Abstract

We study the interplay of polarization bistability, spontaneous emission noise and aperiodic current modulation in vertical cavity surface emitting lasers (VCSELs). We demonstrate the phenomenon of logic stochastic resonance (LSR), by which the laser gives robust and reliable logic response to two logic inputs encoded in an aperiodic signal directly modulating the laser bias current. The probability of a correct response is controlled by the noise strength, and is equal to 1 in a wide region of noise strengths. LSR is associated with optimal noise-activated polarization switchings (the so-called “inter-well” dynamics if one considers the VCSEL as a bistable system described by a double-well potential) and optimal sensitivity to spontaneous emission in each polarization (the “intra-well” dynamics in the double-well potential picture). The robust nature of LSR in VCSELs offers interesting perspectives for novel applications and provides yet another example of a driven nonlinear optical system where noise can be employed constructively.

© 2010 Optical Society of America

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  1. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502–4513 (2006).
    [CrossRef]
  2. G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
    [CrossRef]
  3. H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
    [CrossRef]
  4. T. Ackemann, and M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
    [CrossRef]
  5. S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
    [CrossRef]
  6. J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
    [CrossRef]
  7. M. Sciamanna, and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
    [CrossRef]
  8. P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
    [CrossRef]
  9. J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
    [CrossRef]
  10. T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
    [CrossRef]
  11. H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17, 265–274 (2009).
    [CrossRef]
  12. T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
    [CrossRef]
  13. K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
    [CrossRef] [PubMed]
  14. K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
    [CrossRef]
  15. L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
    [CrossRef]
  16. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
    [CrossRef]
  17. M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
    [CrossRef]
  18. P. Mandel, Theoretical Problems in Cavity Nonlinear Optics, (Cambridge University Press, Cambridge, England, 1997).
    [CrossRef]
  19. C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
    [CrossRef]
  20. J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
    [CrossRef] [PubMed]
  21. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
    [CrossRef]
  22. C. Masoller, and N. B. Abraham, “Low-frequency uctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
    [CrossRef]
  23. S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
    [CrossRef]
  24. G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
    [CrossRef]
  25. C. Masoller, and M. S. Torre, “Modeling thermal effects and polarization competition in vertical-cavity surface emitting lasers,” Opt. Express 16, 21282–21296 (2008).
    [CrossRef] [PubMed]
  26. M. Borromeo, and F. Marchesoni, “Asymmetric probability densities in symmetrically modulated bistable devices,” Phys. Rev. E 71, 031105 (2005).
    [CrossRef]
  27. S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
    [CrossRef]
  28. S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted transmission of binary information: theory and experiment,” Phys. Rev. E 63, 051110 (2001).
    [CrossRef]
  29. D. V. Dylov, and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
    [CrossRef]

2010 (2)

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

D. V. Dylov, and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

2009 (5)

T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
[CrossRef]

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17, 265–274 (2009).
[CrossRef]

T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
[CrossRef]

K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

2008 (1)

C. Masoller, and M. S. Torre, “Modeling thermal effects and polarization competition in vertical-cavity surface emitting lasers,” Opt. Express 16, 21282–21296 (2008).
[CrossRef] [PubMed]

2006 (4)

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502–4513 (2006).
[CrossRef]

M. Sciamanna, and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

2005 (1)

M. Borromeo, and F. Marchesoni, “Asymmetric probability densities in symmetrically modulated bistable devices,” Phys. Rev. E 71, 031105 (2005).
[CrossRef]

2004 (2)

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

2002 (3)

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
[CrossRef]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

2001 (2)

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted transmission of binary information: theory and experiment,” Phys. Rev. E 63, 051110 (2001).
[CrossRef]

T. Ackemann, and M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

2000 (1)

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
[CrossRef]

1999 (3)

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

C. Masoller, and N. B. Abraham, “Low-frequency uctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

1998 (3)

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

Abraham, N. B.

C. Masoller, and N. B. Abraham, “Low-frequency uctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

Ackemann, T.

T. Ackemann, and M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

Ahopelto, J.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Albert, J.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

Balle, S.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

Bandyopadhyay, S.

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Barbay, S.

