Abstract

We present an experimental and theoretical study of the polarization and time-resolved nonlinear dynamics of a long-wavelength single-mode linearly polarized vertical-cavity surface-emitting laser (VCSEL) subject to orthogonal optical injection. Special attention is paid to the correlation properties of both linear polarizations emitted by the VCSEL. We measure simultaneous time traces of both linearly polarized output signals for several values of the bias current, the strength of the optical injection, and the frequency detuning between master and the free-running VCSEL. Different dynamical regimes, including periodic, period doubling, and irregular dynamics, are observed for both polarizations. For positive frequency detuning we usually find that the orthogonal polarization is the only polarization that contributes to the dynamics of the total power. Only for large values of the bias current and for small values of the optical injection strength, near the border of the periodic region, have we found correlated periodic dynamics in both linear polarizations. For negative frequency detuning we find anticorrelated dynamics in both linear polarizations. The average and dispersion of the time between consecutive pulses that appear in the anticorrelated regime increase with the injected power. The irregular dynamics, characterized by broadened power spectra, is related to large values of the dispersion of the time between pulses. A good overall qualitative agreement is found between our theoretical and experimental results.

© 2011 Optical Society of America

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  1. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
    [CrossRef]
  2. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254–2256 (2006).
    [CrossRef] [PubMed]
  3. G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
    [CrossRef]
  4. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24, 4502–4513 (2006).
    [CrossRef]
  5. D. Parekh, B. Zhang, X. Zhao, Y. Yue, W. Hofmann, M. C. Amann, A. Willner, and C. J. Chang-Hasnain, “Long distance single-mode fiber transmission of multimode VCSELs by injection locking,” Opt. Express 18, 20552–20557 (2010).
    [CrossRef] [PubMed]
  6. H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
    [CrossRef]
  7. Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
    [CrossRef]
  8. J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (2006).
    [CrossRef]
  9. I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
    [CrossRef]
  10. K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
    [CrossRef]
  11. M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
    [CrossRef]
  12. D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
    [CrossRef]
  13. A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs),” Opt. Express 18, 9423–9428(2010).
    [CrossRef] [PubMed]
  14. P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
    [CrossRef]
  15. R. Al-Seyab, K. Schires, N. A. Khan, A. Hurtado, I. D. Henning, and M. J. Adams, “Dynamics of polarized optical injection in 1550 nm VCSELs: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 17, 1242–1249 (2011).
    [CrossRef]
  16. Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, and R. E. Leibenguth, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
    [CrossRef]
  17. K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
    [CrossRef]
  18. A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
    [CrossRef]
  19. A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
    [CrossRef]
  20. M. S. Torre, A. Quirce, A. Valle, and L. Pesquera, “Wavelength-induced polarization bistability in 1550 nm VCSELs subject to orthogonal optical injection,” J. Opt. Soc. Am. B 27, 2542–2548(2010).
    [CrossRef]
  21. S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
    [CrossRef]
  22. 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]
  23. B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
    [CrossRef]
  24. L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
    [CrossRef]
  25. J. M. Martín-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]
  26. J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
    [CrossRef]
  27. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber AM-to-FM upconversion using and optically injected semiconductor laser,” Opt. Lett. 31, 2254–2256 (2006).
    [CrossRef] [PubMed]

2011

P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
[CrossRef]

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

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

2010

2009

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

2008

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
[CrossRef]

A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
[CrossRef]

2007

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

2006

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (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]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber AM-to-FM upconversion using and optically injected semiconductor laser,” Opt. Lett. 31, 2254–2256 (2006).
[CrossRef] [PubMed]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over-fiber AM-to-FM upconversion using an optically injected semiconductor laser,” Opt. Lett. 31, 2254–2256 (2006).
[CrossRef] [PubMed]

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

2005

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

2003

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

2001

J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
[CrossRef]

1999

D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
[CrossRef]

1997

J. M. Martín-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]

1996

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

1995

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[CrossRef]

1993

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

Abraham, N. B.

J. M. Martín-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]

Adams, M. J.

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

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs),” Opt. Express 18, 9423–9428(2010).
[CrossRef] [PubMed]

A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
[CrossRef]

Al-Seyab, R.

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

Amann, A.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Amann, M. C.

Asom, M. T.

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

Bandyopadhyay, S.

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Besnard, P.

D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
[CrossRef]

Boiko, D. L.

D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
[CrossRef]

Bonatto, C.

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

Buckley, K.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Buesa, J.

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (2006).
[CrossRef]

Chan, S. C.

Chang-Hasnain, C. J.

Dagenais, M.

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

Gatare, I.

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (2006).
[CrossRef]

Gomez-Molina, M.

A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
[CrossRef]

Hegarty, S. G.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Hegarty, S. P.

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

Henning, I. D.

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

A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
[CrossRef]

Hofmann, W.

Hong, Y.

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Hurtado, A.

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

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs),” Opt. Express 18, 9423–9428(2010).
[CrossRef] [PubMed]

A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
[CrossRef]

Huyet, G.

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Hwang, S. K.

