VCSELs pp 181-231 | Cite as

Polarization Dynamics of VCSELs

Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 166)

Abstract

In this chapter we wrap up the experimental and theoretical results on polarization dynamics of solitary vertical-cavity surface-emitting lasers. Experiments have shown that VCSELs emit a linearly polarized fundamental transverse mode either along the [110] or \([1\overline 10]\) crystallographic direction. Polarization switching between these modes can occur when the injection current is increased, showing either a frequency shift from the higher to the lower frequency mode (type I) or the reverse (type II). The two modes of linear polarization are strongly anti-correlated. The switching can happen through a region of mode hopping, with a dwell time scaling over eight orders of magnitude with the switching current, or through a region of hysteresis. Thermal (carrier) effects influence the polarization behavior of VCSELs through a red (blue) shift of the gain maximum. Also, in-plane anisotropic strain can strongly modify the polarization behavior of VCSELs. All these experimental results call for explanations, as there is no a priori intrinsic polarization selection mechanism in VCSELs. We present different gain equalization models to explain type I, type II or double polarization switching. Alternatively, the spin-flip model can explain both types polarization switching by involving a microscopic spin-flip relaxation mechanism. Its predictive power has been experimentally established as, e.g., polarization switching through elliptically polarized states and dynamical instabilities. Finally, we highlight some perspective applications using polarization dynamics of VCSELs.

Keywords

Linearly Polarize Polarization Switching Modal Gain Relative Intensity Noise Spectral Hole Burning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

Some of the works presented in this chapter have been undertaken with other past and present colleagues, as acknowledged via the relevant reference citations. KP wishes to acknowledge the FWO (Fund for Scientific Research - Flanders) and the Research Council (OZR) of the Vrije Universiteit Brussel.

References

  1. 1.
    H. Li, K. Iga (eds.), Vertical-Cavity Surface-Emitting Laser Devices (Springer, Berlin, 2003)Google Scholar
  2. 2.
    C. Wilmsen, H. Temkin, L.A. Coldren (eds.), Vertical-Cavity Surface-Emitting Lasers (Cambridge University Press, Cambridge, 1999)Google Scholar
  3. 3.
    L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995)Google Scholar
  4. 4.
    W.W. Chow, S.W. Koch, M. Sargent III, Semiconductor-Laser Physics (Springer, Berlin, 1994)Google Scholar
  5. 5.
    S.L. Chuang, Physics of Optoelectronics Devices (Wiley, New York, 1995)Google Scholar
  6. 6.
    C.J. Chang-Hasnain, J.P. Harbison, G. Hasnain, A.C. Von Lehmen, L.T. Florez, N.G. Stoffel, Dynamic, polarization, and transverse-mode characteristics of vertical cavity surface emitting lasers. IEEE J. Quantum Electron. 27, 1402 (1991)ADSGoogle Scholar
  7. 7.
    K.D. Choquette, D.A. Richie, R.E. Leibenguth, Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization. Appl. Phys. Lett. 64, 2062 (1994)ADSGoogle Scholar
  8. 8.
    A.K. Jansen van Doorn, M.P. van Exter, J.P. Woerdman, Elasto-optic anisotropy and polarization orientation of guided vertical-cavity surface-emitting semiconductor lasers. Appl. Phys. Lett. 69, 1041 (1996)ADSGoogle Scholar
  9. 9.
    K.D. Choquette, R.E. Leibenguth, Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries. IEEE Photon. Technol. Lett. 6, 40 (1994)ADSGoogle Scholar
  10. 10.
    K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, I. Veretennicoff, Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 77, 1590 (2000)ADSGoogle Scholar
  11. 11.
    K. Panajotov, M. Camarena, M.C. Moreno, H.J. Unold, R. Michalzik, H. Thienpont, J. Danckaert, I. Veretennicoff, G. Verschaffelt, Polarization behavior and mode structure of vertical-cavity surface-emitting lasers with elliptical surface relief. Proceedings of SPIE, vol. 4994 (2003), p. 127ADSGoogle Scholar
  12. 12.
    K. Panajotov, J. Danckaert, G. Verschaffelt, M. Peeters, B. Nagler, J. Albert, B. Ryvkin, H. Thienpont, I. Veretennicoff, Polarization behavior of vertical-cavity surface-emitting lasers: experiments, models and applications. Am. Inst. Phys. Conf. Proc. 560, 403 (2001)ADSGoogle Scholar
  13. 13.
