## Polarization correlations in pulsed, vertical-cavity, surface-emitting lasers

Optics Express, Vol. 7, Issue 7, pp. 249-259 (2000)

http://dx.doi.org/10.1364/OE.7.000249

Acrobat PDF (847 KB)

### 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.

© Optical Society of America

## 1. Introduction

2. F. Koyama, K. Mont, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. **27**, 1410–1416 (1991). [CrossRef]

15. K. Panajotov, B. Kyvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Tech. Lett. **10**, 6–8 (1998). [CrossRef]

2. F. Koyama, K. Mont, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. **27**, 1410–1416 (1991). [CrossRef]

8. M.B. Willemsen, M.P. van Exter, and J.P. Woerdman, “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 vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. **67**, 2141–2143 (1995). [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]

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

## 2. Experiments

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]

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]

**16**, 2124–2130 (1999). [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.

*n*

_{0}and

*n*

_{90}, where the subscripts refer to the polarization) for 10

^{6}pulses. From this data we generate two-dimensional histograms which represent joint probability distributions for the photoelectron numbers in the 0° and 90° polarizations. We use 128 bins along each coordinate, and the histogram bin widths are δ

*n*

_{0}and δ

*n*

_{90}. We normalize the histograms according to

*P*(

*n*

_{0},

*n*

_{90}) represents a joint probability density. These joint distributions, displayed as contour plots, provide a great deal of information about the correlations between the 0° and 90° outputs. Furthermore, from these distributions we calculate the marginal probability densities

*P*(

*n*

_{0}),

*P*(

*n*

_{90}),

*P*(

*n*), where the subscript

_{t}*t*refers to the total number of photoelectrons

*n*=

_{t}*n*

_{0}+

*n*

_{90}. For example, the one-dimensional marginal distribution

*P*(

*n*

_{90}) is given by the expression

*n*〉 and variance 〈(Δ

*n*)

^{2}〉 of

*n*

_{0},

*n*

_{90}and

*n*.

_{t}*σ*

_{0}and

*σ*

_{90}are the standard deviations of the photoelectron output for each polarization. The correlation coefficient quantifies how the outputs in the two polarizations vary with respect to each other from pulse to pulse. It takes on values -1<

*C*

_{0,90}<1, with

*C*

_{0,90}=0 corresponding to no correlation between the two outputs, C0,90=1 corresponding to perfect correlation, and

*C*

_{0,90}=-1 corresponding to perfect anticorrelation.

*M*[7

7. J.-L. Vey, C. Degen, K. Auen, and W. Elsäßer, “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. Woerdman, “Correlated fluctuations in the polarization modes of a vertical-cavity semiconductor laser,” Phys. Rev. A **60**, 4105–4113 (1999). [CrossRef]

*M*is given by

## 3. Results for 10 ns pulses

*n*〉 plotted as a function of laser drive current for 10 ns current pulses; these plots are essentially the LI (light-current) curves for our laser. We plot 〈

*n*〉 for each polarization and the total. As can be seen from the figure, the light output does not increase linearly with current but rather has kinks. Such behavior has been observed before, and these kinks correspond to points where an additional mode comes above its threshold [2

2. F. Koyama, K. Mont, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. **27**, 1410–1416 (1991). [CrossRef]

**16**, 2124–2130 (1999). [CrossRef]

*P*(

*n*

_{0},

*n*

_{90}) that there will be

*n*

_{0}photoelectrons generated in the detector monitoring the 0° polarization and

*n*

_{90}photoelectrons in the detector monitoring the 90° polarization. Fig. 3 shows an example of a typical two-dimensional distribution and its relationship to the 1-dimensional marginal distributions. The ID distribution for the 90° polarization

*P*(

*n*

_{90}) can be formed by integrating out the 0° information, that is by summing along vertical lines in Fig. 3(a) and essentially projecting

*P*(

*n*

_{0},

*n*

_{90}) onto the horizontal axis [Eq. (2)]. This distribution is plotted in Fig. 3(b). Similarly,

*P*(

*n*

_{0}), Fig. 3(c), can be formed by integrating out the 90° information (i.e., projecting the 2D distribution onto the vertical axis.) It so happens that the distribution for the total output

*P*(

*n*), Fig. 3(d), can be found by integrating along lines that make a slope of -1 in Fig. 3(a), and thus projects the joint distribution onto an axis that makes a 45° angle.

_{t}*n*

_{90}will tend to have a lower

*n*

_{0}, and vice versa. This is shown clearly in Fig. 4(a); at this drive current of 10.5 mA there are more than six modes lasing, and the anticorrelations are very strong.