Jeong, K. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Jiang, S.

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

Kelleher, B.

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

Khan, N. A.

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

Kim, K. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Kojima, K.

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

Koyama, F.

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Lee, M. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Lee, S. H.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Leibenguth, R. E.

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

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[CrossRef]

Li, H.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

Liu, J. M.

Lucas, T.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

Martín-Regalado, J. M.

J. M. Martín-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]

McInerney, J. G.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

Miguel, M. San

J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
[CrossRef]

J. M. Martín-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]

Mirasso, C. R.

J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
[CrossRef]

Morgan, R. A.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

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

Mulet, J.

J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
[CrossRef]

Nizette, M.

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

O’Brien, S.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Olejniczak, L.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
[CrossRef]

Osborne, S.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Pan, Z. G.

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

Panajotov, K.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (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]

Parekh, D.

Pérez, P.

P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
[CrossRef]

Pesquera, L.

P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
[CrossRef]

M. S. Torre, A. Quirce, A. Valle, and L. Pesquera, “Wavelength-induced polarization bistability in 1550 nm VCSELs subject to orthogonal optical injection,” J. Opt. Soc. Am. B 27, 2542–2548(2010).
[CrossRef]

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs),” Opt. Express 18, 9423–9428(2010).
[CrossRef] [PubMed]

A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
[CrossRef]

Prati, F.

J. M. Martín-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]

Quirce, A.

Rees, P.

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Ryan, G.

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[CrossRef]

Schires, K.

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

Sciamanna, M.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (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]

Shore, K. A.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Spencer, P. S.

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Stéphan, G. M.

D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
[CrossRef]

Thienpont, H.

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
[CrossRef]

M. Nizette, M. Sciamanna, I. Gatare, H. Thienpont, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers with optical injection: a two-mode model approach,” J. Opt. Soc. Am. B 26, 1603–1613 (2009).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (2006).
[CrossRef]

Torre, M. S.

Valle, A.

P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
[CrossRef]

M. S. Torre, A. Quirce, A. Valle, and L. Pesquera, “Wavelength-induced polarization bistability in 1550 nm VCSELs subject to orthogonal optical injection,” J. Opt. Soc. Am. B 27, 2542–2548(2010).
[CrossRef]

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm vertical-cavity surface-emitting lasers (VCSELs),” Opt. Express 18, 9423–9428(2010).
[CrossRef] [PubMed]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
[CrossRef]

van Tartwijk, G. H. M.

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[CrossRef]

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Willner, A.

Wright, M.

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

Yoo, B. S.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

Yue, Y.

Zhang, B.

Zhao, X.

Appl. Phys. Lett.

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

IEEE J. Quantum Electron.

J. M. Martín-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]

H. Li, T. Lucas, J. G. McInerney, M. Wright, and R. A. Morgan, “Injection locking dynamics of vertical cavity semiconductor lasers under conventional and phase conjugate injection,” IEEE J. Quantum Electron. 32, 227–235 (1996).
[CrossRef]

J. Buesa, I. Gatare, K. Panajotov, H. Thienpont, and M. Sciamanna, “Mapping of the dynamics induced by orthogonal optical injection in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 42, 198–207 (2006).
[CrossRef]

K. Panajotov, I. Gatare, A. Valle, H. Thienpont, and M. Sciamanna, “Polarization- and transverse-mode dynamics in optically injected and gain-switched vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 45, 1473–1481(2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

P. Pérez, A. Quirce, L. Pesquera, and A. Valle, “Polarization-resolved nonlinear dynamics induced by orthogonal optical injection in long-wavelength VCSELs,” IEEE J. Sel. Top. Quantum Electron. 17, 1228–1235 (2011).
[CrossRef]

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

A. Hurtado, I. D. Henning, and M. J. Adams, “Two-wavelength switching with a 1550 nm VCSEL under single orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 911–917(2008).
[CrossRef]

A. Valle, M. Gomez-Molina, and L. Pesquera, “Polarization bistability in 1550 nm wavelength single-mode vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Sel. Top. Quantum Electron. 14, 895–902(2008).
[CrossRef]

IEEE Photon. Technol. Lett.

K. H. Jeong, K. H. Kim, S. H. Lee, M. H. Lee, B. S. Yoo, and K. A. Shore, “Optical injection-induced polarization switching dynamics in 1.5 μm wavelength single-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 20, 779–781 (2008).
[CrossRef]

J. Appl. Phys.

D. L. Boiko, G. M. Stéphan, and P. Besnard, “Fast polarization switching with memory effect in a vertical cavity surface emitting laser subject to modulated optical injection,” J. Appl. Phys. 86, 4096–4099 (1999).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, “Polarization resolved chaos and instabilities in a VCSEL subject to optical injection,” Opt. Commun. 216, 185–187(2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[CrossRef]

Phys. Rev. A

I. Gatare, M. Sciamanna, M. Nizette, and K. Panajotov, “Bifurcation to polarization switching and locking in vertical-cavity surface-emitting lasers with optical injection,” Phys. Rev. A 76, 031803(R) (2007).
[CrossRef]

