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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 6 — Mar. 12, 2012
  • pp: 6286–6305

Self-mixing in multi-transverse mode semiconductor lasers: model and potential application to multi-parametric sensing

L. Columbo, M. Brambilla, M. Dabbicco, and G. Scamarcio  »View Author Affiliations

Optics Express, Vol. 20, Issue 6, pp. 6286-6305 (2012)

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A general model is proposed for a Vertical Cavity Surface Emitting Laser (VCSEL) with medium aspect ratio whose field profile can be described by a limited set of Gauss-Laguerre modes. The model is adapted to self-mixing schemes by supposing that the output beam is reinjected into the laser cavity by an external target mirror. We show that the self-mixing interferometric signal exhibits features peculiar of the spatial distribution of the emitted field and the target-reflected field and we suggest an applicative scheme that could be exploited for experimental displacement measurements. In particular, regimes of transverse mode-locking are found, where we propose an operational scheme for a sensor that can be used to simultaneously measure independent components of the target displacement like target translations along the optical axis (longitudinal axis) and target rotations in a plane orthogonal to the optical axis (transverse plane).

© 2012 OSA

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(140.5960) Lasers and laser optics : Semiconductor lasers
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(280.3420) Remote sensing and sensors : Laser sensors
(280.4788) Remote sensing and sensors : Optical sensing and sensors

ToC Category:
Lasers and Laser Optics

Original Manuscript: October 11, 2011
Revised Manuscript: December 9, 2011
Manuscript Accepted: January 2, 2012
Published: March 5, 2012

L. Columbo, M. Brambilla, M. Dabbicco, and G. Scamarcio, "Self-mixing in multi-transverse mode semiconductor lasers: model and potential application to multi-parametric sensing," Opt. Express 20, 6286-6305 (2012)

