Abstract

We have examined noise behavior and polarization correlations in the output of a pulsed, multitransverse-mode, vertical-cavity, surface-emitting laser (VCSEL). We have measured the output of the laser simultaneously in two orthogonal, linear polarizations as a function of drive current for pulse widths of 3 ns, 10 ns, and 30 ns. We present joint probability distributions for the number of detected photoelectrons in each of the two polarization-resolved outputs. The joint distributions indicate that the correlations can be quite complicated, and are not completely described by a single number (i.e., the correlation coefficient). Furthermore, we find that the number of lasing modes appears to be the most important parameter in determining the degree of polarization correlation.

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References

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  1. C. J. Chang-Hasnain, "Vertical-cavity surface emitting lasers," in Semiconductor Lasers: Past, Present, and Future, G. R Agrawal, ed. (American Institute of Physics, Melville, N.Y, 1995), pp. 145-180.
  2. F Koyarna, K. Morit, and K. Iga, "Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers," IEEE J. Quantum Electron. 27, 1410-1416 (1991).
    [CrossRef]
  3. T. Mukaihara, N. Ohnoki, Y Hayashi, N. Hatori, F Koyarna, and K. Iga, "Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 7, 1113-1115 (1995).
    [CrossRef]
  4. D. C. Kilper, P.A. Roos, U. Carlsten, and K.L. Lear, "Squeezed light generated by a microcavity laser," Phys. Rev. A 55, R3323-113326 (1997).
    [CrossRef]
  5. M.P. van Exter, M.B. Willemsen, and J.P. Woerdman, "Polarization fluctuations in vertical-cavity semiconductor lasers," Phys. Rev. A 58, 4191-4205 (1998).
    [CrossRef]
  6. Ci Giacomelli, E Martin, M. Gabrysch, K.H. Gulden, and M. Moser, "Polarization competition and noise properties ofVCSELs," Opt. Comm. 146, 136-140 (1998).
    [CrossRef]
  7. J.-L. Vey, C. Degen, K. Auen, and W ElsaBer, "Quantum noise and polarization properties of vertical-cavity, surface-emitting lasers," Phys. Rev. A 60, 3284-3295 (1999).
    [CrossRef]
  8. M.B. Willemsen, M.P. van Exter, and J.P. WoeTdman, "Correlated fluctuations in the polarization modes of a vertical-cavity semiconductor laser," Phys. Rev.A 60, 4105-4113 (1999).
    [CrossRef]
  9. D.V. Kuksenkov, H. Temkin, and S. Swirhun, "Polarization instability and relative intensity noise in verticalcavity surface-emitting lasers," Appl. Phys. Lett. 67, 2141-2143 (1995).
    [CrossRef]
  10. D.V. Kuksenkov, H. Temkin, and S. Swirhun, "Polarization instability and performance of free-space optical links based on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 8, 703-705 (1996).
    [CrossRef]
  11. T.W. S. Garrison, M. Beck, and D.H. Christensen, "Noise behavior of pulsed vertical-cavity, surface-emitting lasers," J. Opt. Soc. Am. B 16, 2124-2130 (1999).
    [CrossRef]
  12. K.D. Choquette, R.P. Schneider, and K.L. Lear, "Gain-dependent polarization properties ofverfical cavity lasers," IEEE J. Select. Topics Quantum Electron. 1, 661-666 (1995).
    [CrossRef]
  13. M. San Miguel, Q. Feng, and J.V. Molony, "Light-polarization dynamics in surface-emitfing semiconductor lasers," Phys. Rev. A 1-52, 1728-1739 (1995).
    [CrossRef] [PubMed]
  14. A. Valle, L. Pesquera, and K.A. Shore, "Polarization behavior ofbirefringent multitransverse mode vertical cavity surface-emitting lasers," IEEE Photon. Tech. Lett 9, 557-559 (1997).
    [CrossRef]
  15. K. Panaiotov, B. Kyvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretenincoff "Polarization switching in VCSEL's due to thermal lensing," IEEE Photon. Tech. Lett. 10, 6-8 (1999).
    [CrossRef]
  16. M. Giudici, J.R. Tredicce, G. Vaschenko, J.J. Rocca, and C.S. Menom, "Spatio-temporal dynamics in vertical cavity surface emitting lasers excited by fast electrical pulses," Opt. Comm. 158, 313-321 (1998).
    [CrossRef]
  17. While quantum mechanics states that losses can significantly effect correlations between optical fields, we find that the measured noise levels of our fields are more than an order of magnitude above the shot-noise level. This means that the fields are well described by classical mechanics, and we do not anticipate that this additional loss will impact the results described here.
  18. J.P. Hermier, A. Bramati, A.Z. Khoury, E. Giacobino, J.P. Poizat, T.J. Chang, P. Grangier, "Spatial quantum noise ofsemiconductor lasers," J. Opt. Soc. Am. B 16, 2140-2146 (1999).
    [CrossRef]

Other (18)

C. J. Chang-Hasnain, "Vertical-cavity surface emitting lasers," in Semiconductor Lasers: Past, Present, and Future, G. R Agrawal, ed. (American Institute of Physics, Melville, N.Y, 1995), pp. 145-180.