    A.K. Jansen van Doorn, M.P. van Exter, J.P. Woerdman, Tailoring the birefringence in a vertical-cavity semiconductor laser. Appl. Phys. Lett. 69, 3635 (1996)ADSGoogle Scholar
  14. 14.
    A.K. Jansen van Doorn, M.P. van Exter, A.M. van der Lee, J.P. Woerdman, Coupled-mode description for the polarization state of a vertical-cavity semiconductor laser. Phys. Rev. 55, 1473 (1997)ADSGoogle Scholar
  15. 15.
    M.P. van Exter, A.K. Jansen van Doorn, J.P. Woerdman, Electro-optic effect and birefringence in semiconductor vertical-cavity lasers. Phys. Rev. A 56, 845 (1997)ADSGoogle Scholar
  16. 16.
    P. Debernardi, G.P. Bava, C. Degen, I. Fischer, W. Elsäßer, Influence of anisotropies on transverse modes in oxide-confined VCSELs. IEEE J. Quantum Electron 38, 73 (2002)ADSGoogle Scholar
  17. 17.
    R.F.M. Hendriks, M.P. van Exter, J.P. Woerdman, A. van Geelen, L. Weegels, K.H. Gulden, M. Moser, Electro-optic birefringence in semiconductor vertical-cavity lasers. Appl. Phys. Lett. 71, 2599 (1997)ADSGoogle Scholar
  18. 18.
    D. Vakhshoori, Symmetry considerations in vertical-cavity surface-emitting lasers: prediction of removal of polarization isotropicity on (001) substrates. Appl. Phys. Lett. 65, 259 (1994)ADSGoogle Scholar
  19. 19.
    Z.G. Pan, S. Jiang, M. Dagenais, R.A. Morgan, K. Kojima, M.T. Asom, R.E. Leibenguth, G.D. Guth, M.W. Focht, Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 63, 2999 (1993)ADSGoogle Scholar
  20. 20.
    S. Jiang, Z. Pan, M. Dagenais, R.A. Morgan, K. Kojiama, High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 63, 3545 (1993)ADSGoogle Scholar
  21. 21.
    K.D. Choquette, K.L. Lear, R.E. Leibenguth, M.T. Asom, Polarization modulation of cruciform vertical-cavity laser diodes. Appl. Phys. Lett. 64, 2767 (1994)ADSGoogle Scholar
  22. 22.
    H. Kawaguchi, I.S. Hidayat, Y. Takahashi, Y. Yamayoshi, Pitchfork bifurcation polarization bistability in vertical-cavity surface-emitting lasers. Electron. Lett. 31, 109 (1995)Google Scholar
  23. 23.
    K.D. Choquette, R.P. Schneider Jr., K.L. Lear, R.E. Leibenguth, Gain-dependent polarization properties of vertical-cavity lasers. IEEE J. Select. Topics Quantum Electron. 1, 661 (1995)Google Scholar
  24. 24.
    J.E. Epler, S. Gehrsitz, K.H. Gulden, M. Moser, H.G. Sigg, H.W. Lehmann, Mode behavior and high resolution spectra of circularly symmetric GaAs-AlGaAs air-post vertical cavity surface emitting lasers. Appl. Phys. Lett. 69, 722 (1996)ADSGoogle Scholar
  25. 25.
    U. Fiedler, G. Reiner, P. Schnitzer, K.J. Ebeling, Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission. IEEE Photon. Technol. Lett. 8, 746 (1996)ADSGoogle Scholar
  26. 26.
    J. Martin-Regalado, J.L.A. Chilla, J.J. Rocca, P. Brusenbach, Polarization switching in vertical-cavity surface emitting lasers observed at constant active region temperature. Appl. Phys. Lett. 70, 3350 (1997)ADSGoogle Scholar
  27. 27.
    H. Kawaguchi, Bistable laser diodes and their applications: state of the art. IEEE J. Select. Topics Quantum Electron 3, 1254 (1997)Google Scholar
  28. 28.
    C.L. Chua, R.L Thornton, D.W. Treat, R.M. Donaldson, Anisotropic apertures for polarization-stable laterally oxidized vertical-cavity lasers. Appl. Phys. Lett. 73, 1631 (1998)Google Scholar
  29. 29.
