Abstract

We demonstrate a compact in-line interferometer for direction-sensitive displacement measurement by optical feedback detection with a semiconductor laser (SL) light source. Two reflected beams from a semitransparent reference mirror and a reflecting test object interfere in the SL medium, causing a variation in its output power. The reference mirror is located between the SL output facet and the test object. The performance of the interferometer is investigated numerically and experimentally to determine its optimal operating conditions. We have verified the operating conditions where the behavior of the SL output power profile could indicate accurately the displacement magnitude and direction of the moving test object. The profile behavior is robust against variations in optical feedback and scale of the interferometer configuration.

© 2005 Optical Society of America

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References

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  1. P. Hariharan, Optical Interferometry, 2nd ed. (Academic, New York, 2003).
  2. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999).
    [CrossRef]
  3. R. Lang, K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  4. D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
    [CrossRef]
  5. H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
    [CrossRef]
  6. M. Pan, B. Shi, G. Gray, “Semiconductor laser dynamics subject to strong optical feedback,” Opt. Lett. 22, 166–168 (1997).
    [CrossRef] [PubMed]
  7. Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
    [CrossRef]
  8. M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
    [CrossRef]
  9. M. R. Daza, C. Saloma, “Jitter dynamics of a gain switched semiconductor laser under self-feedback and external optical injection,” IEEE J. Quantum Electron. 37, 254–264 (2001).
    [CrossRef]
  10. P. J. Rodrigo, M. Lim, C. Saloma, “Optical-feedback semiconductor laser Michelson interferometer for displacement measurements with directional discrimination,” Appl. Opt. 40, 506–513 (2001).
    [CrossRef]
  11. P. Rodrigo, M. Lim, C. Saloma, “Direction-sensitive sub-wavelength displacement measurements at diffraction-limited resolution,” Opt. Lett. 27, 25–27 (2002).
    [CrossRef]
  12. I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
    [CrossRef] [PubMed]
  13. R. Juskaitis, N. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
    [CrossRef] [PubMed]
  14. R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
    [CrossRef]
  15. L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).
  16. T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).
  17. S. K. Ozdemir, T. Takasu, S. Shinohara, H. Yoshida, M. Sumi, “Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes,” Appl. Opt. 38, 1968–1974 (1999).
    [CrossRef]
  18. S. Donati, G. Giuliani, S. Merlo, “Laser diode feedback interferometer for measurement of displacement without ambiguity,” IEEE J. Quantum Electron. 31, 113–119 (1995).
    [CrossRef]

2003 (1)

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

2002 (1)

2001 (2)

P. J. Rodrigo, M. Lim, C. Saloma, “Optical-feedback semiconductor laser Michelson interferometer for displacement measurements with directional discrimination,” Appl. Opt. 40, 506–513 (2001).
[CrossRef]

M. R. Daza, C. Saloma, “Jitter dynamics of a gain switched semiconductor laser under self-feedback and external optical injection,” IEEE J. Quantum Electron. 37, 254–264 (2001).
[CrossRef]

1999 (3)

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

S. K. Ozdemir, T. Takasu, S. Shinohara, H. Yoshida, M. Sumi, “Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes,” Appl. Opt. 38, 1968–1974 (1999).
[CrossRef]

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

1997 (2)

M. Pan, B. Shi, G. Gray, “Semiconductor laser dynamics subject to strong optical feedback,” Opt. Lett. 22, 166–168 (1997).
[CrossRef] [PubMed]

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

1995 (1)

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

1994 (4)

R. Juskaitis, N. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

1984 (1)

D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

1980 (1)

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

Alarousu, E.

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999).
[CrossRef]

Daza, M.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Daza, M. R.

M. R. Daza, C. Saloma, “Jitter dynamics of a gain switched semiconductor laser under self-feedback and external optical injection,” IEEE J. Quantum Electron. 37, 254–264 (2001).
[CrossRef]

Donati, S.

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

Elsasser, W.

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Fischer, I.

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Fujita, K.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Giuliani, G.

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

Gobel, E.

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Gray, G.

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, New York, 2003).

Hast, J.

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

Hess, O.

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Ikeda, H.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

Jaskorzyñska, B.

D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Juskaitis, R.

R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

R. Juskaitis, N. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

Kakiuchida, H.

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

Kobayashi, K.

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

Krehut, L.

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

Lang, R.

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

Leristra, D.

D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Lim, M.

Liu, Y.

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

Merlo, S.

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

Myllyla, R.

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

Ohtsubo, J.

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

Ozdemir, S. K.

Pan, M.

Rea, N.

R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

R. Juskaitis, N. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

Rodrigo, P.

Rodrigo, P. J.

Saloma, C.