F Koyarna, K. Morit, and K. Iga, "Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers," IEEE J. Quantum Electron. 27, 1410-1416 (1991).
[CrossRef]

T. Mukaihara, N. Ohnoki, Y Hayashi, N. Hatori, F Koyarna, and K. Iga, "Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 7, 1113-1115 (1995).
[CrossRef]

D. C. Kilper, P.A. Roos, U. Carlsten, and K.L. Lear, "Squeezed light generated by a microcavity laser," Phys. Rev. A 55, R3323-113326 (1997).
[CrossRef]

M.P. van Exter, M.B. Willemsen, and J.P. Woerdman, "Polarization fluctuations in vertical-cavity semiconductor lasers," Phys. Rev. A 58, 4191-4205 (1998).
[CrossRef]

Ci Giacomelli, E Martin, M. Gabrysch, K.H. Gulden, and M. Moser, "Polarization competition and noise properties ofVCSELs," Opt. Comm. 146, 136-140 (1998).
[CrossRef]

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

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

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

D.V. Kuksenkov, H. Temkin, and S. Swirhun, "Polarization instability and performance of free-space optical links based on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 8, 703-705 (1996).
[CrossRef]

T.W. S. Garrison, M. Beck, and D.H. Christensen, "Noise behavior of pulsed vertical-cavity, surface-emitting lasers," J. Opt. Soc. Am. B 16, 2124-2130 (1999).
[CrossRef]

K.D. Choquette, R.P. Schneider, and K.L. Lear, "Gain-dependent polarization properties ofverfical cavity lasers," IEEE J. Select. Topics Quantum Electron. 1, 661-666 (1995).
[CrossRef]

M. San Miguel, Q. Feng, and J.V. Molony, "Light-polarization dynamics in surface-emitfing semiconductor lasers," Phys. Rev. A 1-52, 1728-1739 (1995).
[CrossRef] [PubMed]

A. Valle, L. Pesquera, and K.A. Shore, "Polarization behavior ofbirefringent multitransverse mode vertical cavity surface-emitting lasers," IEEE Photon. Tech. Lett 9, 557-559 (1997).
[CrossRef]

K. Panaiotov, B. Kyvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretenincoff "Polarization switching in VCSEL's due to thermal lensing," IEEE Photon. Tech. Lett. 10, 6-8 (1999).
[CrossRef]

M. Giudici, J.R. Tredicce, G. Vaschenko, J.J. Rocca, and C.S. Menom, "Spatio-temporal dynamics in vertical cavity surface emitting lasers excited by fast electrical pulses," Opt. Comm. 158, 313-321 (1998).
[CrossRef]

While quantum mechanics states that losses can significantly effect correlations between optical fields, we find that the measured noise levels of our fields are more than an order of magnitude above the shot-noise level. This means that the fields are well described by classical mechanics, and we do not anticipate that this additional loss will impact the results described here.

J.P. Hermier, A. Bramati, A.Z. Khoury, E. Giacobino, J.P. Poizat, T.J. Chang, P. Grangier, "Spatial quantum noise ofsemiconductor lasers," J. Opt. Soc. Am. B 16, 2140-2146 (1999).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (1376 KB)     
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Figures (8)

Fig. 1.
Fig. 1.

The experimental apparatus.

Fig. 2.
Fig. 2.

Plot of the mean (a) and variance (b) of the number of photoelectrons as a function of drive current for 10 ns pulses. Data is shown for the individual polarizations and the total output. Arrows indicate current values where new modes turn on, and are labeled by the polarization of the new mode.

Fig. 3.
Fig. 3.

Distributions at a drive current of 3.3 mA (one mode lasing) for 10 ns pulses: a) joint distribution p(n 0, n 90), b) distribution for the 90° output, c) distribution for the 0° output, d) distribution for the total output.

Fig. 4.
Fig. 4.

[a) 1.4 MB, b) 600 KB] Animation of P(n 0, n 90) as a function of drive current for 10 ns pulses: a) closeup of the shape of the distributions, b) all distributions shown on the same scale.

Fig. 5.
Fig. 5.

The correlation coefficient and polarization splitting ratio are plotted as a function of laser drive current for 10 ns pulses. Arrows indicate current values where new modes turn on, and are labeled by the polarization of the new mode.

Fig. 6.
Fig. 6.

[a) 980 KB, b) 850 KB] Animation of P(n 0, n 90) as a function of drive current: a) 3 ns duration pulses, b) 30 ns duration pulses.

Fig. 7.
Fig. 7.

The correlation coefficient (a) and the polarization splitting ratio (b) are plotted as a function of normalized drive current for three different pulse durations.

Fig. 8.
Fig. 8.

The relative noise is plotted as a function of normalized drive current for three different pulse durations.

Equations (5)

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n 0 n 90 P ( n 0 , n 90 ) δ n 0 δ n 90 = 1 ,
P ( n 90 ) = n 0 P ( n 0 , n 90 ) δ n 0 .
C 0,90 = ( n 0 n 0 ) ( n 90 n 90 ) σ 0 σ 90 = n 0 n 90 n 0 n 90 σ 0 σ 90 ,
M = n 90 n 0 .
RN = ( Δ n t ) 2 n t 2 .

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