    K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, I. Veretennicoff, Polarization switching in VCSEL’s due to thermal lensing. IEEE Photon. Technol. Lett. 10, 6 (1998)ADSGoogle Scholar
  30. 30.
    M.P. van Exter, A. Al-Remawi, J.P. Woerdman, Polarization fluctuations demonstrate nonlinear anisotropy of a vertical-cavity semiconductor laser. Phys. Rev. Lett. 80, 4875 (1998)ADSGoogle Scholar
  31. 31.
    M.P. van Exter, M.B. Willemsen, J.P. Woerdman, Polarization fluctuations in vertical-cavity semiconductor lasers. Phys. Rev. A 58, 4191 (1998)ADSGoogle Scholar
  32. 32.
    M.B. Willemsen, M.P. van Exter, J.P. Woerdman, Correlated fluctuations in the polarization modes of a vertical-cavity semiconductor laser. Phys. Rev. A 60, 4105 (1999)ADSGoogle Scholar
  33. 33.
    B. Ryvkin, K. Panajotov, A. Georgievski, J. Danckaert, M. Peeters, G. Verschaffelt, H. Thien pont, I. Veretennicoff, Effect of photon-energy-dependent loss and gain mechanisms on polarization switching in vertical-cavity surface-emitting lasers. J. Opt. Soc. Am. B 16, 2106 (1999)Google Scholar
  34. 34.
    M.B. Willemsen, M.P. van Exter, J.P. Woerdman, Anatomy of a polarization switch of a vertical-cavity semiconductor laser. Phys. Rev. Lett. 84, 4337 (2000)ADSGoogle Scholar
  35. 35.
    T. Ackemann, M. Sondermann, Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 78, 3574 (2001)ADSGoogle Scholar
  36. 36.
    G. Verschaffelt, J. Albert, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, F. Marin, Frequency response of current-driven polarization modulation in vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 80, 2248 (2002)ADSGoogle Scholar
  37. 37.
    Y. Matsui, D. Vakhshoori, P. Wang, P. Chen, C.-C. Lu, M. Jiang, K. Knopp, S. Burroughs, P. Tayebati, Complete polarization mode control of long-wavelength tunable vertical-cavity surface-emitting lasers over 65-nm tuning up to 14-mW output power. IEEE J. Quantum Electron. 39, 1037 (2003)ADSGoogle Scholar
  38. 38.
    M. Sondermann, M. Weinkath, T. Ackemann, Polarization switching to the gain-disfavored mode in vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 40, 97 (2004)ADSGoogle Scholar
  39. 39.
    M. Sondermann, T. Ackemann, S. Balle, J. Mulet, K. Panajotov, Experimental and theoretical investigations on elliptically polarized dynamical transition states in the polarization switching of vertical-cavity surface-emitting lasers. Opt. Commun. 235, 421 (2004)ADSGoogle Scholar
  40. 40.
    G. Giacomelli, F. Marin, M. Gabrysch, K.H. Gulden, M. Moser, Polarization competition and noise properties of VCSELs. Opt. Commun. 146, 136 (1998)ADSGoogle Scholar
  41. 41.
    G. Giacomelli, F. Marin, I. Rabbiosi, Stochastic and bona fide resonance: an experimental investigation. Phys. Rev. Lett. 82, 675 (1999)ADSGoogle Scholar
  42. 42.
    M.B. Willemsen, M.U.F. Khalid, M.P. van Exter, J.P. Woerdman, Polarization switching of a vertical-cavity semiconductor laser as a Kramers hopping problem. Phys. Rev. Lett. 82, 4815 (1999)ADSGoogle Scholar
  43. 43.
    B. Nagler, M. Peeters, J. Albert, G. Verschaffelt, K. Panajotov, H. Thienpont, I. Veretennicoff, J. Danckaert, S. Barbay, G. Giacomelli, F. Marin, Polarization-mode hopping in single-mode vertical-cavity surface-emitting lasers: theory and experiment. Phys. Rev. A 68, 013813 (2003)ADSGoogle Scholar
  44. 44.
