Abstract

We investigate the effect of coexisting transverse modes on the operation of self-mixing sensors based on vertical-cavity surface-emitting lasers (VCSELs). The effect of multiple transverse modes on the measurement of displacement and distance were examined by simulation and in laboratory experiment. The simulation model shows that the periodic change in the shape and magnitude of the self-mixing signal with modulation current can be properly explained by the different frequency-modulation coefficients of the respective transverse modes in VCSELs. The simulation results are in excellent agreement with measurements performed on single-mode and multimode VCSELs and on self-mixing sensors based on these VCSELs.

© 2007 Optical Society of America

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  1. R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. QE-16, 347-355 (1980).
  2. K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
  3. K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, 1991).
  4. S. Donati, Electro-Optical Instrumentation (Prentice Hall, 2004).
  5. D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).
  6. G. P. Agrawal, "Line narrowing in a single-mode injection laser due to external optical feedback," IEEE J. Quantum Electron. 20, 468-471 (1984).
  7. S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
  8. G. Beheim and K. Fritsch, "Range finding using frequency-modulated laser diode," Appl. Opt. 25, 1439-1442 (1986).
    [PubMed]
  9. J. H. Churnside, "Laser Doppler velocimetry by modulating a CO2 laser with backscattered light," Appl. Opt. 23, 61-66 (1984).
    [PubMed]
  10. G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
  11. F. F. M. de Mul, M. H. Koelink, A. L. Weijers, J. Greve, J. G. Aarnoudse, R. Graaff, and A. C. M. Dassel, "Self-mixing laser-Doppler velocimetry of liquid flow and of blood perfusion in tissue," Appl. Opt. 31, 5844-5851 (1992).
  12. K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
    [PubMed]
  13. T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).
  14. E. Gagnon and J. F. Rivest, "Laser range imaging using the self-mixing effect in a laser diode," IEEE Trans. Instrum. Meas. 48, 693-699 (1999).
  15. Y. Katagiri and S. Hara, "Scanning-probe microscope using an ultrasmall coupled-cavity laser distortion sensor based on mechanical negative-feedback stabilization," Meas. Sci. Technol. 9, 1441-1445 (1998).
  16. G. Giuliani and M. Norgia, "Laser diode linewidth measurement by means of self-mixing interferometry," IEEE Photon. Technol. Lett. 12, 1028-1030 (2000).
  17. Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).
  18. P. J. de Groot, "Range-dependent optical feedback effects on the multimode spectrum of laser diodes," J. Mod. Opt. 37, 1199-1214 (1990).
  19. H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).
  20. Y. Yu and J. Yao, "View for the development of theory on the self-mixing interference and general model of the displacement measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 235-241 (2002).
  21. L. Lv, H. Gui, J. Xie, T. Zhao, X. Chen, A. Wang, F. Li, D. He, J. Xu, and H. Ming, "Effect of external cavity length on self-mixing signals in a multilongitudinal-mode Fabry-Perot laser diode," Appl. Opt. 44, 568-571 (2005).
    [PubMed]
  22. J. R. Tucker, Y. L. Leng, and A. D. Rakic, "Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser," in Proceedings of the 2002 Conference on Optoelectronic and Microelectronic Materials and Devices Proceedings (IEEE, 2002), pp. 583-586.
    [PubMed]
  23. K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).
  24. C. Gorecki and D. Heinis, "A miniaturized SNOM sensor based on the optical feedback inside the VCSEL cavity," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 183-187 (2004).
  25. T. Maier and E. Gornik, "Integrated sensor chip for interferometric displacement measurements," Electron. Lett. 36, 792-794 (2000).
  26. F. Vogel and B. Toulouse, "A low-cost medium-resolution rangefinder based on the self-mixing effect in a VCSEL," IEEE Trans. Instrum. Meas. 54, 428-431 (2005).
  27. E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).
  28. R. Wang, A. D. Rakic, and M. L. Majewski, "Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays," Appl. Opt. 41, 3469-3478 (2002).
    [PubMed]
  29. F.-C. F. Tsai, C. J. O'Brien, N. S. Petrovic, and A. D. Rakic, "Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes," Appl. Opt. 44, 6380-6387 (2005).
    [PubMed]
  30. P. J. de Groot, G. M. Gallatin, and S. H. Macomber, "Ranging and velocimetry signal generation in a backscatter-modulated laser diode," Appl. Opt. 27, 4475-4480 (1988).
    [PubMed]
  31. M. H. Koelink, M. Slot, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, and J. G. Aarnoudse, "Laser Doppler velocimeter based on the self-mixing effect in a fiber-couple semiconductor laser: theory," Appl. Opt. 31, 3401-3408 (1992).
    [PubMed]
  32. R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).
  33. K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).
  34. M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).
  35. R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).
  36. T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).
  37. T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).
  38. S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).
  39. R. Michalzik and K. J. Ebeling, "Operating principles of VCSELs," in Vertical-Cavity Surface-Emitting Laser Devices, H.E.Li and K.Iga, eds. (Springer, 2003), pp. 53-98.
  40. R. Michalzik and K. J. Ebeling, "Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes," IEEE J. Quantum Electron. 31, 1371-1379 (1995).
  41. 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. 217-256.
  42. J. J. Dudley, D. L. Crawford, and J. E. Bowers, "Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices," IEEE Photon. Technol. Lett. 4, 311-314 (1992).
  43. W. Nakwaski and R. P. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Commun. 148, 63-69 (1998).
  44. C. Degen, I. Fischer, and W. Elsasser, "Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects," Opt. Express 5, 38-47 (1999).
    [PubMed]

