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

Davies, A. G.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Dean, P.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

den Boef, A.

G. Acket, D. Lenstra, A. den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[Crossref]

Donati, S.

S. Donati and R.-H. Horng, “The diagram of feedback regimes revisited,” IEEE J. Sel. Top. Quantum Electron. 19, 1500309 (2013).
[Crossref]

S. Donati, “Responsivity and noise of self-mixing photodetection schemes,” IEEE J. Quantum Electron. 47, 1428–1433 (2011).
[Crossref]

G. Giuliani and S. Donati, “Laser interferometry,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane and K. A. Shore, eds. (Wiley, 2005), pp. 217–255.

Freakley, C. S.

Fuentes, M. A.

Giuliani, G.

G. Giuliani and S. Donati, “Laser interferometry,” in Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, D. M. Kane and K. A. Shore, eds. (Wiley, 2005), pp. 217–255.

Harder, C.

J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “The intrinsic electrical equivalent-circuit of a laser diode,” IEEE J. Quantum Electron. 17, 4–7 (1981).
[Crossref]

Harrison, P.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Herbert, J.

Hertsens, T.

T. Hertsens, “Measuring diode laser characteristics,” ILX Lightwave Appl. Note 5 (2005).

Höfling, S.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Horng, R.-H.

S. Donati and R.-H. Horng, “The diagram of feedback regimes revisited,” IEEE J. Sel. Top. Quantum Electron. 19, 1500309 (2013).
[Crossref]

Ikonic, Z.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Indjin, D.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Jagtap, V.

Juskaitis, R.

Kamp, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Katz, J.

J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “The intrinsic electrical equivalent-circuit of a laser diode,” IEEE J. Quantum Electron. 17, 4–7 (1981).
[Crossref]

Khanna, S. P.

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Kim, B.

Kliese, R.

R. S. Matharu, J. Perchoux, R. Kliese, Y. L. Lim, and A. D. Rakić, “Maintaining maximum signal-to-noise ratio in uncooled vertical-cavity surface-emitting laser-based self-mixing sensors,” Opt. Lett. 36, 3690–3692 (2011).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Koeth, J.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Kou, K.

Lachab, M.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
[Crossref]

Lenstra, D.

G. Acket, D. Lenstra, A. den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[Crossref]

Li, L.

Li, X.

Lim, Y. L.

J. R. Tucker, A. Mowla, J. Herbert, M. A. Fuentes, C. S. Freakley, K. Bertling, Y. L. Lim, R. S. Matharu, J. Perchoux, T. Taimre, S. J. Wilson, and A. D. Rakić, “Self-mixing sensing system based on uncooled vertical-cavity surface-emitting laser array: linking multichannel operation and enhanced performance,” Opt. Lett. 39, 394–397 (2014).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

R. S. Matharu, J. Perchoux, R. Kliese, Y. L. Lim, and A. D. Rakić, “Maintaining maximum signal-to-noise ratio in uncooled vertical-cavity surface-emitting laser-based self-mixing sensors,” Opt. Lett. 36, 3690–3692 (2011).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Linfield, E. H.

M. Ravaro, S. Barbieri, G. Santarelli, V. Jagtap, C. Manquest, C. Sirtori, S. P. Khanna, and E. H. Linfield, “Measurement of the intrinsic linewidth of terahertz quantum cascade lasers using a near-infrared frequency comb,” Opt. Express 20, 25654–25661 (2012).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Locquet, A.

Manquest, C.

Margalit, S.

J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “The intrinsic electrical equivalent-circuit of a laser diode,” IEEE J. Quantum Electron. 17, 4–7 (1981).
[Crossref]

Mashanovitch, M. L.

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

Matharu, R. S.

Mitsuhashi, Y.

Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. 17, 1216–1225 (1981).
[Crossref]

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

Mitsutsuka, S.

Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. 17, 1216–1225 (1981).
[Crossref]

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

Morikawa, T.

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

Mowla, A.

Nikolic, M.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Perchoux, J.

Plantier, G.

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).

Rakic, A. D.

J. R. Tucker, A. Mowla, J. Herbert, M. A. Fuentes, C. S. Freakley, K. Bertling, Y. L. Lim, R. S. Matharu, J. Perchoux, T. Taimre, S. J. Wilson, and A. D. Rakić, “Self-mixing sensing system based on uncooled vertical-cavity surface-emitting laser array: linking multichannel operation and enhanced performance,” Opt. Lett. 39, 394–397 (2014).
[Crossref]

T. Taimre and A. D. Rakić, “On the nature of Acket’s characteristic parameter C in semiconductor lasers,” Appl. Opt. 53, 1001–1006 (2014).
[Crossref]

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

R. S. Matharu, J. Perchoux, R. Kliese, Y. L. Lim, and A. D. Rakić, “Maintaining maximum signal-to-noise ratio in uncooled vertical-cavity surface-emitting laser-based self-mixing sensors,” Opt. Lett. 36, 3690–3692 (2011).
[Crossref]

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Ravaro, M.