    G. Verschaffelt, J. Albert, B. Nagler, M. Peeters, J. Danckaert, S. Barbay, G. Giacomelli, F. Marin, Frequency response of polarization switching in vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 39, 1177 (2003)ADSGoogle Scholar
  45. 45.
    J. Danckaert, M. Peeters, C. Mirasso, M.S. Miguel, G. Verschaffelt, J. Albert, B. Nagler, H. Unold, R. Michalzik, G. Giacomelli, F. Marin, Stochastic polarization switching dynamics in vertical-cavity surface-emitting lasers: theory and experiment. IEEE J. Select. Topics Quantum Electron. 10, 911 (2004)Google Scholar
  46. 46.
    G. van der Sande, M. Peeters, I. Veretennicoff, J. Danckaert, G. Verschaffelt, S. Balle, The effect of stress, temperature, and spin flip on polarization switching in vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 42, 898 (2006)Google Scholar
  47. 47.
    M. Ohtsu, Y. Teramachi, Y. Otsuka, A. Osaki, Analysis of mode-hopping phenomena in an AlGaAs laser. IEEE J. Quantum Electron. 22, 535 (1986)ADSGoogle Scholar
  48. 48.
    R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light (North-Holland Elsevier, Amsterdam, 1987)Google Scholar
  49. 49.
    F. Koyama, K. Morito, K. Iga, Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers. IEEE J. Quantum Electron. 27, 1410 (1991)ADSGoogle Scholar
  50. 50.
    D.V. Kuksenkov, H. Temkin, S. Swirhun, Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers. Appl. Phys. Lett. 67, 2141 (1995)ADSGoogle Scholar
  51. 51.
    E. Goobar, J.W. Scott, B. Thibeault, G. Robinson, Y. Akulova, L.A. Coldren, Calibrated intensity noise measurements in microcavity laser diodes. Appl. Phys. Lett. 67, 3697 (1995)ADSGoogle Scholar
  52. 52.
    D. Wiedenmann, P. Schnitzer, C. Jung, M. Grabherr, R. Jäger, R. Michalzik, K.J. Ebeling, Noise characteristics of 850 nm single-mode vertical cavity surface emitting lasers. Appl. Phys. Lett. 73, 717 (1998)ADSGoogle Scholar
  53. 53.
    J.-L. Vey, C. Degen, K. Auen, W. Elsäßer, Quantum noise and polarization properties of vertical-cavity surface-emitting lasers. Phys. Rev. A 60, 3284 (1999)ADSGoogle Scholar
  54. 54.
    D.C. Kilper, R.A. Ross, J.L. Carlsten, K.L. Lear, Squeezed light generated by a microcavity laser. Phys. Rev. A 55, R3323 (1997)ADSGoogle Scholar
  55. 55.
    V. Badilita, J.-F. Carlin, M. Ilegems, M. Brunner, G. Verschaffelt, K. Panajotov, Control of polarization switching in vertical coupled-cavities surface emitting lasers. IEEE Photon. Techn. Lett. 16, 365 (2004)ADSGoogle Scholar
  56. 56.
    R.P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, C. Weisbuch, Coupled semiconductor microcavities. Appl. Phys. Lett. 65, 2093 (1994)ADSGoogle Scholar
  57. 57.
    K. Panajotov, V. Badilita, J.-F. Carlin, H. Thienpont, I. Veretennicoff, Quantum confined Stark effect in coupled-cavity VCSELs. Proceedings of SPIE, vol. 5359 (2004), p. 360ADSGoogle Scholar
  58. 58.
    D.M. Grasso, K.D. Choquette, Temperature-dependent polarization characteristics of composite-resonator vertical-cavity lasers. IEEE J. Quantum Electron. 41, 127 (2005)ADSGoogle Scholar
  59. 59.
    S. Hallstein, J.D. Berger, M. Hilpert, H.C. Schneider, W.W. Rühle, F. Janke, S.W. Koch, H.M. Gibbs, G. Khitrova, M. Oestreich, Manifistation of coherent spin precession in stimulated semiconductor emission dynamics. Phys. Rev. B 56, R7076 (1997)ADSGoogle Scholar
  60. 60.
    H. Ando, T. Sogawa, H. Gotoh, Photon-spin controlled lasing oscillation in surface-emitting lasers. Appl. Phys. Lett. 73, 566 (1998)ADSGoogle Scholar
  61. 61.