P. Rodrigo, M. Lim, C. Saloma, “Direction-sensitive sub-wavelength displacement measurements at diffraction-limited resolution,” Opt. Lett. 27, 25–27 (2002).
[CrossRef]

M. R. Daza, C. Saloma, “Jitter dynamics of a gain switched semiconductor laser under self-feedback and external optical injection,” IEEE J. Quantum Electron. 37, 254–264 (2001).
[CrossRef]

P. J. Rodrigo, M. Lim, C. Saloma, “Optical-feedback semiconductor laser Michelson interferometer for displacement measurements with directional discrimination,” Appl. Opt. 40, 506–513 (2001).
[CrossRef]

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Shi, B.

Shibata, T.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

Shinohara, S.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

S. K. Ozdemir, T. Takasu, S. Shinohara, H. Yoshida, M. Sumi, “Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes,” Appl. Opt. 38, 1968–1974 (1999).
[CrossRef]

Sumi, M.

S. K. Ozdemir, T. Takasu, S. Shinohara, H. Yoshida, M. Sumi, “Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes,” Appl. Opt. 38, 1968–1974 (1999).
[CrossRef]

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

Takasu, T.

Tarun, A.

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Van Vaalen, M.

D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Wilson, T.

R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

R. Juskaitis, N. Rea, T. Wilson, “Semiconductor laser confocal microscopy,” Appl. Opt. 33, 578–584 (1994).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999).
[CrossRef]

Yoshida, H.

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

S. K. Ozdemir, T. Takasu, S. Shinohara, H. Yoshida, M. Sumi, “Simultaneous measurement of velocity and length of moving surfaces by a speckle velocimeter with two self-mixing laser diodes,” Appl. Opt. 38, 1968–1974 (1999).
[CrossRef]

Appl. Opt. (3)

IEEE J. Quantum Electron. (5)

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

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

H. Kakiuchida, J. Ohtsubo, “Characteristics of a semiconductor laser with external feedback,” IEEE J. Quantum Electron. 30, 2087–2097 (1994).
[CrossRef]

Y. Liu, J. Ohtsubo, “Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer,” IEEE J. Quantum Electron. 33, 1163–1169 (1997).
[CrossRef]

M. R. Daza, C. Saloma, “Jitter dynamics of a gain switched semiconductor laser under self-feedback and external optical injection,” IEEE J. Quantum Electron. 37, 254–264 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

T. Shibata, S. Shinohara, H. Ikeda, H. Yoshida, M. Sumi, “Automatic measurement of velocity and length of moving plate using self-mixing laser diode,” IEEE Trans. Instrum. Meas. 48, 1062–1067 (1999).

Opt. Commun. (2)

R. Juskaitis, N. Rea, T. Wilson, “Fiber-optic based confocal remote scanning microscopy with laser detection,” Opt. Commun. 99, 105–113 (1994).
[CrossRef]

M. Daza, A. Tarun, K. Fujita, C. Saloma, “Temporal coherence behavior of a semiconductor laser under strong optical feedback,” Opt. Commun. 161, 123–131 (1999).
[CrossRef]

Opt. Lett. (2)

Opto-Electron. Rev. (1)

L. Krehut, J. Hast, E. Alarousu, R. Myllyla, “Low cost velocity sensor based on the self-mixing effect in a laser diode,” Opto-Electron. Rev. 11, 313–319 (2003).

Phys. Rev. Lett. (1)

I. Fischer, O. Hess, W. Elsasser, E. Gobel, “High dimensional chaotic dynamics of an external cavity semiconductor laser,” Phys. Rev. Lett. 73, 2188–2191 (1994).
[CrossRef] [PubMed]

Physica C (1)

D. Leristra, M. Van Vaalen, B. Jaskorzyñska, “On the theory of a single-mode laser with weak optical feedback,” Physica C 125, 255–264 (1984).
[CrossRef]

Other (2)

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, New York, 2003).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Theoretical model. The in-line interferometer consists of a SL, a semitransparent reference mirror Mr, and a test object Mt. It is reduced to an equivalent Fabry–Pérot resonator with a front facet mirror Meff of reflectivity rb + rb1.

Fig. 2
Fig. 2

Experimental setup. The SL output beam is collimated with lens C that also collects the waves reflected from reference mirror Mr and test mirror Mt. The semitransparent Mr is held fixed while Mr is moved by a PZT and a function generator. A precision diode controller provides injection current ISL and monitors IPL.

Fig. 3
Fig. 3

Predicted SL output power versus displacement of Mt in time units where Lr = 0.09 m, Rt = 0.9, Rr = 0.3, and λ = 830 nm. The following are the initial positions of Mt: (a) Lt(0) = 0.12 m and (b) Lr(0) = 0.12 m + 120 nm (solid curve), 0.12 m + 240 nm (circles), and 0.12 m + 360 nm (filled circles). Mt moves toward Mt in the range 0 ≤ t (ms) ≤ 250 and away from Mt in the range 250 ≤ t (ms) ≤ 500.