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  1. D. M. Kane and K. A. Shore, Unlocking Dynamical Diversity. Optical Feedback Effects on Semiconductor Lasers (John Wiley and Sons, 2005). [CrossRef]
  2. S. Donati, G. Giuliani, and S. Merlo, “Laser diode feedback inteferometer for measurement of displacements without ambiguity,” IEEE J. Quantum Electron.31, 113–119 (1995). [CrossRef]
  3. S. Ottonelli, M. Dabbicco, F. De Lucia, and G. Scamarcio, “Simultaneous measurement of linear and transverse displacements by laser self-mixing,” Appl. Opt.48, 1784–1789 (2009). [CrossRef] [PubMed]
  4. J. R. Tucker, J. L. Baque, Y. L. Lim, A. V. Zvyagin, and A. D. Rakic, “Parallel self-mixing imaging system based on an array of vertical-cavity surface-emitting lasers,” Appl. Opt.46, 6237–6246 (2007). [CrossRef] [PubMed]
  5. Y. L. Lim, M. Nikolic, K. Bertling, R. Kliese, and A. D. Rakic, “Self-mixing imaging sensor using a monolithic VCSEL array with parallel readout,” Opt. Express17, 5517–5525 (2009). [CrossRef] [PubMed]
  6. Y. L. Lim, R. Kliese, K. Bertling, K. Tanimizu, P. A. Jacobs, and A. D. Rakic, “Self-mixing flow sensor using a monolithic VCSEL array with parallel readout,” Opt. Express18, 11720–11727 (2010). [CrossRef] [PubMed]
  7. “Z. Liu, D. Lin, H. Jiang, and C. Yin, “Roll angle interferometer by means of wave plates,” Sens. Actuators, A104, 127–131 (2003). [CrossRef]
  8. C-M. Wu and Y-T. Chuang, “Roll angular displacement measurement system with microradian accuracy,” Sens. Actuators, A116, 145–149 (2004). [CrossRef]
  9. W. S. Park and H. S. Cho, “Measurement of fine 6-degrees-of-freedom displacement of rigid bodies through splitting a laser beam: experimental investigation,” Opt. Eng.41, 860–871 (2002). [CrossRef]
  10. C. J. Chen, P. D. Lin, and W. Y. Jywe, “An optoelectronic measurement system for measuring 6-degree-of-freedom motion error of rotary parts,” Opt. Express15, 14601–14617 (2007). [CrossRef] [PubMed]
  11. S. Ottonelli, M. Dabbicco, F. De Lucia, M. di Vietro, and G. Scamarcio, “Laser-self-mixing interferometry for mechatronics applications,” Sensors9, 3527–3548 (2009). [CrossRef]
  12. F. P. Mezzapesa, L. Columbo, M. Brambilla, M. Dabbicco, A. Ancona, T. Sibillano, F. De Lucia, P. M. Lugará, and G. Scamarcio, “Simultaneous measurement of multiple target displacements by self-mixing interferometry in a single laser diode,” Opt. Express19, 16160–16173 (2011). [CrossRef] [PubMed]
  13. C. J. Chang-Hasnain, M. Orenstein, A. Von Lehmen, l. T. Florez, J. P. Harbison, and N. G. Stoffel, “Transverse mode characteristics of vertical cavity surface-emitting lasers,” Appl. Phys. Lett.57, 218–220 (1990). [CrossRef]
  14. H. Lia, T. L. Lucas, J. G. McInerney, and R. A. Morgan, “Transverse modes and patterns of electrically pumped vertical-cavity surface-emitting semiconductor lasers,” Chaos, Solitons Fractals4, 1619–1636 (1994). [CrossRef]
  15. J. U. Nöckel, G. Bourdon, E. Le Ru, R. Adams, I. Robert, J.-M. Moison, and I. Abram, “Mode structure and ray dynamics of a parabolic dome microcavity,” Phys. Rev. E62, 8677–8699 (2000). [CrossRef]
  16. S.-H. Park, Y. Park, H. Kim, H. Jeon, S. M. Hwang, J. K. Lee, S. H. Nam, B. C. Koh, J. Y. Sohn, and D. S. Kim, “Microlensed vertical-cavity surface-emitting laser for stable single fundamental mode operation,” Appl. Phys. Lett.80, 183–185 (2002). [CrossRef]
  17. M. T. Cha and R. Gordon, “Spatially Filtered Feedback for Mode Control in Vertical-Cavity Surface-Emitting Lasers,” J. Lightwave Technol.26, 3893–3900 (2008). [CrossRef]
  18. F. Prati, A. Tesei, L. A. Lugiato, and R.J. Horowicz, “Stable states in surface-emitting semiconductor lasers,” Chaos, Solitons Fractals4, 1637–1654 (1994). [CrossRef]
  19. A. Valle, J. Sarma, and K. A. Shore, “Dynamics of transverse mode competition in vertical cavity surface emitting laser diodes,” Opt. Commun.115, 297–302 (1995). [CrossRef]
  20. L. A. Lugiato, “Spatio-temporal structures. Part I,” Phys. Rep.219, 293–310 (1992). [CrossRef]
  21. F. Prati, M. Travagnin, and L. A. Lugiato, “Logic gates and optical switching with vertical-cavity surface-emitting lasers,” Phys. Rev. A55, 690–700 (1997). [CrossRef]
  22. M. San Miguel, Q. Feng, and J. V. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A52, 1728–1739 (1995). [CrossRef] [PubMed]
  23. F. Prati, G. Tissoni, M. San Miguel, and N. B Abraham, “Vector vortices and polarization state of low-order transverse modes in a VCSEL,” Opt. Commun.143, 133–146 (1997). [CrossRef]
  24. J Martń-Regalado, S. Balle, M. San Miguel, A. Valle, and L. Pesquera, “Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain-guided devices,” Quantum Semi-classic. Opt.9, 713–736 (1997). [CrossRef]
  25. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser proprieties,” IEEE J. Quantum Electron.16, 347–355 (1980). [CrossRef]
  26. J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron.3, 353-3-58 (1997).
  27. M. S. Torre, C. Masoller, and P. Mandel, “Transverse mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A66, 053817 (2002). [CrossRef]
  28. K. Green, B. Krauskopf, and D. Lenstra, “External cavity mode structure of a two-mode VCSEL subject to optical feedback,” Opt. Commun.277, 359–371 (2007). [CrossRef]
  29. G. Oppo and G. Dalessandro, “Gauss–Laguerre modes - a sensible basis for laser dynamics,” Opt. Commun.88, 130–136 (1992). [CrossRef]
  30. L. A. Lugiato, F. Prati, L. M. Narducci, P. Ru, J. R. Tredicce, and D. K. Bandy, “Role of transverse effects in laser instabilities,” Phys. Rev. A37, 3847–3866 (1988). [CrossRef] [PubMed]
  31. M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, G.-L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. DAngelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A49, 1427–1451 (1994). [CrossRef] [PubMed]
  32. A. B. Coates, C. O. Weiss, C. Green, E. J. DAngelo, J. R. Tredicce, M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Prati, A. J. Kent, and G.-L. Oppo, “Dynamical transverse laser patterns. II. Experiments,” Phys. Rev. A49, 1452–1466(1994). [CrossRef] [PubMed]
  33. F. Prati, M. Brambilla, and L. A. Lugiato, “Pattern formation in lasers,” Riv. Nuovo Cimento17, 1–85 (1994). [CrossRef]
  34. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Kndl, M. Miller, and R. Jger, “Cavity solitons as pixels in semiconductor microcavities,” Nature419, 699–702 (2002). [CrossRef] [PubMed]
  35. C. O. Weiss, H. R. Telle, K. Staliunas, and M. Brambilla, “Restless optical vortex,” Phys. Rev. A47, R1616–R1619 (1993). [CrossRef] [PubMed]
  36. E. K. Lau, X. Zhao, H.-K. Sung, D. Parekh, C. Chang-Hasnain, and M. C. Wu, “Strong optical injection-locked semiconductor lasers demonstrating > 100 – GHz resonance frequencies and 80 – GHz intrinsic bandwidths,” Opt. Express16, 6609–6618 (2008). [CrossRef] [PubMed]
  37. G Slekys, I Ganne, I Sagnes, and R Kuszelewicz, “Optical pattern formation in passive semiconductor microresonators,” J. Opt. B: Quantum Semiclassical Opt.2, 443–446 (2000). [CrossRef]
  38. A. C. Tropper, H. D. Foreman, A. Garnache, K. G. Wilcox, and S. H. Hoogland, “Vertical-external-cavity semiconductor lasers,” J. Phys. D: Appl. Phys.37, R75–R85 (2004). [CrossRef]
  39. D. Guo, M. Wang, and S. Tan, “Self-mixing interferometer based on sinusoidal phase modulating technique,” Opt. Express13, 1537–1543 (2005). [CrossRef] [PubMed]
  40. F. A. Chollet, G. M. Hegde, A. K. Asundi, and A. Q. Liu, “Simple extra-short external cavity laser self-mixing interferometer for acceleration sensing,” Proc. SPIE4596, 272–279 (2001). [CrossRef]
  41. G. Giuliani, S. Donati, M. Passerini, and T. Bosch, “Angle measurement by injection detection in a laser diode,” Opt. Eng.40, 95–99 (2001). [CrossRef]
  42. S. Wolff and H. Fouckhardt, “Intracavity stabilization of broad area lasers by structured delayed optical feedback,” Opt. Express7, 222–227 (2000). [CrossRef] [PubMed]
  43. A. E. Siegman, Lasers (University Science Books, 1986).

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