2005

2004

K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).

C. Gorecki and D. Heinis, "A miniaturized SNOM sensor based on the optical feedback inside the VCSEL cavity," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 183-187 (2004).

Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).

2002

Y. Yu and J. Yao, "View for the development of theory on the self-mixing interference and general model of the displacement measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 235-241 (2002).

R. Wang, A. D. Rakic, and M. L. Majewski, "Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays," Appl. Opt. 41, 3469-3478 (2002).
[PubMed]

2001

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

2000

T. Maier and E. Gornik, "Integrated sensor chip for interferometric displacement measurements," Electron. Lett. 36, 792-794 (2000).

G. Giuliani and M. Norgia, "Laser diode linewidth measurement by means of self-mixing interferometry," IEEE Photon. Technol. Lett. 12, 1028-1030 (2000).

1999

E. Gagnon and J. F. Rivest, "Laser range imaging using the self-mixing effect in a laser diode," IEEE Trans. Instrum. Meas. 48, 693-699 (1999).

C. Degen, I. Fischer, and W. Elsasser, "Transverse modes in oxide confined VCSELs: influence of pump profile, spatial hole burning, and thermal effects," Opt. Express 5, 38-47 (1999).
[PubMed]

1998

Y. Katagiri and S. Hara, "Scanning-probe microscope using an ultrasmall coupled-cavity laser distortion sensor based on mechanical negative-feedback stabilization," Meas. Sci. Technol. 9, 1441-1445 (1998).

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

W. Nakwaski and R. P. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Commun. 148, 63-69 (1998).

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).

1997

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

1996

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

1995

K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

R. Michalzik and K. J. Ebeling, "Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes," IEEE J. Quantum Electron. 31, 1371-1379 (1995).

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

1994

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).

1993

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

1992

1990

P. J. de Groot, "Range-dependent optical feedback effects on the multimode spectrum of laser diodes," J. Mod. Opt. 37, 1199-1214 (1990).

1988

1986

1984

J. H. Churnside, "Laser Doppler velocimetry by modulating a CO2 laser with backscattered light," Appl. Opt. 23, 61-66 (1984).
[PubMed]

G. P. Agrawal, "Line narrowing in a single-mode injection laser due to external optical feedback," IEEE J. Quantum Electron. 20, 468-471 (1984).

1980

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

Aarnoudse, J. G.

Agrawal, G. P.

G. P. Agrawal, "Line narrowing in a single-mode injection laser due to external optical feedback," IEEE J. Quantum Electron. 20, 468-471 (1984).

Beheim, G.

Bertling, K.

K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).

Bosch, T.

