Abstract

We study numerically the dynamics of a vertical-cavity surface-emitting laser (VCSEL) with optical injection and show that the interplay of polarization bistability and noise yields a reliable logic output to two logic inputs. Specifically, by encoding the logic inputs in the strength of the light injected into the suppressed polarization mode of the VCSEL (the so-called ‘orthogonal’ injection), and by decoding the output logic response from the polarization state of the emitted light, we demonstrate an all-optical stochastic logic gate that exploits the ubiquitous presence of noise. It gives the correct logic output response for as short as 5 ns bit times when the dimensionless spontaneous emission coefficient, βsp, is within the range 10−4-10−1. Considering that typical values of βsp in semiconductor lasers are in the range 10−5-10−4, the VCSEL-based logic gate can be implemented with nowadays commercially available VCSELs, exploiting either their intrinsic noise, or external and background noise sources.

© 2012 OSA

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  1. K. Murali, S. Sinha, 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(10), 104101 (2009).
    [CrossRef] [PubMed]
  2. L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
    [CrossRef]
  3. J. Zamora-Munt and C. Masoller, “Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability,” Opt. Express 18(16), 16418–16429 (2010).
    [CrossRef] [PubMed]
  4. S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25(15), 1095–1097 (2000).
    [CrossRef] [PubMed]
  5. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
    [CrossRef]
  6. 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(6), 748–750 (2006).
    [CrossRef] [PubMed]
  7. 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(2), 026108 (2006).
    [CrossRef]
  8. Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
    [CrossRef]
  9. M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
    [CrossRef] [PubMed]
  10. A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (2009).
    [CrossRef]
  11. M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
    [CrossRef]
  12. H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17(4), 265–274 (2009).
    [CrossRef]
  13. 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,” J. Quantum Electron. 45(11), 1495–1504 (2009).
    [CrossRef]
  14. F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
    [CrossRef]
  15. A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
    [CrossRef] [PubMed]
  16. K. P. Singh and S. Sinha, “Enhancement of “logical” responses by noise in a bistable optical system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046219 (2011).
    [CrossRef] [PubMed]
  17. S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
    [CrossRef]
  18. J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, 2nd ed. (Springer, Berlin, 2007).
  19. F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
    [CrossRef]
  20. S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martín-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(16), 1121–1123 (1999).
    [CrossRef] [PubMed]
  21. E. L. Blansett, M. G. Raymer, G. Khitrova, H. M. Gibbs, D. K. Serkland, A. A. Allerman, and K. M. Geib, “Ultrafast polarization dynamics and noise in pulsed vertical-cavity surface-emitting lasers,” Opt. Express 9(6), 312–318 (2001).
    [CrossRef] [PubMed]
  22. M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
    [CrossRef]
  23. 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. Quantum Electron. 10(5), 911–917 (2004).
    [CrossRef]
  24. G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
    [CrossRef]
  25. J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
    [CrossRef]
  26. C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
    [CrossRef]
  27. R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
    [CrossRef]

2011 (6)

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

K. P. Singh and S. Sinha, “Enhancement of “logical” responses by noise in a bistable optical system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046219 (2011).
[CrossRef] [PubMed]

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

2010 (1)

2009 (4)

A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (2009).
[CrossRef]

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17(4), 265–274 (2009).
[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,” J. Quantum Electron. 45(11), 1495–1504 (2009).
[CrossRef]

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

2008 (1)

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[CrossRef]

2006 (3)

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(6), 748–750 (2006).
[CrossRef] [PubMed]

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[CrossRef]

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(2), 026108 (2006).
[CrossRef]

2005 (2)

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[CrossRef]

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
[CrossRef] [PubMed]

2004 (1)

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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

2003 (1)

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

2001 (1)

2000 (2)

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25(15), 1095–1097 (2000).
[CrossRef] [PubMed]

F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
[CrossRef]

1999 (1)

1998 (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[CrossRef]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[CrossRef]

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[CrossRef]

Ackemann, T.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

Adams, M.

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

Adams, M. J.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (2009).
[CrossRef]

Albert, J.

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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Ali Khan, N.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Allerman, A. A.

Al-Seyab, R.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Asom, M. T.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Balle, S.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[CrossRef]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martín-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(16), 1121–1123 (1999).
[CrossRef] [PubMed]

Barbay, S.

Barland, S.

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[CrossRef]

Blansett, E. L.

Bulsara, A. R.

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

Dagenais, M.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Danckaert, J.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Dari, A.

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

Ditto, W.

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

Ditto, W. L.

