## Design and analysis of VCSEL based two-dimension wavelength converter

Optics Express, Vol. 11, Issue 14, pp. 1659-1668 (2003)

http://dx.doi.org/10.1364/OE.11.001659

Acrobat PDF (131 KB)

### Abstract

A novel two-dimensional vertical cavity surface emission laser (VCSEL) based wavelength converter is proposed. We developed a two-dimensional transmission line laser model (TLLM) to analyze the proposed wavelength converter. This model takes into account Bragg reflectors by using the modified connecting matrix. Therefore, accurate and efficient modeling of the VCSEL structure is achieved. Extinction ratio of the output signal is investigated by considering input signal power, wavelength, facet reflectivity and cavity diameter.

© 2003 Optical Society of America

## 1. Introduction

1. T. Durhuus, B. Mikkesen, C. Joergensen, S. L. Danieselen, and K. E. Stubjkaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol. **14**, 943–954 (1996) [CrossRef]

2. S.L. Danielsen, P.B Hansen, and K.E. Stubjær, “Wavelength conversion in optical packet switching,” J. Lightwave Technol. **16**, 2095–2108 (1998) [CrossRef]

*λ*(called signal) is used to modulate the carrier density of the SOA. With the modulation of the

_{Signal}*λ*, the (inverted) data can be copied onto another continuous wave on the wavelength

_{Signal}*λ*

_{Pr obe}(called probe). The signal wave and the probe wave can be injected into the SOA either co- or counter-propagating (Fig. 1). However, shortcomings exist in both of these configurations. For the co-propagating injection, an optical filter is needed to suppress the signal wave. For the counter-propagating method, though optical filter is avoided, an additional isolator at the probe input is needed to suppress the strongly amplified input signal. Moreover, in the latter configuration smaller bandwidth as well as an enhanced amplified spontaneous emission (ASE) noise level are suffered [3

3. K. Obermann, S. Kindt, D. Breuer, and K. Petermann, “Performance analysis of wavelength converters based on cross-gain modulation in semiconductor-optical amplifiers,” J. Lightwave Technol. **16**, 78–85 (1998) [CrossRef]

4. K. Nonaka, H. Tsuda, H. Uenohara, H. Iwamura, and T. Kurokawa, “Optical nonlinear characteristics of a side-injection light-controlled laser diode with a multiple-quantum-well saturable absorption region,” IEEE Photon. Technol. Lett. **5**, 139–141 (1993) [CrossRef]

5. K. Nonaka, F. Kobayashi, K. Kishi, T. Tadokoro, Y. Itoh, C. Amano, and T. Kurokawa, “Direct Time Domain Optical Demultiplexing of 10-Gb/s NRZ signals using side-injection light-controlled bistable laser diode,” IEEE Photon. Tech. Lett. **10**, 1484–1486 (1998) [CrossRef]

## 2. VCSEL based two-dimension wavelength converter

*µm*is very difficult to fabricate [6

6. E. Höfling, R. Werner, F. Schäfer, J.P. Reithmaier, and A. Forchel, “Short-cavity edge-emitting lasers with deeply etched distributed Bragg mirrors,” Electron. Lett. **35**, 154–155 (1999) [CrossRef]

7. K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Select. Topics Quantum Electron. **6**, 1201–1215 (2000) [CrossRef]

9. S.F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. **32**, 1168–1179 (1996) [CrossRef]

10. S.F Yu, “An improved Time-Domain Travelling-Wave model for vertical-cavity surface-Emitting lasers,” IEEE J. Quantum Electron. **34**, 1938–1948 (1998) [CrossRef]

## 3. Two-dimension transmission line laser model

11. A. J. Lowery, “Transmission-line modeling of semiconductor lasers: the transmission-line laser model”, Internaltional Journal of numerical modeling: Electronic Networks, Devices and Fields , **2**, 249–265 (1989) [CrossRef]

*F*and

_{P}*B*, and those of the signal wave are named as

_{P}*F*and

_{S}*B*, respectively. We describe the scattering process at time

_{S}*t*of these four waves in the active region as:

*i*denotes the incident wave,

*r*denotes the reflective wave,

*S*is the scattering matrix for the signal wave,

_{S}*S*is the scattering matrix for the probe wave,

_{P}*I*is the spontaneous noise current,

_{sp}*T*is the attenuation factor,

*n*and m are the section numbers in the traveling direction of the probe wave and the signal wave, respectively.