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

Bowers, J. E.

J. J. Dudley, D. L. Crawford, and J. E. Bowers, "Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices," IEEE Photon. Technol. Lett. 4, 311-314 (1992).

Chellali, R.

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

Chen, X.

Choquette, K. D.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

Churnside, J. H.

Coldren, L. A.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Crawford, D. L.

J. J. Dudley, D. L. Crawford, and J. E. Bowers, "Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices," IEEE Photon. Technol. Lett. 4, 311-314 (1992).

Dassel, A. C. M.

de Groot, P. J.

P. J. de Groot, "Range-dependent optical feedback effects on the multimode spectrum of laser diodes," J. Mod. Opt. 37, 1199-1214 (1990).

P. J. de Groot, G. M. Gallatin, and S. H. Macomber, "Ranging and velocimetry signal generation in a backscatter-modulated laser diode," Appl. Opt. 27, 4475-4480 (1988).
[PubMed]

de Mul, F. F. M.

Degen, C.

Deppe, D. G.

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).

Donati, S.

Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

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

S. Donati, Electro-Optical Instrumentation (Prentice Hall, 2004).

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. 217-256.

Dudley, J. J.

J. J. Dudley, D. L. Crawford, and J. E. Bowers, "Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices," IEEE Photon. Technol. Lett. 4, 311-314 (1992).

Ebeling, K. J.

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

R. Michalzik and K. J. Ebeling, "Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes," IEEE J. Quantum Electron. 31, 1371-1379 (1995).

R. Michalzik and K. J. Ebeling, "Operating principles of VCSELs," in Vertical-Cavity Surface-Emitting Laser Devices, H.E.Li and K.Iga, eds. (Springer, 2003), pp. 53-98.

Elsasser, W.

Fiedler, U.

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

Fischer, I.

Fritsch, K.

Gagnon, E.

E. Gagnon and J. F. Rivest, "Laser range imaging using the self-mixing effect in a laser diode," IEEE Trans. Instrum. Meas. 48, 693-699 (1999).

Gallatin, G. M.

Geib, K. M.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

Giuliani, G.

Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

G. Giuliani and M. Norgia, "Laser diode linewidth measurement by means of self-mixing interferometry," IEEE Photon. Technol. Lett. 12, 1028-1030 (2000).

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

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. 217-256.

Gorecki, C.

C. Gorecki and D. Heinis, "A miniaturized SNOM sensor based on the optical feedback inside the VCSEL cavity," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 183-187 (2004).

Gornik, E.

T. Maier and E. Gornik, "Integrated sensor chip for interferometric displacement measurements," Electron. Lett. 36, 792-794 (2000).

Graaff, R.

Grabherr, M.

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

Greve, J.

Gui, H.

Hara, S.

Y. Katagiri and S. Hara, "Scanning-probe microscope using an ultrasmall coupled-cavity laser distortion sensor based on mechanical negative-feedback stabilization," Meas. Sci. Technol. 9, 1441-1445 (1998).

He, D.

Heinis, D.

C. Gorecki and D. Heinis, "A miniaturized SNOM sensor based on the optical feedback inside the VCSEL cavity," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 183-187 (2004).

Huffaker, D. L.

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

Ikeda, H.

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

Jager, R.

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

Jayaraman, V.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Jung, C.

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

Kakiuchida, H.

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).

Kane, D. M.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).

Katagiri, Y.

Y. Katagiri and S. Hara, "Scanning-probe microscope using an ultrasmall coupled-cavity laser distortion sensor based on mechanical negative-feedback stabilization," Meas. Sci. Technol. 9, 1441-1445 (1998).

Kilcoyne, S. P.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

Kobayashi, K.

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

Koelink, M. H.

Lang, R.

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

Lear, K. L.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

Leng, Y. L.

J. R. Tucker, Y. L. Leng, and A. D. Rakic, "Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser," in Proceedings of the 2002 Conference on Optoelectronic and Microelectronic Materials and Devices Proceedings (IEEE, 2002), pp. 583-586.
[PubMed]

Lescure, M.

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

Li, F.

Lv, L.

Macomber, S. H.