    R.F.M. Hendriks, M.P. van Exter, J.P. Woerdman, K.H. Gulden, M. Moser, Memory effects for polarization of pump light in optically pumped vertical-cavity semiconductor lasers. IEEE J. Quantum Electron. 34, 1455 (1998)ADSGoogle Scholar
  62. 62.
    E.L. Blansett, M.G. Raymer, G. Khitrova, H.M. Gibbs, D.K. Serkland, A.A. Allerman, K.M. Geib, Ultrafast polarization dynamics and noise in pulsed vertical-cavity surface-emitting lasers. Opt. Express 9, 312 (2001)ADSGoogle Scholar
  63. 63.
    E.L. Blansett, M.G. Raymer, G. Cui, G. Khitrova, H.M. Gibbs, D.K. Serkland, A.A. Allerman, K.M. Geib, Picosecond polarization dynamics and noise in pulsed vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 41, 287 (2005)ADSGoogle Scholar
  64. 64.
    M.Z. Maialle, M.H. Degani, Electron-spin relaxation in p-type quantum wells via electron-hole exchange interaction: the effects of the valence-band spin mixing and of an applied longitudinal electric field. Phys. Rev. B 55, 13771 (1997)ADSGoogle Scholar
  65. 65.
    N.B. Patel, J.E. Ripper, P. Brosson, Behavior of threshold current and polarization of stimulated emission of GaAs injection lasers under uniaxial stress. IEEE J. Quantum Electron. 9, 338 (1973)ADSGoogle Scholar
  66. 66.
    Y.C. Chen, J.M. Liu, Polarization bistability in semiconductor lasers. Appl. Phys. Lett. 46, 16 (1985)ADSGoogle Scholar
  67. 67.
    Y.C. Chen, J.M. Liu, Polarization bistability in semiconductor laser: rate-equation analysis. Appl. Phys. Lett. 50, 1406 (1987)ADSGoogle Scholar
  68. 68.
    W.E. Lamb, Theory of an optical maser. Phys. Rev. 134, A1429 (1964)ADSGoogle Scholar
  69. 69.
    C. Tang, A. Schremer, T. Fujita, Bistability in two-mode semiconductor lasers via gain saturation. Appl. Phys. Lett. 51, 1392 (1987)ADSGoogle Scholar
  70. 70.
    M. Asada, Y. Suematsu, Density-matrix theory of semiconductor lasers with relaxation broadening model—gain and gain-suppression in semiconductor lasers. IEEE J. Quantum Electron. 21, 434 (1985)ADSGoogle Scholar
  71. 71.
    G.P. Agrawal, Gain nonlinearities in semiconductor lasers: theory and application to distributed feedback lasers. IEEE J. Quantum Electron. 23, 860 (1987)ADSGoogle Scholar
  72. 72.
    M. Sargent III, Theory of a multimode quasi-equilibrium semiconductor-laser. Phys. Rev. A 48, 717 (1993)ADSGoogle Scholar
  73. 73.
    A. Uskov, J. Mørk, J. Mark, Wave mixing in semiconductor-laser amplifiers due to carrier heating and spectral-hole burning. IEEE J. Quantum Electron. 30, 1769 (1994)ADSGoogle Scholar
  74. 74.
    B.M. Yu, J.M. Liu, Polarization-dependent gain, gain nonlinearities, and emission characteristics of internally strained InGaAsP/InP semiconductor lasers. J. Appl. Phys. 69, 7444 (1991)ADSGoogle Scholar
  75. 75.
    Y. Takahashi, H. Kawaguchi, Polarization-dependent gain saturations in quantum-well lasers. IEEE J. Quantum Electron. 36, 864 (2000)ADSGoogle Scholar
  76. 76.
    Y. Takahashi, H. Kawaguchi, Strain-dependence of the gain saturations in InGaAsP/InP quantum-well gain media. IEEE J. Quantum Electron. 38, 1384 (2002)ADSGoogle Scholar
  77. 77.
    J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, T. Erneux, Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers. Opt. Commun. 201, 129 (2002)ADSGoogle Scholar
  78. 78.
    J. Albert, G. van der Sande, B. Nagler, K. Panajotov, I. Veretennicoff, J. Danckaert, T. Erneux, The effects of nonlinear gain on the stability of semi-degenerate two-mode semiconductor lasers: a case study on VCSELs. Opt. Commun. 248, 527 (2005)ADSGoogle Scholar
  79. 79.