*Z*is the cavity wave impedance given as

_{p}*n̅*is the effective index, Scattering matrices

_{e}*S*and

_{S}*S*can be found in [11

_{P}11. A. J. Lowery, “Transmission-line modeling of semiconductor lasers: the transmission-line laser model”, Internaltional Journal of numerical modeling: Electronic Networks, Devices and Fields , **2**, 249–265 (1989) [CrossRef]

*I*, which is represented by three statistically independent Gaussian distributed random processes that satisfy the following correlation [11

_{sp}11. A. J. Lowery, “Transmission-line modeling of semiconductor lasers: the transmission-line laser model”, Internaltional Journal of numerical modeling: Electronic Networks, Devices and Fields , **2**, 249–265 (1989) [CrossRef]

12. H. Lee, H. Yoon, Y. Kim, and J. Jeong, “Theoretical study of frequency chirping and extinction ration of wavelength-converted optical signals by XGM and XPM using SOA’s,” IEEE J. Quantum Electron. **35**, 1213–1219 (1999) [CrossRef]

*β*is the spontaneous coupling factor,

*R*is the spontaneous emission rate which is assumed as bimolecular recombination (

_{sp}*BN*

^{2}),

*δ*(

*x*) is the Delta-function,

*hf*is the photon energy and

*L*is the laser cavity length.

12. H. Lee, H. Yoon, Y. Kim, and J. Jeong, “Theoretical study of frequency chirping and extinction ration of wavelength-converted optical signals by XGM and XPM using SOA’s,” IEEE J. Quantum Electron. **35**, 1213–1219 (1999) [CrossRef]

*a*

_{0},

*a*

_{1}, and

*a*

_{2}are gain constants,

*λ*the gain-peak wavelength,

_{P}*ε*the gain compression factor,

*N*the local carrier density,

*N*

_{0}the transparent carrier density. The gain for the probe wave or the signal wave can be obtained when

*λ*is set as

_{k}*λ*

_{Pr obe}or

*λ*.

_{Signal}**2**, 249–265 (1989) [CrossRef]

*C*is the connecting matrix for the probe wave and

_{P}*C*is the connecting matrix for the signal wave. It should be noted that

_{S}*C*and

_{P}*C*are identity matrices for those sections where there are no distributed Bragg reflectors (DBR) such that no reflections happen between forward waves and backward waves.

_{S}*C*is not identity matrix anymore and should be modified to reflect the wave coupling and reflection in DBR. The connecting process in these sections is described as

_{P}13. A.J Lowery, “Dynamic modeling of distributed-feedback lasers using scattering matrices,” Electron. Lett. **25**, 1307–1308 (1989) [CrossRef]

9. S.F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. **32**, 1168–1179 (1996) [CrossRef]

*n*is the effective index of the low index layer and

_{l}*n*is the effective index of the high index layer.

_{h}**2**, 249–265 (1989) [CrossRef]

14. L.V.T. Nguyen, A.J. Lowey, P.C.R. Gurney, and D. Novak, “A time domain model for high speed quantum well lasers including carrier transport effects,” IEEE J. Sel. Top. Quantum Electron. **1**, 494–504 (1995) [CrossRef]

15. P.J. Annets, M. Asghari, and I.H. White, “The effect of carrier transport on the dynamic performance of gain-saturation wavelength conversion on MQW semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. **3**, 320–329 (1997) [CrossRef]

*N*is the carrier density in the multiple quantum well active layer,

_{MQW}*N*the carrier density in the separate confinement layer,

_{SCH}*d*and

_{MQW}*d*the thickness of the active layer and the separate confinement layer, respectively;

_{SCH}*ν*is the group velocity,

_{g}*τ*the carrier emission constant,

_{e}*τ*the recombination time and

_{rec}*τ*the carrier diffusion time,

_{r}*e*the charge of the electron,

*J*the injection current density,

*P*and

_{S}*P*the photon densities,

_{P}*g*and

_{S}*g*the material gains of the signal wave and the probe wave, respectively.

