Abstract

We study photonic microwave signal generation obtained when single- and multi-transverse-mode vertical-cavity surface-emitting lasers (VCSELs) are subject to two-frequency orthogonal optical injection. Our calculations show that broadly tunable microwave signals can be obtained in these systems. The response of the multi-transverse-mode VCSEL is enhanced with respect to that obtained with a similar single-transverse-mode VCSEL subject to the same two-frequency orthogonal optical injection. The extra degree of freedom given by the multi-transverse-mode operation of the VCSEL under two-frequency orthogonal optical injection enhances the performance of the photonic microwave generation system, because the higher-order transverse mode is excited with a much larger amplitude than that of the fundamental transverse mode. Periodic oscillations are obtained for a very wide range of frequency detunings between the optical injections and transverse modes. A relative maximum of the microwave signal amplitude is obtained when the frequency of one of the optical injections is very close to the frequency of the orthogonally polarized fundamental mode of the VCSEL. Periodic oscillations are demonstrated for symmetric and asymmetric values of the injection strengths. Wide tuning ranges, extended into the THz band, are obtained in our system. Our results show that the proposed microwave signal generation mechanism is independent of the polarization of the master lasers.

© 2012 Optical Society of America

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  4. D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express 16, 21582–21586 (2008).
    [CrossRef]
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  6. 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]
  7. Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
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  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).
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    [CrossRef]
  10. 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]
  11. 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]
  12. 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]
  13. A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
    [CrossRef]
  14. A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
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    [CrossRef]
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    [CrossRef]
  17. A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
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  18. K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
    [CrossRef]
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    [CrossRef]
  20. H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express 19, 22437–22442 (2011).
    [CrossRef]
  21. S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
    [CrossRef]
  22. S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber transmission from an optically injected semiconductor laser in period-one state,” Opt. Express 15, 14921–14935 (2007).
    [CrossRef]
  23. X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1198–1211 (2011).
    [CrossRef]
  24. S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
    [CrossRef]
  25. 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]
  26. C. Cui and S. C. Chan, “Performance analysis on using period-one oscillation of optically injected semiconductor lasers for radio-over-fiber uplinks,” IEEE J. Quantum Electron. 48, 490–499 (2012).
    [CrossRef]
  27. X. Q. Qi and J. M. Liu, “Dynamic scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. 47, 762–769 (2011).
    [CrossRef]
  28. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3, 644–650 (2011).
    [CrossRef]
  29. Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
    [CrossRef]
  30. A. Quirce and A. Valle, “High-frequency microwave signal generation using multi-transverse mode VCSELs subject to two-frequency optical injection,” Opt. Express 20, 13390–13401(2012).
    [CrossRef]
  31. A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
    [CrossRef]
  32. G. H. M. Van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quantum Semiclass. Opt. 7, 87–143 (1995).
    [CrossRef]
  33. 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]
  34. J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity surface-emitting lasers including multiple reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
    [CrossRef]
  35. A. Valle and L. Pesquera, “Relative intensity noise of multitransverse-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 13, 272–274 (2001).
    [CrossRef]
  36. A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 597–606 (2004).
    [CrossRef]
  37. J. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
    [CrossRef]
  38. A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
    [CrossRef]

2012 (4)

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[CrossRef]

H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B 29, 867–873 (2012).
[CrossRef]

C. Cui and S. C. Chan, “Performance analysis on using period-one oscillation of optically injected semiconductor lasers for radio-over-fiber uplinks,” IEEE J. Quantum Electron. 48, 490–499 (2012).
[CrossRef]

A. Quirce and A. Valle, “High-frequency microwave signal generation using multi-transverse mode VCSELs subject to two-frequency optical injection,” Opt. Express 20, 13390–13401(2012).
[CrossRef]

2011 (5)

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1198–1211 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Dynamic scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. 47, 762–769 (2011).
[CrossRef]

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3, 644–650 (2011).
[CrossRef]

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
[CrossRef]

H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express 19, 22437–22442 (2011).
[CrossRef]

2010 (2)

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[CrossRef]

J. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
[CrossRef]

2009 (2)

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (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]

2008 (6)

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]

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]

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]

D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express 16, 21582–21586 (2008).
[CrossRef]

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

2007 (3)

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]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber transmission from an optically injected semiconductor laser in period-one state,” Opt. Express 15, 14921–14935 (2007).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[CrossRef]

2006 (3)

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

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]

2004 (1)

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 597–606 (2004).
[CrossRef]

2003 (1)

C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9, 1386–1393 (2003).
[CrossRef]

2001 (1)

A. Valle and L. Pesquera, “Relative intensity noise of multitransverse-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 13, 272–274 (2001).
[CrossRef]

2000 (1)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

1999 (1)

1996 (2)

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
[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]

1995 (3)

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

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

1993 (1)

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]

1991 (1)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Adams, M. J.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[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]

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]

Bacou, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

Balle, S.

J. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
[CrossRef]

Basnet, A. J.

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.

C. Cui and S. C. Chan, “Performance analysis on using period-one oscillation of optically injected semiconductor lasers for radio-over-fiber uplinks,” IEEE J. Quantum Electron. 48, 490–499 (2012).
[CrossRef]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[CrossRef]

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
[CrossRef]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber transmission from an optically injected semiconductor laser in period-one state,” Opt. Express 15, 14921–14935 (2007).
[CrossRef]

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]

Chang, C. H.

C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9, 1386–1393 (2003).
[CrossRef]

Chang-Hasnain, C. J.

D. Parekh, X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express 16, 21582–21586 (2008).
[CrossRef]

C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9, 1386–1393 (2003).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Chen, Y. C.

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
[CrossRef]

Choquette, K. D.

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

Chrostowski, L.

C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9, 1386–1393 (2003).
[CrossRef]

Cuesta, J. R.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[CrossRef]

Cui, C.

C. Cui and S. C. Chan, “Performance analysis on using period-one oscillation of optically injected semiconductor lasers for radio-over-fiber uplinks,” IEEE J. Quantum Electron. 48, 490–499 (2012).
[CrossRef]

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]

Dellunde, J.

Diaz, R.

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
[CrossRef]

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[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]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[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]

Ghisoni, M.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[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]

Halonen, J.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Hayat, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

Henning, I. D.

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, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

Hurtado, A.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[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]

Hwang, S. K.

Iakovlev, V.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

Javaloyes, J.

J. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
[CrossRef]

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]

Juan, Y. S.

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3, 644–650 (2011).
[CrossRef]

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
[CrossRef]

Kapon, E.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[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.

Lapin, Z. J.

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

Larsson, A.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

Lear, K. L.

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[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.

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[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]

Lenstra, D.

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]

Lin, F. Y.

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
[CrossRef]

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3, 644–650 (2011).
[CrossRef]

Lin, H.

Liu, J. M.

X. Q. Qi and J. M. Liu, “Dynamic scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. 47, 762–769 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1198–1211 (2011).
[CrossRef]

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
[CrossRef]

S. C. Chan, S. K. Hwang, and J. M. Liu, “Radio-over fiber transmission from an optically injected semiconductor laser in period-one state,” Opt. Express 15, 14921–14935 (2007).
[CrossRef]

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]

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]

Malla, B.

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[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]

Mollier, J. C.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[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]

Nizette, M.

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]

Ohtsubo, J.

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2007).

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.

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, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[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]

Parekh, D.

Pesquera, L.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[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]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 597–606 (2004).
[CrossRef]

A. Valle and L. Pesquera, “Relative intensity noise of multitransverse-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 13, 272–274 (2001).
[CrossRef]

J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity surface-emitting lasers including multiple reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
[CrossRef]

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
[CrossRef]

Pierce, D. W.

Qi, X. Q.

X. Q. Qi and J. M. Liu, “Dynamic scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. 47, 762–769 (2011).
[CrossRef]

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1198–1211 (2011).
[CrossRef]

Quirce, A.

Rissons, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Schneider, R. P.

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[CrossRef]

Sciamanna, M.

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, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[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]

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, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity surface-emitting lasers including multiple reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
[CrossRef]

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Sirbu, A.

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

Thienpont, H.

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]

Valle, A.

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[CrossRef]

H. Lin, Y. Zhang, D. W. Pierce, A. Quirce, and A. Valle, “Polarization dynamics of a multimode vertical-cavity surface-emitting laser subject to orthogonal optical injection,” J. Opt. Soc. Am. B 29, 867–873 (2012).
[CrossRef]

A. Quirce and A. Valle, “High-frequency microwave signal generation using multi-transverse mode VCSELs subject to two-frequency optical injection,” Opt. Express 20, 13390–13401(2012).
[CrossRef]

H. Lin, D. W. Pierce, A. J. Basnet, A. Quirce, Y. Zhang, and A. Valle, “Two-frequency injection on a multimode vertical-cavity surface-emitting laser,” Opt. Express 19, 22437–22442 (2011).
[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]

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]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[CrossRef]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 597–606 (2004).
[CrossRef]

A. Valle and L. Pesquera, “Relative intensity noise of multitransverse-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 13, 272–274 (2001).
[CrossRef]

J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity surface-emitting lasers including multiple reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
[CrossRef]

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[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]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

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]

Zenteno, L. A.