Maier, T.

T. Maier and E. Gornik, "Integrated sensor chip for interferometric displacement measurements," Electron. Lett. 36, 792-794 (2000).

Majewski, M. L.

McDaniel, M. R.

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

Merlo, S.

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

Michalzik, R.

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

R. Michalzik and K. J. Ebeling, "Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes," IEEE J. Quantum Electron. 31, 1371-1379 (1995).

R. Michalzik and K. J. Ebeling, "Operating principles of VCSELs," in Vertical-Cavity Surface-Emitting Laser Devices, H.E.Li and K.Iga, eds. (Springer, 2003), pp. 53-98.

Ming, H.

Mito, K.

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

Mondry, M.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Nakwaski, W.

W. Nakwaski and R. P. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Commun. 148, 63-69 (1998).

Norgia, M.

G. Giuliani and M. Norgia, "Laser diode linewidth measurement by means of self-mixing interferometry," IEEE Photon. Technol. Lett. 12, 1028-1030 (2000).

O'Brien, C. J.

Oh, T. H.

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).

Ohtsubo, J.

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).

Passerini, M.

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

Petermann, K.

K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).

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

Peters, F. H.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Peters, M. G.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Petrovic, N. S.

Rakic, A. D.

F.-C. F. Tsai, C. J. O'Brien, N. S. Petrovic, and A. D. Rakic, "Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes," Appl. Opt. 44, 6380-6387 (2005).
[PubMed]

K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).

R. Wang, A. D. Rakic, and M. L. Majewski, "Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays," Appl. Opt. 41, 3469-3478 (2002).
[PubMed]

J. R. Tucker, Y. L. Leng, and A. D. Rakic, "Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser," in Proceedings of the 2002 Conference on Optoelectronic and Microelectronic Materials and Devices Proceedings (IEEE, 2002), pp. 583-586.
[PubMed]

Reiner, G.

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

Rivest, J. F.

E. Gagnon and J. F. Rivest, "Laser range imaging using the self-mixing effect in a laser diode," IEEE Trans. Instrum. Meas. 48, 693-699 (1999).

Robinson, G. D.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Sarzala, R. P.

W. Nakwaski and R. P. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Commun. 148, 63-69 (1998).

Schneider, R. P.

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

Schnitzer, P.

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

Servagent, N.

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

Shchekin, O. B.

T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).

Shinohara, S.

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

Shore, K. A.

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).

Slot, M.

Strzelecka, E. M.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Sumi, M.

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

Thibeault, B. J.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Thompson, G. B.

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

Toulouse, B.

F. Vogel and B. Toulouse, "A low-cost medium-resolution rangefinder based on the self-mixing effect in a VCSEL," IEEE Trans. Instrum. Meas. 54, 428-431 (2005).

Tsai, F.-C. F.

Tucker, J. R.

K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).

J. R. Tucker, Y. L. Leng, and A. D. Rakic, "Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser," in Proceedings of the 2002 Conference on Optoelectronic and Microelectronic Materials and Devices Proceedings (IEEE, 2002), pp. 583-586.
[PubMed]

Vogel, F.

F. Vogel and B. Toulouse, "A low-cost medium-resolution rangefinder based on the self-mixing effect in a VCSEL," IEEE Trans. Instrum. Meas. 54, 428-431 (2005).

Wang, A.

Wang, R.

Weigl, B.

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

Weijers, A. L.

Wiedenmann, D.

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

Xie, J.

Xu, J.

Yao, J.

Y. Yu and J. Yao, "View for the development of theory on the self-mixing interference and general model of the displacement measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 235-241 (2002).

Yu, S. F.

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).

Yu, Y.

Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).

Y. Yu and J. Yao, "View for the development of theory on the self-mixing interference and general model of the displacement measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 235-241 (2002).

Zhao, T.

Appl. Opt.

