Abstract

We have measured on ps time scales the temporal behavior of the intensity noise of, and correlations between, orthogonally polarized modes in an optically pumped VCSEL. Measurements were made in both the circular and the linear bases. Sub-ps optical pumping with circular polarization leads to positively correlated intensity noise for emission in orthogonal linear polarizations. Optical pumping with linear polarization leads to anti-correlated intensity noise for emission in orthogonal linear polarizations, due to random orientation of linearly polarized emission. Intensity noise for circularly polarized emission is uncorrelated or anti-correlated depending on spin-flip rates which determine the strength of gain competition. We have generalized the theoretical treatment of San Miguel, Feng, and Moloney to successfully model these phenomena.

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References

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  1. M. San Miguel, Q. Feng, J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
    [CrossRef] [PubMed]
  2. J. Martin-Regalado, F. Prati, M. San Miguel, N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J.Quantum Electron. 33, 765-783 (1997).
    [CrossRef]
  3. H. F. Hofmann, O. Hess, "Quantum noise and polarization fluctuations in vertical-cavity surface-emittinglasers," Phys. Rev. A 97, 868-876 (1997).
    [CrossRef]
  4. A. Gahl, S. Balle, M. San Miguel, "Polarization dynamics of optically pumped VCSEL's," IEEE J.Quantum Electron. 35, 342-351 (1999).
    [CrossRef]
  5. M. B. Willemsen, M. P. van Exter, J. P. Woerdman, "Correlated fluctuations in the polarization modes of vertical-cavity semiconductor laser," Phys. Rev. A 60, 4105-4113 (1999).
    [CrossRef]
  6. R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, K. H. Gulden, M. Moser, "Memory effect for polarization of pump light in optically pumped vertical-cavity semiconductor lasers," IEEE J.Quantum Electron. 34, 1455-1460 (1998).
    [CrossRef]
  7. D. V. Kuksenkov, H. Temkin, S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
    [CrossRef]
  8. 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 (1998).
    [CrossRef]
  9. J. L. Vey, C. Degen, K. Auen, W. Elsa�er, "Quantum noise and polarization properties of vertical-cavity surface-emitting lasers," Phys. Rev. A 60, 3284-3295 (1999).
    [CrossRef]
  10. D. R. Shelly, T. W. S. Garrison, M. Beck, D. H. Christensen, "Polarization correlations in pulsed, vertical-cavity, surface-emitting lasers," Opt. Express 7,249-259 (2000). http://www.opticsexpress.org/oearchive/source/23232.htm
    [CrossRef] [PubMed]
  11. U. Fiedler, F. Reiner, P. Schnitzer, K. J. Ebeling, "Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission," IEEE Photon. Technol. Lett. 8, 746-748 (1996).
    [CrossRef]
  12. D. F. McAlister, M. G. Raymer, "Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection," Phys. Rev. A 55, R1609-R1612 (1997).
    [CrossRef]
  13. V. P. Karasev, A. V. Masalov, "Unpolarized light states in quantum optics," Opt. Spectrosc. 74, 551-555 (1993).
  14. L. Vina, "Spin relaxation in low-dimensional systems," J. Phys. Condens. Matter 11, 5929-5952 (1999).
    [CrossRef]
  15. J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2nd ed. (Springer, Berlin, 1999).

Other (15)

M. San Miguel, Q. Feng, J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef] [PubMed]

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

H. F. Hofmann, O. Hess, "Quantum noise and polarization fluctuations in vertical-cavity surface-emittinglasers," Phys. Rev. A 97, 868-876 (1997).
[CrossRef]

A. Gahl, S. Balle, M. San Miguel, "Polarization dynamics of optically pumped VCSEL's," IEEE J.Quantum Electron. 35, 342-351 (1999).
[CrossRef]

M. B. Willemsen, M. P. van Exter, J. P. Woerdman, "Correlated fluctuations in the polarization modes of vertical-cavity semiconductor laser," Phys. Rev. A 60, 4105-4113 (1999).
[CrossRef]

R. F. M. Hendriks, M. P. van Exter, J. P. Woerdman, K. H. Gulden, M. Moser, "Memory effect for polarization of pump light in optically pumped vertical-cavity semiconductor lasers," IEEE J.Quantum Electron. 34, 1455-1460 (1998).
[CrossRef]

D. V. Kuksenkov, H. Temkin, S. Swirhun, "Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
[CrossRef]

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 (1998).
[CrossRef]

J. L. Vey, C. Degen, K. Auen, W. Elsa�er, "Quantum noise and polarization properties of vertical-cavity surface-emitting lasers," Phys. Rev. A 60, 3284-3295 (1999).
[CrossRef]

D. R. Shelly, T. W. S. Garrison, M. Beck, D. H. Christensen, "Polarization correlations in pulsed, vertical-cavity, surface-emitting lasers," Opt. Express 7,249-259 (2000). http://www.opticsexpress.org/oearchive/source/23232.htm
[CrossRef] [PubMed]

U. Fiedler, F. Reiner, P. Schnitzer, K. J. Ebeling, "Top surface-emitting vertical-cavity laser diodes for 10-Gb/s data transmission," IEEE Photon. Technol. Lett. 8, 746-748 (1996).
[CrossRef]

D. F. McAlister, M. G. Raymer, "Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection," Phys. Rev. A 55, R1609-R1612 (1997).
[CrossRef]

V. P. Karasev, A. V. Masalov, "Unpolarized light states in quantum optics," Opt. Spectrosc. 74, 551-555 (1993).

L. Vina, "Spin relaxation in low-dimensional systems," J. Phys. Condens. Matter 11, 5929-5952 (1999).
[CrossRef]

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2nd ed. (Springer, Berlin, 1999).

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Figures (3)

Fig. 1.
Fig. 1.

Mean photon numbers per sampling time 〈n〉 and noise correlations g (2) for UA sample. (a) and (b) Right circularly polarized pump. (a) 〈ni 〉 for left circularly polarized mode (blue, solid line) and the right circularly polarized mode (red, dotted line). (b) Noise correlation between the two circularly polarized modes. (c) and (d) Horizontally polarized pump. (c) 〈nj 〉 for vertically polarized mode (blue, solid line) and horizontally polarized mode (red, dotted line). (d) Noise correlation between the two linearly polarized modes.

Fig. 2.
Fig. 2.

Noise correlations between right and left circularly polarized modes for SNL sample with linearly polarized pump. (a) Experimental result. (b) Numerical simulations.

Fig. 3.
Fig. 3.

Simulated mean intensities 〈I〉=〈|E|2〉 (arb. units) and noise correlations g (2). (a) and (b) Right circularly polarized pump. (a) 〈Ii 〉 for left circularly polarized mode (blue, solid line) and the right circularly polarized mode (red, dotted line). (b) Noise correlation between the two circularly polarized modes. (c) and (d) Horizontally polarized pump. (c) 〈Ij 〉 for vertically polarized mode (blue, solid line) and horizontally polarized mode (red, dotted line). (d) Noise correlation between the two linearly polarized modes.

Equations (3)

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δ E ± δ t = κ E ± + g ( 1 i α ) N ± E ± i γ p E γ α E + f ±
δ N ± δ t = Γ N ± ± γ s ( N N + ) 4 g E ± 2 N ± + γ r N ± H ( 1 N ± N ± T )
δ N ± H δ t = R ± p ( t ) ± γ s ( N H N + H ) γ r N ± H ( 1 N ± N ± T ) ,

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