    B.S. Ryvkin, E.A. Avrutin, M. Pessa, Polarization-dependent intersubband absorption saturation and its effect on polarization selection in vertical cavity surface-emitting lasers. J. Appl. Phys. 93, 2353 (2003)ADSGoogle Scholar
  80. 80.
    B.S. Ryvkin, E.A. Avrutin, M. Pessa, Spontaneous emission, light-current characteristics, and polarization bistability range in vertical-cavity surface-emitting lasers. J. Appl. Phys. 94, 4267 (2003)ADSGoogle Scholar
  81. 81.
    B.S. Ryvkin, E.A. Avrutin, A.C. Walker, Photon energy dependence of the sign of the current-induced absorption polarization sensitivity in degenerate semiconductors. Appl. Phys. Lett. 78, 2655 (2001)ADSGoogle Scholar
  82. 82.
    B.S. Ryvkin, E.A. Avrutin, A.C. Walker, Current-directionality-induced giant absorption dichroism in III-V semiconductors and its potential for polarization control in vertical cavity surface-emitting lasers. J. Appl. Phys. 91, 3516 (2002)ADSGoogle Scholar
  83. 83.
    H. Kawaguchi, I.H. White, M.J. Offside, J.E. Carroll, Ultrafast switching in polarization-bistable laser-diodes. Opt. Lett. 17, 130 (1992)ADSGoogle Scholar
  84. 84.
    A. Valle, L. Pesquera, K.A. Shore, Polarization behaviour of birefringent multitransverse mode vertical-cavity surface-emitting lasers. IEEE Photon. Technol. Lett. 9, 557 (1997)ADSGoogle Scholar
  85. 85.
    M. San Miguel, Q. Feng, J.V. Moloney, Light-polarization dynamics in surface-emitting semiconductor lasers. Phys. Rev. A 52, 1728 (1995)ADSGoogle Scholar
  86. 86.
    A. Tackeuchi, Y. Nishikawa, O. Wada, Room-temperature electron spin dynamics in GaAs/ AlGaAs quantum wells. Appl. Phys. Lett. 68, 797 (1996)ADSGoogle Scholar
  87. 87.
    A. Tackeuchi, O. Wada, Y. Nishikawa, Electron spin relaxation in InGaAs/InP multiple-quantum wells. Appl. Phys. Lett. 70, 1131 (1997)ADSGoogle Scholar
  88. 88.
    S. Akasaka, S. Miyata, T. Kuroda, A. Tackeuchi, Exciton spin relaxation dynamics in InGaAs/InP quantum wells. Appl. Phys. Lett. 85, 2083 (2004)ADSGoogle Scholar
  89. 89.
    M.I. D’yakonov, V.I. Perel, Optical orientation in a system of electrons and lattice nuclei in semiconductors: theory. Zh. Eksp. Teor. Fiz. 65, 362 (1973)Google Scholar
  90. 90.
    M.I. D’yakonov, V.I. Perel, Optical orientation in a system of electrons and lattice nuclei in semiconductors. Sov. Phys. JETP 38, 177 (1974)ADSGoogle Scholar
  91. 91.
    R.J. Elliott, Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors. Phys. Rev. 96, 266 (1954)ADSMATHGoogle Scholar
  92. 92.
    Y. Yafet, g factors and spin-lattice relaxation of conduction electrons, in Solid State Physics, vol. 14, ed. by F. Seitz, D. Turnbull (Academic Press, New York, 1963), pp. 1–98Google Scholar
  93. 93.
    G.L. Bir, A.G. Aronov, G.E. Pikus, Spin relaxation of electrons scattered by holes. Zh. Eksp. Teor. Fiz. 69, 1382 (1975)Google Scholar
  94. 94.
    G.L. Bir, A.G. Aronov, G.E. Pikus, Spin relaxation of electrons scattered by holes. Sov. Phys. JETP 42, 705 (1976)ADSGoogle Scholar
  95. 95.
    T. Adachi, Y. Ohno, R. Terauchi, F. Matsukura, H. Ohno, Mobility dependence of electron spin relaxation time in n-type InGaAs/InAlAs multiple quantum wells. Physica E 7, 1015 (2000)Google Scholar
  96. 96.