J. H. Churnside, "Laser Doppler velocimetry by modulating a CO2 laser with backscattered light," Appl. Opt. 23, 61-66 (1984).
[PubMed]

G. Beheim and K. Fritsch, "Range finding using frequency-modulated laser diode," Appl. Opt. 25, 1439-1442 (1986).
[PubMed]

P. J. de Groot, G. M. Gallatin, and S. H. Macomber, "Ranging and velocimetry signal generation in a backscatter-modulated laser diode," Appl. Opt. 27, 4475-4480 (1988).
[PubMed]

M. H. Koelink, M. Slot, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, and J. G. Aarnoudse, "Laser Doppler velocimeter based on the self-mixing effect in a fiber-couple semiconductor laser: theory," Appl. Opt. 31, 3401-3408 (1992).
[PubMed]

F. F. M. de Mul, M. H. Koelink, A. L. Weijers, J. Greve, J. G. Aarnoudse, R. Graaff, and A. C. M. Dassel, "Self-mixing laser-Doppler velocimetry of liquid flow and of blood perfusion in tissue," Appl. Opt. 31, 5844-5851 (1992).

R. Wang, A. D. Rakic, and M. L. Majewski, "Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays," Appl. Opt. 41, 3469-3478 (2002).
[PubMed]

L. Lv, H. Gui, J. Xie, T. Zhao, X. Chen, A. Wang, F. Li, D. He, J. Xu, and H. Ming, "Effect of external cavity length on self-mixing signals in a multilongitudinal-mode Fabry-Perot laser diode," Appl. Opt. 44, 568-571 (2005).
[PubMed]

F.-C. F. Tsai, C. J. O'Brien, N. S. Petrovic, and A. D. Rakic, "Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes," Appl. Opt. 44, 6380-6387 (2005).
[PubMed]

Electron. Lett.

R. Jager, M. Grabherr, C. Jung, R. Michalzik, G. Reiner, B. Weigl, and K. J. Ebeling, "57% wallplug efficiency oxide-confined 850 nm wavelength GaAs VCSELs," Electron. Lett. 33, 330-331 (1997).

K. L. Lear, K. D. Choquette, R. P. Schneider, Jr., S. P. Kilcoyne, and K. M. Geib, "Selectively oxidised vertical cavity surface emitting lasers with 50% power conversion efficiency," Electron. Lett. 31, 208-209 (1995).

T. Maier and E. Gornik, "Integrated sensor chip for interferometric displacement measurements," Electron. Lett. 36, 792-794 (2000).

IEEE J. Quantum Electron.

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).

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

G. P. Agrawal, "Line narrowing in a single-mode injection laser due to external optical feedback," IEEE J. Quantum Electron. 20, 468-471 (1984).

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

R. Michalzik and K. J. Ebeling, "Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes," IEEE J. Quantum Electron. 31, 1371-1379 (1995).

IEEE J. Sel. Top. Quantum Electron.

R. Michalzik, P. Schnitzer, U. Fiedler, D. Wiedenmann, and K. J. Ebeling, "High-bit-rate data transmission with short-wavelength oxidized VCSEL's, toward bias-free operation," IEEE J. Sel. Top. Quantum Electron. 3, 396-404 (1997).

K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).

IEEE Photon. Technol. Lett.

G. Giuliani and M. Norgia, "Laser diode linewidth measurement by means of self-mixing interferometry," IEEE Photon. Technol. Lett. 12, 1028-1030 (2000).

Y. Yu, G. Giuliani, and S. Donati, "Measurement of the linewidth enhancement factor of semiconductor lasers based on the optical feedback self-mixing effect," IEEE Photon. Technol. Lett. 16, 990-992 (2004).

T. H. Oh, M. R. McDaniel, D. L. Huffaker, and D. G. Deppe, "Cavity-induced antiguiding in a selectively oxidized vertical-cavity surface-emitting laser," IEEE Photon. Technol. Lett. 10, 12-14 (1998).

T. H. Oh, O. B. Shchekin, and D. G. Deppe, "Single-mode operation in an antiguided vertical-cavity surface-emitting laser using a low-temperature grown AlGaAs dielectric aperture," IEEE Photon. Technol. Lett. 10, 1064-1066 (1998).

M. Grabherr, R. Jager, R. Michalzik, B. Weigl, G. Reiner, and K. J. Ebeling, "Efficient single-mode oxide-confined GaAs VCSEL's emitting in the 850-nm wavelength regime," IEEE Photon. Technol. Lett. 9, 1304-1306 (1997).