*n*〉 changes in each polarization, as well as how the size of the distribution changes, as a function of drive current. The drawback to this animation is that at low drive currents the distributions themselves are so small that they can barely be seen. For full benefit of Fig. 4, both animations should be played simultaneously, side by side.

*M*and

*C*

_{0,90}; smaller polarization imbalance (

*M*approaches 1) corresponds to stronger anticorrelation, as predicted for CW lasers in Ref. [7

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

*M*.

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

**60**, 3284–3295 (1999). [CrossRef]

## 4. Results for other pulse widths

_{ro}, and the damping of the relaxation oscillations, τ

_{ro}. While we have not directly measured these timescales in our laser, we expect them to be on the order of 0.1–1 ns for T

_{ro}, and on the order of 1 ns for τ

_{ro}[8

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

*M*and

*C*

_{0,90}; smaller polarization imbalance (larger M) corresponds to stronger anticorrelation, as predicted in Ref. [7

**60**, 3284–3295 (1999). [CrossRef]

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

*C*

_{0,90}with pulsewidth [7

**60**, 3284–3295 (1999). [CrossRef]

**60**, 4105–4113 (1999). [CrossRef]

*RN*of the laser output as a function of the normalized current for the three different pulsewidths. The relative noise is defined as [11

**16**, 2124–2130 (1999). [CrossRef]

## 5. Conclusions

*C*

_{0,90}, we find that this is a drastic oversimplification of the problem. The correlation coefficient is derived from second order moments of the joint probability density for the polarization fluctuations

*P*(

*n*

_{0},

*n*

_{90})· For Gaussian statistics moments up to second order can fully characterize the fluctuations; to a good approximation this is the case for our laser when it is between 1.8 and 5 times above threshold. However, closer to threshold we find that the statistics are not Gaussian (Figs. 4 & 6), and the correlations are of a much more complicated form.

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

## Acknowledgments

## References and links

1. | C. J. Chang-Hasnam, “Vertical-cavity surface emitting lasers,” in |

2. | F. Koyama, K. Mont, and K. Iga, “Intensity noise and polarization stability of GaAlAs-GaAs surface emitting lasers,” IEEE J. Quantum Electron. |

3. | T. Mukaihara, N. Ohnoki, Y. Hayashi, N. Hatori, F. Koyama, and K. Iga, “Excess intensity noise originated from polarization fluctuation in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. |

4. | D.C. Kilper, P.A. Roos, J.L. Carlsten, and K.L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A |

5. | M.P. vanExter, M.B. Willemsen, and J.P. Woerdman, “Polarization fluctuations in vertical-cavity semiconductor lasers,” Phys. Rev. A |

6. | G. Giacomelli, F. Martin, M. Gabrysch, K.H. Gulden, and M. Moser, “Polarization competition and noise properties of VCSELs,” Opt. Comm. |

7. | J.-L. Vey, C. Degen, K. Auen, and W. Elsäßer, “Quantum noise and polarization properties of vertical-cavity, surface-emitting lasers,” Phys. Rev. A |

8. | M.B. Willemsen, M.P. van Exter, and J.P. Woerdman, “Correlated fluctuations in the polarization modes of a vertical-cavity semiconductor laser,” Phys. Rev. A |

9. | D.V. Kuksenkov, H. Temkin, and S. Swirhun, “Polarization instability and relative intensity noise in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. |

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. |

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 |

12. | K.D. Choquette, R.P. Schneider, and K.L. Lear, “Gain-dependent polarization properties of vertical cavity lasers,” IEEE J. Select. Topics Quantum Electron. |

13. | M. San Miguel, Q. Feng, and J.V. Molony, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A |

14. | A. Valle, L. Pesquera, and K.A. Shore, “Polarization behavior of birefringent multitransverse mode vertical-cavity surface-emitting lasers,” IEEE Photon. Tech. Lett. |

15. | K. Panajotov, B. Kyvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photon. Tech. Lett. |

16. | M Giudici, J.R. Tredicce, G. Vaschenko, J.J. Rocca, and C.S. Menoni, “Spatio-temporal dynamics in vertical cavity surface emitting lasers excited by fast electrical pulses,” Opt. Comm. |

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, and P. Grangier, “Spatial quantum noise of semiconductor lasers,” J. Opt. Soc. Am. B |

**OCIS Codes**

(140.5960) Lasers and laser optics : Semiconductor lasers

(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

**ToC Category:**

Research Papers

**History**

Original Manuscript: August 2, 2000

Published: September 25, 2000

**Citation**

David Shelly, T. Garrison, Mark Kevin Beck, and D. Christensen, "Polarization correlations in pulsed, vertical cavity, surface-emitting lasers," Opt. Express **7**, 249-259 (2000)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-7-249

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### References

- 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]

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