Abstract

This paper presents the calculation of amplitude and relative phase of signals at the three outputs available in a self-mixing interferometer, i.e. the front output on the target side, the back output on the rear of the chip, and, for diode laser, the junction voltage output. Front and rear outputs are observed to be in phase for the He-Ne laser while they are in phase opposition in the diode laser. This discrepancy can now be explained theoretically. It will also be shown how the junction voltage output is always in phase opposition with respect to the rear output. Experimental measurements were carried out on two sources: a laser diode and a He-Ne laser, validating the calculations.

© 2006 Optical Society of America

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References

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  1. S. Donati: "Laser interferometry by induced modulation of the cavity field," J. Appl. Phys. 49, 495-497 (1978).
    [CrossRef]
  2. S. Donati: Electrooptical iInstrumentation, (Prentice Hall, 2004), Chap. 2.2.
  3. S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
    [CrossRef]
  4. S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
    [CrossRef]
  5. W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
    [CrossRef]
  6. S. Donati, and S. Merlo, "A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-947 (1996).
    [CrossRef]
  7. M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
    [CrossRef]
  8. T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
    [CrossRef]
  9. S. Donati, and C. Mirasso, eds., "Optical Chaotic Cryptography," IEEE J. Quantum Electron. 38, 1338 (2002).
  10. R. Lang, and K. Kobayashi: "External optical feedback effects on semiconductor laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
    [CrossRef]
  11. R. Juskaitis, N. P. Rea, and T. Wilson: "Semiconductor laser confocal microscopy," Appl. Opt. 33, 578-584 (1994).
    [CrossRef] [PubMed]
  12. R. H. Webb, and F. J. Rogomentich: "Microlaser microscope using self-mixing detection for confocality," Opt. Lett. 20, 533-535 (1995).
    [CrossRef] [PubMed]
  13. see Ref.2, Sect.A1.1, A1.2.
  14. M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
    [CrossRef]

2002 (1)

S. Donati, and C. Mirasso, eds., "Optical Chaotic Cryptography," IEEE J. Quantum Electron. 38, 1338 (2002).

2001 (2)

M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
[CrossRef]

1996 (1)

S. Donati, and S. Merlo, "A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-947 (1996).
[CrossRef]

1995 (2)

R. H. Webb, and F. J. Rogomentich: "Microlaser microscope using self-mixing detection for confocality," Opt. Lett. 20, 533-535 (1995).
[CrossRef] [PubMed]

S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
[CrossRef]

1994 (1)

1992 (2)

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

1989 (1)

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

1980 (1)

R. Lang, and K. Kobayashi: "External optical feedback effects on semiconductor laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

1978 (1)

S. Donati: "Laser interferometry by induced modulation of the cavity field," J. Appl. Phys. 49, 495-497 (1978).
[CrossRef]

Bosch, T.

T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
[CrossRef]

Boyd, J. T.

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

Boyle, W. J. O.

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

d'Alessandro, D.

M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Donati, S.

S. Donati, and C. Mirasso, eds., "Optical Chaotic Cryptography," IEEE J. Quantum Electron. 38, 1338 (2002).

T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
[CrossRef]

M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

S. Donati, and S. Merlo, "A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-947 (1996).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
[CrossRef]

S. Donati: "Laser interferometry by induced modulation of the cavity field," J. Appl. Phys. 49, 495-497 (1978).
[CrossRef]

Giuliani, G.

S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
[CrossRef]

Grattan, K. T. W.

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

Ikeda, H.

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

Jackson, H. E.

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

Juskaitis, R.

Kobayashi, K.

R. Lang, and K. Kobayashi: "External optical feedback effects on semiconductor laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Kumar, M.

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

Lang, R.

R. Lang, and K. Kobayashi: "External optical feedback effects on semiconductor laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Merlo, S.

S. Donati, and S. Merlo, "A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-947 (1996).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
[CrossRef]

Mirasso, C.

S. Donati, and C. Mirasso, eds., "Optical Chaotic Cryptography," IEEE J. Quantum Electron. 38, 1338 (2002).

Naito, H.

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

Norgia, M.

M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Palmer, A. W.

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

Rea, N. P.

Rogomentich, F. J.

Servagent, N.

T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
[CrossRef]

Shinoara, S.

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

Sumi, M.

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

Wang, W.

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

Webb, R. H.

Weiss, B. L.

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

Wilson, T.

Yoshida, H.

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

Appl. Opt. (1)

IEEE J. Lightwave Technol. (1)

W. Wang, W. J. O. Boyle, K. T. W. Grattan, and A. W. Palmer: "Self-mixing Interference in a diode laser for optical sensing applications," IEEE J. Lightwave Technol. 12, 1577-1587 (1992).
[CrossRef]

IEEE J. Quantum Electron. (5)

M. Norgia, S. Donati, and D. d'Alessandro, "Interferometric measurements of displacement on a diffusing target by a speckle-tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo: "Laser diode feedback interferometer for measurement of displacement without ambiguity," IEEE J. Quantum Electron. 31,113-119 (1995).
[CrossRef]

S. Donati, and C. Mirasso, eds., "Optical Chaotic Cryptography," IEEE J. Quantum Electron. 38, 1338 (2002).

R. Lang, and K. Kobayashi: "External optical feedback effects on semiconductor laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

M. Kumar, J. T. Boyd, H. E. Jackson, and B. L. Weiss: "Birefringent properties of GaAlAs multiple quantum well planar optical waveguides," IEEE J. Quantum Electron. 28, 1678-1689 (1992).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