Zhang, Y.

Zhao, X.

Appl. Phys. Lett. (1)

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]

Electron. Lett. (1)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, “Pure frequency-polarisation bistability in vertical-cavity surface-emitting lasers subject to optical injection,” Electron. Lett. 36, 2019–2020 (2000).
[CrossRef]

IEEE J. Quantum Electron. (10)

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]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 27, 1402–1409 (1991).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial holeburning effects on the dynamics of vertical cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, “Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection,” IEEE J. Quantum Electron. 43, 322–333 (2007).
[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]

C. Cui and S. C. Chan, “Performance analysis on using period-one oscillation of optically injected semiconductor lasers for radio-over-fiber uplinks,” IEEE J. Quantum Electron. 48, 490–499 (2012).
[CrossRef]

X. Q. Qi and J. M. Liu, “Dynamic scenarios of dual-beam optically injected semiconductor lasers,” IEEE J. Quantum Electron. 47, 762–769 (2011).
[CrossRef]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[CrossRef]

A. Valle and L. Pesquera, “Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 40, 597–606 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (6)

X. Q. Qi and J. M. Liu, “Photonic microwave applications of the dynamics of semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 17, 1198–1211 (2011).
[CrossRef]

A. Quirce, J. R. Cuesta, A. Valle, A. Hurtado, L. Pesquera, and M. J. Adams, “Polarization bistability induced by orthogonal optical injection in 1550 nm multimode VCSELs,” IEEE J. Sel. Top. Quantum Electron. 18, 772–778 (2012).
[CrossRef]

K. D. Choquette, R. P. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
[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]

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]

C. H. Chang, L. Chrostowski, and C. J. Chang-Hasnain, “Injection locking of VCSELs,” IEEE J. Sel. Top. Quantum Electron. 9, 1386–1393 (2003).
[CrossRef]

IEEE Photon. J. (1)

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3, 644–650 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Valle and L. Pesquera, “Relative intensity noise of multitransverse-mode vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 13, 272–274 (2001).
[CrossRef]

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]

IEEE Trans. Microwave Theory Tech. (1)

A. Hayat, A. Bacou, A. Rissons, J. C. Mollier, V. Iakovlev, A. Sirbu, and E. Kapon, “Long-wavelength VCSEL-by-VCSEL optical injection locking,” IEEE Trans. Microwave Theory Tech. 57, 1850–1858 (2009).
[CrossRef]

J. Lightwave Technol. (2)

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

A. Valle, K. A. Shore, and L. Pesquera, “Polarization selection in birefringent vertical cavity surface emitting lasers,” J. Lightwave Technol. 14, 2062–2068 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (4)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

S. C. Chan, R. Diaz, and J. M. Liu, “Novel photonic applications of nonlinear semiconductor laser dynamics,” Opt. Quantum Electron. 40, 83–95 (2008).
[CrossRef]

Phys. Rev. A (3)

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. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

Proc. SPIE (1)

Y. C. Chen, Y. S. Juan, and F. Y. Lin, “High-frequency microwave signal generation in a semiconductor laser under double injection locking,” Proc. SPIE 7936, 793609 (2011).
[CrossRef]

Quantum Semiclass. Opt. (1)

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

Other (1)

J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos, Springer Series in Optical Sciences (Springer, 2007).

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Figures (9)

Fig. 1.
Fig. 1.

Temporal and spectral dynamics of the single-transverse-mode VCSEL when Δ f = 100 GHz and Δ ν = 0 GHz , with (a) no injection, (b)  κ s = 10 5 , (c)  κ s = 2 · 10 4 , and (d)  κ s = 10 2 . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Fig. 2.
Fig. 2.

Temporal and spectral dynamics of the single-transverse-mode VCSEL when Δ f = 30 , 63, and 500 GHz and Δ ν = 0 GHz , κ s = 10 2 . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Fig. 3.
Fig. 3.

Temporal and spectral dynamics of the multi-transverse-mode VCSEL when Δ f = 100 GHz and Δ ν = 0 GHz , with (a) no injection, (b)  κ s = 10 5 , (c)  κ s = 2 · 10 4 , and (d)  κ s = 10 2 . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Fig. 4.
Fig. 4.

Temporal and spectral dynamics of the multi-transverse-mode VCSEL when Δ f = 100 GHz and κ s = 10 2 when (a)  Δ ν = 100 GHz , (b)  Δ ν = 30 GHz , and (c)  Δ ν = 40 GHz . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Fig. 5.
Fig. 5.