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

Focht, M. W.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Forchel, A.

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

Gahl, A.

Gammaitoni, L.

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[CrossRef]

Gavrielides, A.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

Geib, K. M.

Giacomelli, G.

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25(15), 1095–1097 (2000).
[CrossRef] [PubMed]

Gibbs, H. M.

Guth, G. D.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Hanggi, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[CrossRef]

Hartmann, F.

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

Henning, I. D.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (2009).
[CrossRef]

Hong, Y.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[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(6), 748–750 (2006).
[CrossRef] [PubMed]

Hurtado, A.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (2009).
[CrossRef]

Jiang, S.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Jung, P.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[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,” J. Quantum Electron. 45(11), 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,” J. Quantum Electron. 45(11), 1495–1504 (2009).
[CrossRef]

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17(4), 265–274 (2009).
[CrossRef]

Khitrova, G.

Kia, B.

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

Kojima, K.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Leibenguth, R. E.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Mandel, P.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[CrossRef]

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(2), 026108 (2006).
[CrossRef]

Marchesoni, F.

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[CrossRef]

Marin, F.

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
[CrossRef]

S. Barbay, G. Giacomelli, and F. Marin, “Noise-assisted binary information transmission in vertical cavity surface emitting lasers,” Opt. Lett. 25(15), 1095–1097 (2000).
[CrossRef] [PubMed]

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[CrossRef]

Martín-Regalado, J.

Masoller, C.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

J. Zamora-Munt and C. Masoller, “Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability,” Opt. Express 18(16), 16418–16429 (2010).
[CrossRef] [PubMed]

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[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(6), 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(2), 026108 (2006).
[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. Quantum Electron. 10(5), 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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Morgan, R. A.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Mulet, J.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

Murali, K.

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Neri, I.

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[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,” J. Quantum Electron. 45(11), 1495–1504 (2009).
[CrossRef]

Pan, Z. G.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

Panajotov, K.

Paul, J.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[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(6), 748–750 (2006).
[CrossRef] [PubMed]

Peeters, M.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Pesquera, L.

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

Prati, F.

F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[CrossRef]

Quirce, A.

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

Raymer, M. G.

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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

S. Balle, E. Tolkachova, M. San Miguel, J. R. Tredicce, J. Martín-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(16), 1121–1123 (1999).
[CrossRef] [PubMed]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[CrossRef]

Schires, K.

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

Sciamanna, M.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

M. Sciamanna and K. Panajotov, “Two-mode injection locking in vertical-cavity surface-emitting lasers,” Opt. Lett. 30(21), 2903–2905 (2005).
[CrossRef] [PubMed]

Serkland, D. K.

Shore, K. A.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[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(6), 748–750 (2006).
[CrossRef] [PubMed]

Singh, K. P.

K. P. Singh and S. Sinha, “Enhancement of “logical” responses by noise in a bistable optical system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046219 (2011).
[CrossRef] [PubMed]

Sinha, S.

K. P. Singh and S. Sinha, “Enhancement of “logical” responses by noise in a bistable optical system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046219 (2011).
[CrossRef] [PubMed]

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

Sondermann, M.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

Spencer, P. S.

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[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(6), 748–750 (2006).
[CrossRef] [PubMed]

Spinicelli, P.

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[CrossRef]

Sukow, D.

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

Tolkachova, E.

Torre, M.

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

Torre, M. S.

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(2), 026108 (2006).
[CrossRef]

Tredicce, J. R.

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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Valle, A.

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

Van der Sande, G.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[CrossRef]

Veretennicoff, I.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[CrossRef]

Verschaffelt, G.

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

Wang, X.

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

Weinkath, M.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

Worschech, L.

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

Zamora-Munt, J.

Appl. Phys. Lett. (2)

F. Hartmann, A. Forchel, I. Neri, L. Gammaitoni, and L. Worschech, “Nanowatt logic stochastic resonance in branched resonant tunneling diodes,” Appl. Phys. Lett. 98(3), 032110 (2011).
[CrossRef]

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(22), 2999–3001 (1993).
[CrossRef]

IEEE J. Quantum Electron. (6)

R. Al-Seyab, K. Schires, N. Ali Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550-nm VCSELs: theory and experiments,” IEEE J. Quantum Electron. 17(5), 1242–1249 (2011).
[CrossRef]

S. Barland, P. Spinicelli, G. Giacomelli, and F. Marin, “Measurement of the working parameters of an air-post vertical-cavity surface-emitting laser,” IEEE J. Quantum Electron. 41(10), 1235–1243 (2005).
[CrossRef]