    K. Jarasiunas, V. Gudelis, R. Aleksiejunas, M. Sudzius, S. Iwamoto, M. Nishioka, T. Shimura, K. Kuroda, Y. Arakawa, Picosecond dynamics of spin-related optical nonlinearities in \(\hbox{In}_x \hbox{Ga}_{1-x}\) As multiple quantum wells at 1064 nm. Appl. Phys. Lett. 84, 1043 (2004)Google Scholar
  97. 97.
    J. Martin-Regalado, M. San Miguel, N.B. Abraham, F. Prati, Polarization switching in quantum-well vertical-cavity surface-emitting lasers. Opt. Lett. 21, 351 (1996)ADSGoogle Scholar
  98. 98.
    J. Martin-Regalado, F. Prati, M. San Miguel, N.B. Abraham, Polarization properties of vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron 33, 765 (1997)ADSGoogle Scholar
  99. 99.
    M. Travagnin, M.P. van Exter, A.K. Jansen van Doorn, J.P. Woerdman, Role of optical anisotropies in the polarization properties of surface-emitting semiconductor lasers. Phys. Rev. A 54, 1647 (1996)ADSGoogle Scholar
  100. 100.
    C. Serrat, N.B. Abraham, M. San Miguel, R. Vilaseca, J. Martin-Regalado, Polarization dynamics in a vertical-cavity laser with an axial magnetic field. Phys. Rev. A 53, R3731 (1996)ADSGoogle Scholar
  101. 101.
    M. Travagnin, Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers. Phys. Rev. A 56, 4094 (1997)ADSGoogle Scholar
  102. 102.
    H.F. Hofmann, O. Hess, Quantum noise and polarization fluctuations in vertical-cavity surface-emitting lasers. Phys. Rev. A 56, 868 (1997)ADSGoogle Scholar
  103. 103.
    H. van der Lem, D. Lenstra, Saturation-induced frequency shift in the noise spectrum of a birefringent vertical-cavity surface emitting laser. Opt. Lett. 22, 1698 (1997)ADSGoogle Scholar
  104. 104.
    M.P. van Exter, R.F.M. Hendriks, J.P. Woerdman, Physical insight into the polarization dynamics of semiconductor vertical-cavity lasers. Phys. Rev. A 57, 2080 (1998)ADSGoogle Scholar
  105. 105.
    S. Balle, E. Tolkachova, M. San Miguel, J.R. Tredicce, J. Martin-Regalado, A. Gahl, Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics. Opt. Lett. 24, 1121 (1999)ADSGoogle Scholar
  106. 106.
    J. Martin-Regalado, S. Balle, M. San Miguel, Polarization and transverse-mode dynamics of gain-guided vertical-cavity surface-emitting lasers. Opt. Lett. 22, 460 (1997)ADSGoogle Scholar
  107. 107.
    J. Martin-Regalado, S. Balle, M. San Miguel, A. Valle, L. Pesquera, Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index and gain-guided devices. J. Opt. B. Quantum Semiclass. Opt. 9, 713 (1997)ADSGoogle Scholar
  108. 108.
    J. Mulet, S. Balle, Spatio-temporal modeling of the optical properties of VCSELs in the presence of polarization effects. IEEE J. Quantum Electron. 38, 291 (2002)ADSGoogle Scholar
  109. 109.
    M.S. Torre, C. Masoller, P. Mandel, Transverse and polarization effects in index-guided vertical-cavity surface-emitting lasers. Phys. Rev. A 74, 043808 (2006)ADSGoogle Scholar
  110. 110.
    C. Masoller, M.S. Torre, K.A. Shore, Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 43, 1074 (2007)ADSGoogle Scholar
  111. 111.
    F. Prati, G. Giacomelli, F. Marin, Competition between orthogonally polarized transverse modes in vertical-cavity surface-emitting lasers and its influence on intensity noise. Phys. Rev. A 62, 033810 (2000)ADSGoogle Scholar
  112. 112.
    D. Burak, J.V. Moloney, R. Binder, Microscopic theory of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers. Phys. Rev. A 61, 053809 (2000)ADSGoogle Scholar
  113. 113.