J. Mulet, C. R. Mirasso, and M. San Miguel, “Polarization resolved intensity noise in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 023817 (2001).
[CrossRef]

S. Osborne, A. Amann, K. Buckley, G. Ryan, S. G. Hegarty, G. Huyet, and S. O’Brien, “Antiphase dynamics in a multimode semiconductor laser with optical injection,” Phys. Rev. A 79, 023834 (2009).
[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]

L. Olejniczak, K. Panajotov, H. Thienpont, and M. Sciamanna, “Self-pulsations and excitability in optically injected quantum dot lasers: impact of the excited states and spontaneous emission noise,” Phys. Rev. A 82, 023807(2010).
[CrossRef]

Phys. Rev. E

B. Kelleher, C. Bonatto, G. Huyet, and S. P. Hegarty, “Excitability in optically injected semiconductor lasers: contrasting quantum-well and quantum-dot-based devices,” Phys. Rev. E 83, 026207 (2011).
[CrossRef]

Quantum Semiclass. Opt.

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental setup of orthogonal optical injection in a VCSEL.

Fig. 2
Fig. 2

Stability map of the VCSEL subject to orthogonal optical injection for applied bias current of (a)  4 mA and (b)  8 mA [14]. Different regions are observed: SL, stable injection locking; P1, period 1; P2, period 2; IR, irregular dynamics; PS, polarization switching. The stars mark the situations analyzed in Figs. 3, 4, 5, 6.

Fig. 3
Fig. 3

(Left) RF spectra of the total and polarized powers. (Right) Time traces of the total power and of the power of both linear polarizations. Several values of injected power are considered: (a), (b)  P inj = 47 μW , (c), (d)  P inj = 76.4 μW , (e), (f)  P inj = 158 μW , (g), (h)  P inj = 240.3 μW , and (i), (j)  P inj = 1275.5 μW . The frequency detuning is Δ ν = 4 GHz , and the bias current is 4 mA .

Fig. 4
Fig. 4

(Left) RF spectra of the total and polarized powers. (Right) Time traces of the total power and of the power of both linear polarizations. Several values of injected power are considered: (a), (b)  P inj = 26.9 μW , (c), (d)  P inj = 35.5 μW , (e), (f)  P inj = 42.4 μW , and (g), (h)  P inj = 53.6 μW . The frequency detuning is Δ ν = 2 GHz , and the applied bias current is 4 mA .

Fig. 5
Fig. 5

(Left) RF spectra of the total and polarized powers. (Right) Time traces of the total power and of the power of both linear polarizations. Several values of injected power are considered: (a), (b)  P inj = 96.1 μW , (c), (d)  P inj = 127.6 μW , (e), (f)  P inj = 197.3 μW , (g), (h)  P inj = 287.8 μW , and (i), (j)  P inj = 3301.8 μW . The frequency detuning is Δ ν = 5 GHz , and the applied bias current is 8 mA .

Fig. 6
Fig. 6

(Left) RF spectra of the total and polarized powers. (Right) Time traces of the total power and of the power of both linear polarizations. Several values of injected power are considered: (a), (b)  P inj = 58.5 μW , (c), (d)  P inj = 67.6 μW , (e), (f)  P inj = 84 μW , and (g), (h)  P inj = 111.2 μW . The frequency detuning is Δ ν = 1.5 GHz , and the applied bias current is 8 mA .

Fig. 7
Fig. 7

Theoretical time traces of the (a) total power and power of both linear polarizations and (b) total population inversion (solid line) and k E inj cos ( Δ ω t ϕ x ( t ) ) term (dashed line). The frequency detuning is Δ ν = 5 GHz , μ = 5 , and E inj = 0.29 .

Fig. 8
Fig. 8

Theoretical time traces of the (a), (b) total power and power of both linear polarizations, (c), (d) total population inversion and k E inj cos ( Δ ω t ϕ x ( t ) ) term, and (e), (f) RF spectra. The frequency detuning is Δ ν = 2 GHz , μ = 2.44 , (left)  E inj = 0.0445 , and (right)  E inj = 0.047 .

Equations (5)

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C ( τ ) = ( P ( t + τ ) P ¯ ) ( P ( t ) P ¯ ) σ σ ¯ ,
d E x d t = κ ( 1 + i α ) ( N E x + i n E y E x ) i γ p E x γ a E x + κ E inj e i Δ ω t + β s p γ e / 2 ( N + n ξ + ( t ) + N n ξ ( t ) ) ,
d E y d t = κ ( 1 + i α ) ( N E y i n E x E y ) + i γ p E y + γ a E y + β s p γ e / 2 ( N + n ξ + ( t ) + N n ξ ( t ) ) ,
d N d t = γ e ( N ( 1 + | E x | 2 + | E y | 2 ) ) + γ e μ i γ e n ( E y E x * E x E y * ) ,
d n d t = γ s n γ e n ( | E x | 2 + | E y | 2 ) i γ e N ( E y E x * E x E y * ) ,

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