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted transmission of binary information: theory and experiment,” Phys. Rev. E 63, 051110 (2001).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
[CrossRef]

Borromeo, M.

M. Borromeo, and F. Marchesoni, “Asymmetric probability densities in symmetrically modulated bistable devices,” Phys. Rev. E 71, 031105 (2005).
[CrossRef]

Bulsara, A. R.

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

Choquette, K. D.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

Curtin, D. P.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
[CrossRef]

Danckaert, J.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

Dari, A.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Ditto, W. L.

K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

Dylov, D. V.

D. V. Dylov, and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

Fleischer, J. W.

D. V. Dylov, and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

Forchel, A.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Gabrysch, M.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

Gahl, A.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

Gammaitoni, L.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Gavrielides, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

Giacomelli, G.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted transmission of binary information: theory and experiment,” Phys. Rev. E 63, 051110 (2001).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
[CrossRef]

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

Gulden, K. H.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

Hänggi, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Hartmann, F.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Hofling, S.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

Hong, Y.

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

Jung, P.

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Kamp, M.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Katayama, T.

T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
[CrossRef]

Kawaguchi, H.

T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
[CrossRef]

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17, 265–274 (2009).
[CrossRef]

T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
[CrossRef]

Khalid, M. U. F.

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

Kim, T. Y.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Koyama, F.

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502–4513 (2006).
[CrossRef]

Li, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

Mandel, P.

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
[CrossRef]

Marchesoni, F.

M. Borromeo, and F. Marchesoni, “Asymmetric probability densities in symmetrically modulated bistable devices,” Phys. Rev. E 71, 031105 (2005).
[CrossRef]

L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70, 223–287 (1998).
[CrossRef]

Marin, F.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted transmission of binary information: theory and experiment,” Phys. Rev. E 63, 051110 (2001).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
[CrossRef]

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

Martin-Regalado, J.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

Masoller, C.

C. Masoller, and M. S. Torre, “Modeling thermal effects and polarization competition in vertical-cavity surface emitting lasers,” Opt. Express 16, 21282–21296 (2008).
[CrossRef] [PubMed]

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
[CrossRef]

C. Masoller, and N. B. Abraham, “Low-frequency uctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

McInerney, J. G.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
[CrossRef]

Michalzik, R.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

Mirasso, C.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

Mori, T.

T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
[CrossRef]

Moser, M.

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

Murali, K.

K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

Nagler, B.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

Neri, I.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Ooi, T.

T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
[CrossRef]

Panajotov, K.

M. Sciamanna, and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

Paul, J.

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

Peeters, M.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

Porta, P. A.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
[CrossRef]

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

Rajamohamed, I.

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

San Miguel, M.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

Sato, Y.

T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
[CrossRef]

Sciamanna, M.

M. Sciamanna, and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

Shina, S.

K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

Shore, K. A.

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Sondermann, M.

T. Ackemann, and M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

Soriano, M. C.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

Spencer, P. S.

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Tolkachova, E.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

Torre, M. S.

C. Masoller, and M. S. Torre, “Modeling thermal effects and polarization competition in vertical-cavity surface emitting lasers,” Opt. Express 16, 21282–21296 (2008).
[CrossRef] [PubMed]

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
[CrossRef]

Tredicce, J. R.

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

Unold, H.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

van Exter, M. P.

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

Veretennicoff, I.

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

Verschaffelt, G.

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

Willemsen, M. B.

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

Woerdman, J. P.

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

Worschech, L.

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

Appl. Phys. Lett. (5)

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical cavity surface-emitting lasers,” Appl. Phys. Lett. 72, 2355–2357 (1998).
[CrossRef]

T. Ackemann, and M. Sondermann, “Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 78, 3574–3576 (2001).
[CrossRef]

K. Murali, I. Rajamohamed, S. Shina, W. L. Ditto, and A. R. Bulsara, “Realization of reliable and flexible logic gates using noisy nonlinear circuits,” Appl. Phys. Lett. 95, 194102 (2009).
[CrossRef]