Rea, N. P.

Rochford, K. B.

Rose, A. H.

Sahai, A. A.

Sakurai, K.

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

Santarelli, G.

Scalise, L.

T. Bosch, C. Bes, L. Scalise, and G. Plantier, “Optical feedback interferometry,” Encyclopedia Sens. X, 1–20 (2006).

Shimada, J.

Y. Mitsuhashi, J. Shimada, and S. Mitsutsuka, “Voltage change across the self-coupled semiconductor laser,” IEEE J. Quantum Electron. 17, 1216–1225 (1981).
[Crossref]

Y. Mitsuhashi, T. Morikawa, J. Shimada, K. Sakurai, and S. Mitsutsuka, “Polarization-rotated optical feedback in self-coupled optical pickup,” Opt. Commun. 34, 309–310 (1980).
[Crossref]

Sirtori, C.

Taimre, T.

Tucker, J. R.

Valavanis, A.

Y. L. Lim, P. Dean, M. Nikolić, R. Kliese, S. P. Khanna, M. Lachab, A. Valavanis, D. Indjin, Z. Ikonić, P. Harrison, E. H. Linfield, A. G. Davies, S. J. Wilson, and A. D. Rakić, “Demonstration of a self-mixing displacement sensor based on terahertz quantum cascade lasers,” Appl. Phys. Lett. 99, 081108 (2011).
[Crossref]

Verbeek, B.

G. Acket, D. Lenstra, A. den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[Crossref]

von Edlinger, M.

K. Bertling, Y. L. Lim, T. Taimre, D. Indjin, P. Dean, R. Weih, S. Höfling, M. Kamp, M. von Edlinger, J. Koeth, and A. D. Rakić, “Demonstration of the self-mixing effect in interband cascade lasers,” Appl. Phys. Lett. 103, 231107 (2013).
[Crossref]

Weih, R.

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Figures (8)

Fig. 1.
Fig. 1. Experimental setup for measuring velocity of a rotating disk. The disk is tilted around the vertical axis by 10° to produce a small velocity component in the direction of the laser beam.
Fig. 2.
Fig. 2. (a) Output power as a function of laser injection current at different temperatures (in the temperature range from 40 ° C to + 80 ° C in steps of 5 ° C ), and (b) slope efficiency and threshold current as a function of temperature. Slope efficiency decreases with temperature, while injection current threshold increases.
Fig. 3.
Fig. 3. Dependence of the PD signal strength on injection current: measured (red solid); modeled (constant slope efficiency of an ideal laser diode, green dashed); modeled (behavioral slope efficiency, blue solid).
Fig. 4.
Fig. 4. Dependence of the LV signal strength on injection current: measured (red solid); modeled (constant slope efficiency of an ideal laser diode, green dashed); modeled (behavioral slope efficiency, blue solid).
Fig. 5.
Fig. 5. Dependence of the PD signal strength on temperature: measured (red solid); modeled (behavioral slope efficiency, blue solid).
Fig. 6.
Fig. 6. Dependence of the LV signal strength on temperature: measured (red solid); modeled (behavioral slope efficiency, blue solid).
Fig. 7.
Fig. 7. PD signal strength as a function of the injection current and temperature: (a) measured and (b) modeled.
Fig. 8.
Fig. 8. LV signal strength as a function of the injection current and temperature: (a) measured and (b) modeled.

Equations (18)

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d E d t = 1 2 [ G N ( N N tr ) 1 τ p ] E + κ E ( t τ D ) cos ( ω τ D ) ,
d N d t = I q V N τ e G N ( N N tr ) E 2 .
κ = 1 τ L ( 1 R 2 ) R ext R 2 ,
P = P 0 [ 1 + m cos ( ω τ D ) ] ,
m = 2 κ τ p ( 1 + 1 S 0 G N τ e ) ,
1 τ p = G N ( N th N tr ) ,
m = 2 κ τ p ( 1 + I th ( N th N tr ) N th ( I I th ) ) ,
Δ P = 2 κ τ p η ( I ) ( I I th N tr N th ) .
Δ v = 2 k T q N th Δ N ,
Δ N = G N ( N th N tr ) 1 τ e + G N S 0 Δ S ,
Δ N = τ e τ p · Δ S 1 + G N S 0 τ e .
Δ N = τ e τ p ( m 2 κ τ p ) S 0 .
Δ N = 2 κ τ e S 0 I th ( N th N tr ) N th ( I I th ) .
S 0 = τ p V ω η ( I ) ( I I th ) ,
Δ v = 4 κ τ e η ( I ) τ p V ω · k T q N th I th ( 1 N tr N th ) .
Δ v = 4 κ τ p η ( I ) k T ω ( 1 N tr N th ) .
I th ( T + Δ T ) = I th ( T ) e Δ T T 0 ,
η ( T + Δ T ) = η ( T ) e Δ T T η ,

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