Fig. 4
Fig. 4

Predicted SL output power as a function of Mt displacement for Mr locations of (a) Lr = Lr(0) + 150 nm (cross hairs); (b) Lr(0) + 240 nm (circles), Lr(0) + 360 nm; (c) Lr(0) + 450 nm (circles), Lr(0) + 570 nm (cross hairs). Parameter values: Lr(0) = 0.09 m, Lt(0) = 0.12 m, Rt = 0.9, Rr = 0.3, and λ = 830 nm.

Fig. 5
Fig. 5

Peak-to-peak amplitude of the SL output power versus Mr displacement from the initial position of Lr(0) = 0.09 m with Lt(0) = 0.12 m, Rt = 0.9, Rr = 0.3, and λ = 830 nm.

Fig. 6
Fig. 6

Predicted SL output power versus Mt displacement for different Mt and Mt reflectivity values with Lr = 0.09 m and Lt(0) = 0.12 m: (a) rt = 0.2 (circles), 0.4 (filled circles), 0.9 (squares), and rr = 0.3; (b) rr = 0.1 (circles), 0.4 (filled circles), 0.9 (squares), and rt = 0.9.

Fig. 7
Fig. 7

Predicted peak-to-peak amplitude of the modulated SL output power as a function of the reflectivity of Mr (circles; rt = 0.9) and M, (filled circles; rr = 0.3), where Lr = 0.09 m and Lt(0) = 0.12 m.

Fig. 8
Fig. 8

Photodiode output IPD versus the SL injection current: Absence of OF (circles), OF from Mr only with rr ≈ 0.3 (filled circles), OF from Mt only with rt ≈ 1 (squares), and OF from both Mr (filled squares).

Fig. 9
Fig. 9

Comparison of experimental results (circles) with theory (solid curves) for rt = 0.9 and rr = 0.3. SL output power (a.u.) versus Mt displacement in time units: (a) Lt = 0.122 m, Lr = 0.1155 m, (b)Lt = 0.051 m, Lr = 0.132 m, and (c) Lt = 0.071 nm, Lr = 0.112 m. Constant bias in the SL output power was removed before normalization.

Fig. 10
Fig. 10

Comparison of experimental results (circles) with theory (solid curves) for different rt values with rr = 0.74, Lt(0) = 0.071 m, and Lr = 0.112 m. SL output power (a.u.) versus Mt displacement in time units for (a) rt = 0.53 (Mt moves toward Mr and (b) rt = 0.53 (Mt moves away from Mr). Constant bias in the SL output power was removed before normalization.

Fig. 11
Fig. 11

Comparison of experimental results (circles) with theory (solid curves) for different rr values with rt = 0.8, Lt(0) = 0.071 m, and Lr = 0.112 m. SL output power (a.u.) versus Mt displacement in time units for (a) rr = 0.61 (Mt moves toward Mr) and (b) rt = 0.775 (Mt moves away from Mr). Constant bias in the SL output power was removed before normalization.

Fig. 12
Fig. 12

Peak-to-peak amplitude of the SL output power as a function of (a) reflectivity rr with rt = 0.775, Lt(0) = 0.12 m, Lr = 0.1175 m, and (b) reflectivity rt with Lt(0) = 0.122 m, Lr = 0.1155 m, and rr = 0.775. Solid curves in (a): SL output = −0.83rr + 0.81 (theory, circles) and SL output = −0.53rr + 0.54 (experimental, filled circles). Solid curves in (b): SL output = 0.12rt + 0.12 (theory, circles) and SL output = 0.72rt − 0.47 (experimental, filled circles).

Tables (1)

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Table 1 Summary of Parameters

Equations (5)

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g 0 = σ + 2 τ [ ln ( 1 r a ) ln ( 1 r b ) ] .
1 τ ph 1 1 τ ph 0 = 2 τ ln ( r b r b + r b 1 ) .
E = E 0 { r b + q = 1 t b 2 t r 2 q r t q r b ( q 1 ) exp [ j 2 q k ( L r + L t ) ] } + E 0 n = 1 t b 2 r r q r 2 n r b ( q 1 ) exp [ j 2 q k L t ) ,
E E 0 = r b + t b 2 t r 2 r t exp [ j 2 k ( L r + L t ) ] 1 r b t r 2 r t exp [ j 2 k ( L r + L t ) ] + t b 2 r r exp ( j 2 k L r ) 1 r b r r exp ( j 2 k L r ) .
p 1 = 2 n 1 g 1 g 0 2 τ n 0 q L [ ( g 0 n 0 g 1 n 1 ) i th + n 0 g 1 n 1 i 0 ] × [ ln r b + | r b 1 | r b ] ,

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