S. Shinoara, H. Naito, H. Yoshida, H. Ikeda, and M. Sumi: "Compact and versatile self-mixing type semiconductor laser doppler velocimemeter with direction discrimination circuit," IEEE Trans. Instrum. Meas. 38, 574-577 (1989).
[CrossRef]

S. Donati, and S. Merlo, "A PC-interfaced, compact laser-diode feedback interferometer for displacement measurements," IEEE Trans. Instrum. Meas. 45, 942-947 (1996).
[CrossRef]

J. Appl. Phys. (1)

S. Donati: "Laser interferometry by induced modulation of the cavity field," J. Appl. Phys. 49, 495-497 (1978).
[CrossRef]

Opt. Eng. (1)

T. Bosch, N. Servagent, and S. Donati, "Optical feedback interferometry for sensing applications," Opt. Eng. 40, 20-27 (2001).
[CrossRef]

Opt. Lett. (1)

Other (2)

see Ref.2, Sect.A1.1, A1.2.

S. Donati: Electrooptical iInstrumentation, (Prentice Hall, 2004), Chap. 2.2.

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Figures (6)

Fig. 1.
Fig. 1.

Different pickups of the output signal from a self-mixing interferometer: from rear and front mirror, and from the junction voltage of the laser diode.

Fig. 2.
Fig. 2.

Electric field E0 has unity gain along path 1–4, and the self-mix contribution comes from propagation on the 1–6 (bottom) path. Another contribution to E1 comes from the reflection at mirror M1, point 4 of the bottom feedback path.

Fig. 3.
Fig. 3.

Self-mixing waveforms detected at the front PD1 (top trace) and rear PD2 (bottom trace) photodiodes in a 17cm length, 0.5mW He-Ne laser subjected to self-mixing feedback from a remote (s=40cm) loudspeaker driven with a sinusoidal signal at 40Hz, showing the in-phase condition. Preamplifier output voltages had dc components of 192mV and 11mV, respectively, and the modulation indexes were m1=0.239 (front output) and m2=0.358 (rear output). The trace of PD2 is noisier than that of PD1 but we didn’t use balanced noise performance for the two preamplifiers of the photodiodes.

Fig. 4.
Fig. 4.

Typical self-mixing waveforms obtained with a semiconductor laser well above threshold. Left side: front (top) and rear (bottom) photodiode outputs are in phase-opposition. Right hand side shows the front output (top) and junction-voltage (bottom) output. Ratio of the modulation indexes of PD1 and PD2 was m1/m2=- 0.57 at Idc=70mA bias current. Peak-to-peak amplitudes were approximately: Iph1≈50µA, Iph2≈5µA, ΔVak≈100µV, and distance to target was 40cm.

Fig. 5.
Fig. 5.

The I-P characteristic of the laser diode (threshold is 40mA) and the modulation index ratio m1/m2 as a function of dc drive current. Inversion of the sign is at ≈ 60mA.

Fig. 6.
Fig. 6.

The ratio m1/m2 of modulation indexes for the front and rear mirror outputs, as given by Eq. (12), plotted versus the front mirror reflectivity R1, for some values of the (power) round trip gain 2γL: left, for the diode laser, right, for the He-Ne laser. Ellipse is the experimental point for a 633nm He-Ne laser with R1=0.97, in which the self-mixing outputs have m1/m2=0.67, implying a gain per pass 2γL=0.06. Dots are for the 832nm GaAlAs diode laser with R1=R2=0.288: the measured values of m1/m2 plotted here should match theoretical values (from top to bottom) of 2γL=2.4, 4.94, 6.5 and 9.0, indicated by the short dotted lines.

Equations (15)

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Δ E = E 0 i t 1 e 2 iks A i t 1 e γ L + 2 ikL r 2 = E 0 ( t 1 2 ) e 2 iks A r 1
E 2 = E 0 r 1 e γL 2 + iks i t 2 = E 0 ( r 1 r 2 ) i t 2
( d dt ) E = [ α βE 2 Γ ] E + ( c 2 L ) Re { Δ E }
Δ E sm = Δ E cos 2 ks ( c 2 L ) 2 ( α Γ ) .
Δ E sm = Δ E cos 2 ks ( 2 γ L + ln R 1 R 2 ) 1
E 01 + Δ E sm 1 = i t 1 E 0 [ 1 ( t 1 2 r 1 ) A cos 2 ks ( 2 γL + ln R 1 R 2 ) 1 ]
E 02 + Δ E sm 2 = ( r 1 r 2 ) i t 2 E 0 [ 1 ( t 1 2 r 1 ) A cos 2 ks ( 2 γL + ln R 1 R 2 ) 1 ] .
Δ E ref = E 0 i t 1 e 2 iks A r 1 = Δ E r 1 2 i t 1
E 01 + Δ E tot = i t 1 E 0 { 1 ( t 1 2 r 1 ) A cos 2 ks [ ( 2 γL + ln R 1 R 2 ) 1 r 1 2 t 1 2 ] } .
m 1 = Δ E tot 1 E 01 = ( t 1 2 r 1 ) A cos 2 ks [ ( 2 γL + ln R 1 R 2 ) 1 R 1 2 T 1 2 ] .
m 2 = Δ E tot 2 E 02 = ( t 1 2 r 1 ) A cos 2 ks [ ( 2 γL + ln R 1 R 2 ) 1 ] .
m 1 m 2 = 1 ( R 1 T 1 ) ( 2 γL + ln R 1 R 2 ) .
( d dt ) N = J ed N τ r G ( N N 0 ) E 2
Δ N = ( 1 τ r + GE 0 ) 1 G ( N N 0 ) Δ E
Δ V ak = ( 1 τ r + GE 0 ) 1 ( 2 kT e ) G ( N N 0 ) / N 0 Δ E

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