Abstract

In this Letter, we experimentally show that transient phenomenons in self-mixing signals from a moving target contain information about the target reflectivity and distance. These transient phenomenons are well explained with a dynamical model of the laser diode, which is used to trace an abacus giving the target reflectivity and distance from a measured high-bandwidth, self-mixing signal.

© 2012 Optical Society of America

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References

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  1. K. Petermann, Laser Diode Modulation and Noise(Springer, 1991).
  2. G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
    [CrossRef]
  3. R. Kliese, Y. L. Lim, T. Bosch, and A. D. Rakic, Opt. Lett. 35, 814 (2010).
    [CrossRef]
  4. F. P. Mezzapesa, A. Ancona, T. Sibillano, F. De Lucia, M. Dabbicco, P. Mario Lugarà, and G. Scamarcio, Opt. Lett. 36, 822 (2011).
    [CrossRef]
  5. U. Zabit, O. Bernal, T. Bosch, and F. Bony, Opt. Lett. 36, 612 (2011).
    [CrossRef]
  6. M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
    [CrossRef]
  7. D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity (Wiley, 2005).

2011 (2)

2010 (1)

2007 (1)

M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
[CrossRef]

1984 (1)

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Acket, G. A.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Ancona, A.

Bernal, O.

Boef, A. J. Den

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Bony, F.

Bosch, T.

Dabbicco, M.

De Lucia, F.

Donati, S.

M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
[CrossRef]

Guiliani, G.

M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
[CrossRef]

Kane, D. M.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity (Wiley, 2005).

Kliese, R.

Lenstra, D.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Lim, Y. L.

Lugarà, P. Mario

Mezzapesa, F. P.

Norgia, M.

M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
[CrossRef]

Petermann, K.

K. Petermann, Laser Diode Modulation and Noise(Springer, 1991).

Rakic, A. D.

Scamarcio, G.

Shore, K. A.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity (Wiley, 2005).

Sibillano, T.

Verbeek, B. H.

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

Zabit, U.

IEEE J. Quantum Electron. (1)

G. A. Acket, D. Lenstra, A. J. Den Boef, and B. H. Verbeek, IEEE J. Quantum Electron. 20, 1163 (1984).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. Norgia, G. Guiliani, and S. Donati, IEEE Trans. Instrum. Meas. 56, 1894 (2007).
[CrossRef]

Opt. Lett. (3)

Other (2)

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity (Wiley, 2005).

K. Petermann, Laser Diode Modulation and Noise(Springer, 1991).

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Figures (6)

Fig. 1.
Fig. 1.

Typical steady-state simulation in the moderate feedback regime for a target moving at 1m/s.

Fig. 2.
Fig. 2.

Schematic of the experimental setup.

Fig. 3.
Fig. 3.

Solid: measured time series of a typical signal for a medium r3 (τext=14.9ns, averaging on 512 acquisitions). Dashed: the same signal, filtered.

Fig. 4.
Fig. 4.

Measured period of the damped oscillations versus time of flight to the target, for a tenfold variation of r3, fitted by a least square method.

Fig. 5.
Fig. 5.

Simulated signal in the dynamical model for two different r3 and τext. Compare with Fig. 3.

Fig. 6.
Fig. 6.

(a) Abacus giving the oscillations period 2π/Ω and decay time τ versus τext and r3. (b) Using the abacus with experimental data corresponding to Fig. 3 to estimate τext and r3. (c) Using the abacus with the data points at 14.89 ns in Fig. 4 to evaluate a ratio of r3. The gray areas represent uncertainties on the experimental data.

Equations (8)

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dn(t)dt=IeVn(t)τegvgS(t)V,
dS(t)dt=S(t)τph(g/gth1)+2ζτinS(t)S(tτext)cos(ωthτext+ϕ(t)ϕ(tτext)),
dϕ(t)dt=αvg2gn(n(t)nth)ζτinS(tτext)S(t)·sin(ωthτext+ϕ(t)ϕ(tτext)),
(n(t),S(t),ω(t))=(n0,S0,ω0)+(Δn(t),ΔS(t),Δω(t)),
ΔX=ΔX0ej(Ωt+φX)et/τ,
1=αvga2Δn0ejφnΔω0ejφω+ζτL(1eτext/τjΩτext)·(12S0ΔS0ejφSΔω0ejφωsin(ω0τext)cos(ω0τext)jΩ1/τ),
Δω0ejφωΔS0ejφS=[1τjΩ+g0/gth1τph+aS0τphgthΔn0ejφnΔS0ejφS+ζτL(1+eτext/τjΩτext)cos(ω0τext)]·[2ζτLS0jΩ1/τ(1eτext/τjΩτext)sin(ω0τext)]1,
Δn0ejφnΔS0ejφS=g0Vvg(jΩ1/τ+1/τe)+aS0,

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