J. J. Dudley, D. L. Crawford, and J. E. Bowers, "Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices," IEEE Photon. Technol. Lett. 4, 311-314 (1992).

IEEE Trans. Instrum. Meas.

F. Vogel and B. Toulouse, "A low-cost medium-resolution rangefinder based on the self-mixing effect in a VCSEL," IEEE Trans. Instrum. Meas. 54, 428-431 (2005).

T. Bosch, N. Servagent, R. Chellali, and M. Lescure, "Three-dimensional object construction using a self-mixing type scanning laser range finder," IEEE Trans. Instrum. Meas. 47, 1326-1329 (1998).

E. Gagnon and J. F. Rivest, "Laser range imaging using the self-mixing effect in a laser diode," IEEE Trans. Instrum. Meas. 48, 693-699 (1999).

J. Mod. Opt.

P. J. de Groot, "Range-dependent optical feedback effects on the multimode spectrum of laser diodes," J. Mod. Opt. 37, 1199-1214 (1990).

Meas. Sci. Technol.

Y. Katagiri and S. Hara, "Scanning-probe microscope using an ultrasmall coupled-cavity laser distortion sensor based on mechanical negative-feedback stabilization," Meas. Sci. Technol. 9, 1441-1445 (1998).

Med. Biol. Eng. Comput.

K. Mito, H. Ikeda, M. Sumi, and S. Shinohara, "Self-mixing effect on the semiconductor laser Doppler method for blood flow measurement," Med. Biol. Eng. Comput. 31, 308-310 (1993).
[PubMed]

Opt. Commun.

W. Nakwaski and R. P. Sarzala, "Transverse modes in gain-guided vertical-cavity surface-emitting lasers," Opt. Commun. 148, 63-69 (1998).

Opt. Eng.

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).

Opt. Express

Proc. SPIE

Y. Yu and J. Yao, "View for the development of theory on the self-mixing interference and general model of the displacement measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 235-241 (2002).

E. M. Strzelecka, G. B. Thompson, G. D. Robinson, M. G. Peters, B. J. Thibeault, M. Mondry, V. Jayaraman, F. H. Peters, and L. A. Coldren, "Monolithic integration of refractive lenses with vertical cavity lasers and detectors for optical interconnections," in Optoelectronic Packaging, M. R. Feldman and Y.-C. Lee, eds., Proc. SPIE 2691, 43-53 (1996).

K. Bertling, J. R. Tucker, and A. D. Rakic, "Optimum injection current waveform for a laser rangefinder based on the self-mixing effect," in Photonics: Design, Technology, and Packaging, C. Jagadish, K. D. Choquette, B. J. Eggleton, B. D. Nener, and K. A. Nugent, eds., Proc. SPIE 5277, 334-345 (2004).

C. Gorecki and D. Heinis, "A miniaturized SNOM sensor based on the optical feedback inside the VCSEL cavity," in Optical Micro- and Nanometrology in Manufacturing Technology, C. Gorecki and A. K. Asundi, eds., Proc. SPIE 5458, 183-187 (2004).

Other

J. R. Tucker, Y. L. Leng, and A. D. Rakic, "Laser range finding using the self-mixing effect in a vertical-cavity surface-emitting laser," in Proceedings of the 2002 Conference on Optoelectronic and Microelectronic Materials and Devices Proceedings (IEEE, 2002), pp. 583-586.
[PubMed]

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

S. Donati, Electro-Optical Instrumentation (Prentice Hall, 2004).

D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers (Wiley, 2005).

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. 217-256.

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley, 2003).

R. Michalzik and K. J. Ebeling, "Operating principles of VCSELs," in Vertical-Cavity Surface-Emitting Laser Devices, H.E.Li and K.Iga, eds. (Springer, 2003), pp. 53-98.

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Figures (9)

Fig. 1
Fig. 1

(a) Three mirror Fabry–Perot cavity model of laser and target. (b) Equivalent Fabry–Perot cavity model with combined laser mirror and target.