Peak-to-peak amplitude of the total power (thick solid curve), the LP 01 , y power (thin solid curve), and the LP 11 , y power (dashed curve) as a function of Δ ν . The ratio between A 11 and A 01 is also plotted with a dotted curve. In this figure Δ f = 100 GHz and κ s = 10 2 .

Fig. 6.
Fig. 6.

Temporal and spectral dynamics of the multi-transverse-mode VCSEL when Δ f = 100 GHz and Δ ν = 0 GHz , with (a)  κ 01 = 10 2 , κ 12 = κ 02 = κ 11 = 0 , (b)  κ 12 = 10 2 , κ 01 = κ 02 = κ 11 = 0 , (c)  κ 01 = κ 12 = 10 2 , κ 02 = κ 11 = 0 , and (d)  κ 01 = κ 12 = 10 2 , κ 02 = κ 11 = 5 · 10 4 . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Fig. 7.
Fig. 7.

Peak-to-peak amplitude of the total power as a function of κ 02 when Δ f = 100 GHz , Δ ν = 0 GHz , κ 01 = 10 2 , and (a)  κ 11 = κ 02 , (b)  κ 11 = 0.3 κ 02 , and (c)  κ 11 = 3 κ 02 .

Fig. 8.
Fig. 8.

Peak-to-peak amplitude, A tot , of the total power as a function of the generated frequency, Δ f . In this figure Δ ν = 0 GHz and κ c = κ s / 2 .

Fig. 9.
Fig. 9.

Temporal and spectral dynamics of the multi-transverse-mode VCSEL when Δ f = 100 GHz , κ s = 2 · 10 4 , and (a)  Δ ν = 5 GHz , (b)  Δ ν = 5 GHz . Upper row: time traces of the power of the polarized transverse modes. Middle row: RF spectra of the polarized powers. Lower row: optical spectra of the x -polarized (grey curve), y -polarized (dark grey curve), and total power.

Tables (1)

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Table 1. Device and Material Parameters

Equations (4)

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E ˙ 0 x = k ( 1 + i α ) ( E 0 x ( g 0 x 1 ) + i E 0 y g 0 x y ) ( γ a + i γ p 0 ) E 0 x + β 2 ( N ¯ + n ¯ ξ 0 + ( t ) + N ¯ n ¯ ξ 0 ( t ) ) , E ˙ 0 y = k ( 1 + i α ) ( E 0 y ( g 0 y 1 ) i E 0 x g 0 y x ) + ( γ a + i γ p 0 ) E 0 y + κ 01 τ i n e i Δ ω 1 t + κ 02 τ i n e i Δ ω 2 t i β 2 ( N ¯ + n ¯ ξ 0 + ( t ) N ¯ n ¯ ξ 0 ( t ) ) , E ˙ 1 x = k ( 1 + i α ) ( E 1 x ( g 1 x κ r ) + i E 1 y g 1 x y ) + i γ p t r E 1 x ( γ a + i γ p 1 ) E 1 x + β 2 ( N ¯ + n ¯ ξ 1 + ( t ) + N ¯ n ¯ ξ 1 ( t ) ) , E ˙ 1 y = k ( 1 + i α ) ( E 1 y ( g 1 y κ r ) i E 1 x g 1 y x ) + i γ p t r E 1 y + ( γ a + i γ p 1 ) E 1 y + κ 11 τ i n e i Δ ω 1 t + κ 12 τ i n e i Δ ω 2 t i β 2 ( N ¯ + n ¯ ξ 1 + ( t ) N ¯ n ¯ ξ 1 ( t ) ) , N ( r , t ) t = I ( r ) + D 2 N γ e [ N ( 1 + i = 0 , 1 j = x , y | E i j | 2 ψ i j 2 ( r ) ) i n i = 0 , 1 ( E i x E i y * E i y E i x * ) ψ i x ( r ) ψ i y ( r ) ] , n ( r , t ) t = γ s n + D 2 n γ e [ n i = 0 , 1 j = x , y | E i j | 2 ψ i j 2 ( r ) i N i = 0 , 1 ( E i x E i y * E i y E i x * ) ψ i x ( r ) ψ i y ( r ) ] ,
g i j = 0 N ( r , t ) ψ i j 2 ( r ) r d r 0 ψ i j 2 ( r ) r d r , g i , j k = 0 n ( r , t ) ψ i j ( r ) ψ i k ( r ) r d r 0 ψ i j 2 ( r ) r d r .
κ i m = ( 1 R R ) η i n j P i n j , i m ,
N ¯ = 0 a N ( r , t ) r d r a 2 , n ¯ = 0 a n ( r , t ) r d r a 2 .

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