    D. Burak, J.V. Moloney, R. Binder, Macroscopic versus microscopic description of polarization properties of optically anisotropic vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 36, 956 (2000)ADSGoogle Scholar
  114. 114.
    G. van der Sande, J. Danckaert, I. Veretennicoff, K. Panajotov, S. Balle, Analytical approximation for the quantum-well gain and refractive-index spectra of vertical-cavity surface-emitting lasers including the effect of uniaxial planar stress. Phys. Rev. A 71, 063801 (2005)ADSGoogle Scholar
  115. 115.
    R.F.M. Hendriks, M.P. van Exter, J.P. Woerdman, How the carrier momentum influences the polarization properties of a vertical-cavity semiconductor laser. Phys. Rev. A 59, 765 (1999)ADSGoogle Scholar
  116. 116.
    F. Prati, L. Fratta, M. Travagnin, Band model for light-polarization selection in unstrained quantum-well vertical-cavity surface-emitting laser. Phys. Rev. A 62, 033819 (2000)ADSGoogle Scholar
  117. 117.
    F. Prati, P. Caccia, F. Castelli, Effects of gain saturation on polarization switching in vertical-cavity semiconductor lasers. Phys. Rev. A 66, 063811 (2002)ADSGoogle Scholar
  118. 118.
    T. Erneux, J. Danckaert, K. Panajotov, I. Veretennicoff, Two-variable reduction of the San Miguel–Feng–Moloney model for vertical-cavity surface-emitting lasers. Phys. Rev. A 59, 4660 (1999)ADSGoogle Scholar
  119. 119.
    F. Prati, P. Caccia, M. Bache, F. Castelli, Analysis of elliptically polarized states in vertical-cavity surface-emitting lasers. Phys. Rev. A 69, 033810 (2004)ADSGoogle Scholar
  120. 120.
    C. Masoller, M.S. Torre, P. Mandel, Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers. J. Appl. Phys. 99, 026106 (2006)ADSGoogle Scholar
  121. 121.
    J. Paul, C. Masoller, P. Mandel, Y.H. Hong, P.S. Spencer, K.A. Shore, Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers. Phys. Rev. A 77, 043803 (2008)ADSGoogle Scholar
  122. 122.
    M.S. Torre, C. Masoller, Polarization-resolved modulation response of single-transverse-mode vertical-cavity surface-emitting lasers. IEEE J. Quantum Electron. 45, 206 (2009)ADSGoogle Scholar
  123. 123.
    J. Mulet, C.R. Mirasso, M. San Miguel, Polarization resolved intensity noise in vertical-cavity surface-emitting lasers. Phys. Rev. A 64, 023817 (2001)ADSGoogle Scholar
  124. 124.
    J.M. Liu, Y.C. Chen, Digital optical signal-processing with polarization-bistable semicon- ductor-lasers. IEEE J. Quantum Electron. 21, 298 (1985)ADSGoogle Scholar
  125. 125.
    T. Mori, Y. Yamayoshi, H. Kawaguchi, Low-switching-energy and high-repetition-frequency all-optical flip-flop operation of polarization bistable vertical-cavity surface-emitting laser. Appl. Phys. Lett. 88, 101102 (2006)ADSGoogle Scholar
  126. 126.
    T. Mori, Y. Sato, H. Kawaguchi, Timing jitter reduction by all-optical signal regeneration using a polarization bistable VCSEL. J. Lightwave Technol. 26, 2946 (2008)ADSGoogle Scholar
  127. 127.
    H. Kawaguchi, T. Mori, Y. Sato, Y. Yamayoshi, Optical buffer memory using polarization-bistable vertical-cavity surface-emitting lasers. Jpn. J. Appl. Phys. 45, L894 (2006)ADSGoogle Scholar
  128. 128.
    J. Rudolph, S. Döhrmann, D. Hägele, M. Oestreich, W. Stolz, Room-temperature threshold reduction in vertical-cavity surface-emitting lasers by injection of spin-polarized electrons. Appl. Phys. Lett. 87, 241117 (2005)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Applied Physics and PhotonicsVrije Universiteit BrusselBrusselsBelgium
  2. 2.Institute of Solid State Physics Bulgarian Academy of SciencesSofiaBulgaria
  3. 3.CNISM and Dipartimento di Fisica e MatematicaUniversità à dell’InsubriaComoItaly

Personalised recommendations