M. Torre, A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. Adams, “Polarization switching in long wavelength VCSELs subject to orthogonal optical Injection,” IEEE J. Quantum Electron. 47(1), 92–99 (2011).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, member IEEE, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[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. Quantum Electron. 10(5), 911–917 (2004).
[CrossRef]

G. Van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, and S. Balle, “The effects of stress, temperature, and spin flips on polarization switching in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42(9), 896–906 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Hurtado, I. D. Henning, and M. J. Adams, “Wavelength polarization switching and bistability in a 1550nm-VCSEL subject to polarized optical injection,” IEEE Photon. Technol. Lett. 21(15), 1084–1086 (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(2), 026108 (2006).
[CrossRef]

J. Quantum Electron. (1)

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,” J. Quantum Electron. 45(11), 1495–1504 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Opto-Electron. Rev. (1)

H. Kawaguchi, “Polarization-bistable vertical-cavity surface-emitting lasers: application for optical bit memory,” Opto-Electron. Rev. 17(4), 265–274 (2009).
[CrossRef]

Phys. Rev. A (4)

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarisation switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[CrossRef]

C. Masoller, D. Sukow, A. Gavrielides, and M. Sciamanna, “Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: theory and experiment,” Phys. Rev. A 84(2), 023838 (2011).
[CrossRef]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68(3), 033822 (2003).
[CrossRef]

F. Prati, G. Giacomelli, and F. Marin, “Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise,” Phys. Rev. A 62(3), 033810 (2000).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

A. Dari, B. Kia, X. Wang, A. R. Bulsara, and W. Ditto, “Noise-aided computation within a synthetic gene network through morphable and robust logic gates,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041909 (2011).
[CrossRef] [PubMed]

K. P. Singh and S. Sinha, “Enhancement of “logical” responses by noise in a bistable optical system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 046219 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

K. Murali, S. Sinha, 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(10), 104101 (2009).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys. 70(1), 223–287 (1998).
[CrossRef]

Other (1)

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, 2nd ed. (Springer, Berlin, 2007).

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Figures (4)

Fig. 1
Fig. 1

Time trace of the intensity of the X polarization (red line) for three noise levels (a), (b) βsp = 10−5; (c),(d) βsp = 0.1; and (e), (f) βsp = 1; Tbit = 5 ns, other parameters are as indicated in the text. The black dashed line represents the three-level injection strength and the stars mark bits with wrong logic output. The pannels (b), (d) and (f) indicate a zoom of (a), (c) and (e).

Fig. 2
Fig. 2

Probability of success of an OR logic gate as function of the bit time (a), (b) and as a function of the noise strength (c), (d). The red, black and blue lines indicate the probability calculated using the 90/10, 80/20 and 70/30 criteria respectively (see text for details). ΔE is 0.0015 in panels (a), (c); and 0.005 in (b), (d), the bit time is 7 ns in panels (c), (d), other parameters are as indicated in the text.

Fig. 3
Fig. 3

Probablility of correct operation (in color code) as a function of the noise strength and the bit time (a), (b); and as a function of the modulation amplitude and the bit time (c), (d). The probability is calculated over 500 bits using the 80/20 criterioum of success logic OR operation. The parameters are ΔE = 0.0015 (a), ΔE = 0.005 (b), βsp = 10−4 (c) and βsp = 0.1 (d), other parameters as in the text.

Fig. 4
Fig. 4

Success probablility, P, as a function of the optical injection parameters (the injection modulation amplitude and the frequency detuning) for two bit times, 7 ns (a) and 5 ns (b); P as a function of the laser parameters (the birefringence and the spin-flip rate) (c), (the dicroism and the pump current) (d). The probability is calculated over 500 bits using the 80/20 criterioum of success logic OR operation. The parameters are ΔE = 0.003, βsp = 10−4, other parameters are as indicated in the text.

Tables (1)

Tables Icon

Table 1 Input–output combinations for an OR gate: the input is codified with the injection strength on the Y polarization; the response is decoded from the output polarization.

Equations (4)

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

d E x dt =k( 1+iα )[ ( N1 ) E x +in E y ]( γ a +i γ p +Δω ) E x + β sp γ N N ξ x ,
d E y dt =k( 1+iα )[ ( N1 ) E y in E x ]+( γ a +i γ p Δω ) E y + β sp γ N N ξ y +k E inj ,
dN dt = γ N [ μN( 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 )+iN( E y E x * E x E y * ) ],

Metrics