L. Worschech, F. Hartmann, T. Y. Kim, S. Hofling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, and L. Gammaitoni, “Universal and reconfigurable logic gates in a compact three-terminal resonant tunneling diode,” Appl. Phys. Lett. 96, 042112 (2010).
[CrossRef]

G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, and F. Marin, “Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 80, 2248–2250 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface- emitting lasers,” IEEE J. Quantum Electron. 33, 765–783 (1997).
[CrossRef]

T. Katayama, T. Ooi, and H. Kawaguchi, “Experimental demonstration of multi-bit optical buffer memory using 1.55-mu m polarization bistable vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1495–1504 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

J. Danckaert, M. Peeters, C. Mirasso, M. San Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, and F. Marin, “Stochastic polarization switching dynamics in vertical-cavity surface emitting lasers: theory and experiment,” IEEE J. Sel. Top. Quantum Electron. 10, 911–917 (2004).
[CrossRef]

J. Albert, M. C. Soriano, I. Veretennicoff, K. Panajotov, J. Danckaert, P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry with polarization-bistable VCSELs,” IEEE J. Sel. Top. Quantum Electron. 10, 1006–1012 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. A. Porta, D. P. Curtin, and J. G. McInerney, “Laser Doppler velocimetry by optical self-mixing, in vertical cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 14, 1719–1721 (2002).
[CrossRef]

IEICE Trans. Electron E (1)

T. Mori, Y. Sato, and H. Kawaguchi, “10-Gb/s optical buffer memory using a polarization bistable VCSEL,” IEICE Trans. Electron E 92C, 957–963 (2009).
[CrossRef]

J. Appl. Phys. (1)

C. Masoller, M. S. Torre, and P. Mandel, “Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers,” J. Appl. Phys. 99, 026106 (2006).
[CrossRef]

J. Lightwave Technol. (1)

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502–4513 (2006).
[CrossRef]

Nat. Photonics (1)

D. V. Dylov, and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photonics 4, 323–328 (2010).
[CrossRef]

Opt. Commun. (2)

G. Giacomelli, F. Marin, M. Gabrysch, K. H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Commun. 146, 136–140 (1998).
[CrossRef]

S. Bandyopadhyay, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental observation of anti-phase polarisation dynamics in VCSELS,” Opt. Commun. 202, 145–154 (2002).
[CrossRef]

Opt. Express (1)

C. Masoller, and M. S. Torre, “Modeling thermal effects and polarization competition in vertical-cavity surface emitting lasers,” Opt. Express 16, 21282–21296 (2008).
[CrossRef] [PubMed]

Opt. Lett. (3)

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25, 1095–1097 (2000).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation,” Opt. Lett. 31, 748–750 (2006).
[CrossRef] [PubMed]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martin-Regalado, and A. Gahl, “Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics,” Opt. Lett. 24, 1121–1123 (1999).
[CrossRef]

Opto-Electron. Rev. (1)

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17, 265–274 (2009).
[CrossRef]

Phys. Rev. A (2)

M. Sciamanna, and K. Panajotov, “Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers,” Phys. Rev. A 73, 023811 (2006).
[CrossRef]

C. Masoller, and N. B. Abraham, “Low-frequency uctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

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[CrossRef]

M. Borromeo, and F. Marchesoni, “Asymmetric probability densities in symmetrically modulated bistable devices,” Phys. Rev. E 71, 031105 (2005).
[CrossRef]

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K. Murali, S. Shina, W. L. Ditto, and A. R. Bulsara, “Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor,” Phys. Rev. Lett. 102, 104101 (2009).
[CrossRef] [PubMed]

M. B. Willemsen, M. U. F. Khalid, M. P. van Exter, and J. P. Woerdman, “Polarization switching of a vertical cavity semiconductor laser as a Kramers hopping problem,” Phys. Rev. Lett. 82, 4815–4818 (1999).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

(a) Intensities of the x and y polarizations when the injection current increases and decreases linearly, from μi = 0.95 to μf = 1.4 in a time interval equal to 40 μs. x polarization in red for increasing (red triangles) and decreasing (red solid line) current; y polarization in blue for increasing (blue circles) and decreasing (blue solid line) current. The parameters are k = 300 ns−1, α = 3, γN = 1 ns−1, γa = 0.5 ns−1, γp = 50 rad ns−1, γs = 50 ns−1 and D =10−6 ns−1. (b) Schematic representation of the effective potential at four different pump current values, corresponding to labels I to IV in Fig. 1(a). The solid square indicates the three values that can be used for implementing a logic AND; the dashed square indicates the three values that can be used for implementing a logic OR (see text for details). (c) As Fig. 1(a) but when the injection current varies from μi = 0.95 to μf = 1.4 in a time interval equal to 25 ns. (d) Schematic representation of the current variation within a bit (see text for details).