Fig. 2
Fig. 2

Simulation of the output power for the 850   nm transverse mode (dashed), 850.4   nm transverse mode (dashed–dotted), and total output power (solid) versus displacement from (a) 200 × LCM and (b) 200.25 × LCM .

Fig. 3
Fig. 3

Simulation of the derivative of the output power for the 850 and 850.4   nm transverse modes (with the same FM coefficients) and the total differentiated power versus time for a target at a fixed distance of (a) 200 × LCM and (b) 200 .25 × LCM .

Fig. 4
Fig. 4

Simulation of the derivative of output power for the 850 and 850.4   nm transverse modes (with different FM coefficients) and the total differentiated power versus time for a target at a fixed distance of (a) 200 × LCM and (b) 200.25 × LCM .

Fig. 5
Fig. 5

(a) Emission spectrum of the single-mode VCSEL at 4.5   mA . (b) Emission spectrum of the multimode VCSEL at 4.5   mA .

Fig. 6
Fig. 6

(a) Peak wavelengths of the transverse modes versus injection current for the multimode VCSEL. (b) Derivatives of the change in the transverse mode peak wavelengths with respect to injection current versus injection current for the multimode VCSEL.

Fig. 7
Fig. 7

Block diagram of the experimental setup.

Fig. 8
Fig. 8

Derivative of the total output power waveform (light) and FFT (dark) with the single-mode VCSEL at (a) 36.5   cm and (b) 36.6   cm .

Fig. 9
Fig. 9

Derivative of the total output power waveform (light) and FFT (dark) with the multimode VCSEL at (a) 36.5   cm and (b) 36.6   cm .

Equations (93)

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

M 1
M 2
r 1
r 2 s
n e
L e x t
M 2
r 2 e x t
r e f f
r e f f ( ν ) = r 2 s + ( 1 | r 2 s | 2 ) r 2 e x t   exp ( j 2 π ν τ ext ) ,
τ e x t = 2 L e x t / c
m 2 π
2 π
Δ ϕ L
Δ ϕ L = 2 π τ e x t ( ν ν t h ) + C   sin ( 2 π ν τ e x t + arctan   α ) ,
C = τ e x t τ L r 2 e x t ( 1 | r 2 s | 2 ) r 2 s 1 + α 2 ,
ν t h
τ L
C < 1
λ t h / 2
λ t h
λ t h / 2
P = η ( I o p + κ e x t q V L T s a Γ  cos ( 2 π ν τ e x t ) I t h ) ,
I o p
I t h
κ e x t
T s
Δ λ l m λ 2 / D a
Δ λ l m
λ l m
D a
Δ λ
0.1   nm
20 μ m
10 9
n L
D a
cos ( 2 π ν τ ext )
2 π ν τ ext = m 2 π
2 π
λ M
2 π 2 L e x t λ M = m 2 π
λ M
850.4   nm
1.8071   mm
200.25 × LCM
ν t h
L e x t = c f p 4 i p k f m Ω ,
f p
i p k
f m
850.4   nm
Ω = 60 GHz / mA
200 × LCM
200.25 × LCM
850.4   nm
( p / 2 ) × LCM
Ω 1 = 60 GHz / mA
850.4   nm
Ω 2 = 63 GHz / mA
200 × LCM
200.25 × LCM
( p / 2 ) × LCM
( q / 4 ) × LCM
f p 1
f p 2
cos ( 2 π f p 1 t ) + cos ( 2 π f p 2 t ) = 2   cos ( 2 π f p 1 f p 2 2 t ) × cos ( 2 π f p 1 + f p 2 2 t ) .
f p 1 f p 2 = 4 L e x t f m i p k c ( Ω 1 Ω 2 ) ,
Ω 1
Ω 2
4.5   mA
HG 00
Ω i
Ω i
36.6   cm
1   mm
2   mm
850   nm
850.4   nm
200 × LCM
200.25 × LCM
850.4   nm
200 × LCM
200 .25 × LCM
850.4   nm
200 × LCM
200.25 × LCM
4.5   mA
4.5   mA
36.5   cm
36.6   cm
36.5   cm
36.6   cm

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