Fig. 2.
Fig. 2.

Time traces of the x polarization (solid red), y polarization (solid blue), and the injection current μ − 1 (dashed black) for different noise intensities: (a), (d) D = 5×10−7 ns−1, (b), (e) D = 4×10−4 ns−1 and (c), (f) D = 6×10−3 ns−1. (d)–(f) display a detail of (a)–(c) to show t he main errors in a bit. The asterisks mark the wrong bits. The parameters are: T =31.5 ns, μ 0 =1.3, Δμ =0.27, k = 300 ns−1, α = 3, γN = 1 ns−1, γa = 0.5 ns−1, γp = 50 rad ns−1 and γs = 50 ns−1.

Fig. 3.
Fig. 3.

(a) Success probability P as a function of the noise strength, D, keeping fixed the bit time T =31.5 ns and using a success criterium of 80%-20% (black solid line), 90%-10% (red dashed line) and 70%-30% (blue dashed line), see text for details. (b) Success probability as a function of the bit time T for fixed noise strength D =4×10−4 ns−1. (c) Log-log color plot of the success probability P as a function of the noise intensity, D, and the the bit time, T. Other parameters as in Fig. 2.

Fig. 4.
Fig. 4.

(a) Color plot of the success probability P as a function of the noise intensity, D, and the cw current value, μ 0, for fixed bit length T = 31.5 ns and modulation amplitude Δμ = 0.27. (b) Color plot of the success probability P as a function of the bit time, T, and the cw current value, μ 0 for fixed noise strength D =4×10−4 ns−1 and modulation amplitude Δμ = 0.27. Other parameters are as in Fig. 2.

Fig. 5.
Fig. 5.

Color plot of the success probability P (a) as a function of the noise strength, D, and the current modulation amplitude, Δμ, for a fixed T = 31.5 ns and (b) as a function of the bit time, T, and the current modulation amplitude, Δμ, for a fixed D =4×10−4 ns−1. Other parameters are as in Fig. 2.

Fig. 6.
Fig. 6.

(a) Color plot of the success probability P as a function of the step time, T 1, and the rise/fall time, T 2, the noise level is D =4×10−4 ns−1 and other parameters are as in Fig. 2. (b) P as a function of the noise strength, D, and the feedback strength, κfb . The bit time is T = 31.5 ns, the time delay is 3 ns and other parameters are as in Fig. 2.

Fig. 7.
Fig. 7.

Influence of various model parameters. (a) Success probability in parameter plane (γa , γp ), for γs = 50 ns−1; (b) P in the parameter plane (γs , γp ), for γa = 0.5 ns−1; P in the parameter plane (γa , γs ), for γp = 50 rad ns−1. Other parameters are as in Fig. 2.

Tables (3)

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Table 1. Relationship between the two inputs and the output of the logic operations.

Tables Icon

Table 2. Encoding scheme I: Relationship between the logic inputs, the encoding current levels, the output polarization and the logic output for the AND and OR operations.

Tables Icon

Table 3. Encoding scheme II: Relationship between the logic inputs, the encoding current levels, the output polarization and the logic output for the AND and OR operations.

Equations (3)

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d E x , y dt = k ( 1 + i α ) [ ( N 1 ) E x , y ± in E y , x ] ( γ a + i γ p ) E x , y + β sp γ N N ξ x , y ,
dN dt = γ N [ μ ( t ) N ( 1 + E x 2 + E y 2 ) in ( E y E x * E x E y * ) ] ,
dn dt = γ s n γ N [ n ( E x 2 + E y 2 ) + i N ( E y E x * E x E y * ) ] ,

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