_{P}## 4. Results and discussion

*λ*=1565

_{signal}*nm*and

*λ*=1525

_{probe}*nm*. We observe that the probe signal undergoes overshoot on the rising edge. This can be explained by the fact that the carriers are greatly consumed by the signal wave when it is at high state (‘1’ state), thus the front end of the probe wave experiences overshoot in the gain recovery process when the signal wave at the low state (‘0’ state). The result also reveals that the ‘1’ state power of the signal wave is as high as 25mw to get an extinction ratio of the probe wave larger than 10dB. This is the reason why we have to amplify the signal wave first before cross-gain modulation. In the simulation the input signal powers refer to the power after amplification. Moreover the affect of ASE noise on the probe wave can be seen in Fig. 4. It is shown that ASE noise at low state is smaller than at high state, since gain saturation may reduce the ASE noise at the high input signal power.

*λ*

_{Pr obe}is shorter than

*λ*) leads to a higher extinction ratio than that of up-conversion (

_{Signal}*λ*

_{Pr obe}is longer than

*λ*). It also shows that high extinction ration can be obtained if

_{Signal}*λ*is around the gain peak.

_{Signal}## 5. Conclusion

## Acknowledgements

## References and links

1. | T. Durhuus, B. Mikkesen, C. Joergensen, S. L. Danieselen, and K. E. Stubjkaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol. |

2. | S.L. Danielsen, P.B Hansen, and K.E. Stubjær, “Wavelength conversion in optical packet switching,” J. Lightwave Technol. |

3. | K. Obermann, S. Kindt, D. Breuer, and K. Petermann, “Performance analysis of wavelength converters based on cross-gain modulation in semiconductor-optical amplifiers,” J. Lightwave Technol. |

4. | K. Nonaka, H. Tsuda, H. Uenohara, H. Iwamura, and T. Kurokawa, “Optical nonlinear characteristics of a side-injection light-controlled laser diode with a multiple-quantum-well saturable absorption region,” IEEE Photon. Technol. Lett. |

5. | K. Nonaka, F. Kobayashi, K. Kishi, T. Tadokoro, Y. Itoh, C. Amano, and T. Kurokawa, “Direct Time Domain Optical Demultiplexing of 10-Gb/s NRZ signals using side-injection light-controlled bistable laser diode,” IEEE Photon. Tech. Lett. |

6. | E. Höfling, R. Werner, F. Schäfer, J.P. Reithmaier, and A. Forchel, “Short-cavity edge-emitting lasers with deeply etched distributed Bragg mirrors,” Electron. Lett. |

7. | K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Select. Topics Quantum Electron. |

8. | J. Cheng and N. K Dutta, |

9. | S.F. Yu, “Dynamic behavior of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. |

10. | S.F Yu, “An improved Time-Domain Travelling-Wave model for vertical-cavity surface-Emitting lasers,” IEEE J. Quantum Electron. |

11. | A. J. Lowery, “Transmission-line modeling of semiconductor lasers: the transmission-line laser model”, Internaltional Journal of numerical modeling: Electronic Networks, Devices and Fields , |

12. | H. Lee, H. Yoon, Y. Kim, and J. Jeong, “Theoretical study of frequency chirping and extinction ration of wavelength-converted optical signals by XGM and XPM using SOA’s,” IEEE J. Quantum Electron. |

13. | A.J Lowery, “Dynamic modeling of distributed-feedback lasers using scattering matrices,” Electron. Lett. |

14. | L.V.T. Nguyen, A.J. Lowey, P.C.R. Gurney, and D. Novak, “A time domain model for high speed quantum well lasers including carrier transport effects,” IEEE J. Sel. Top. Quantum Electron. |

15. | P.J. Annets, M. Asghari, and I.H. White, “The effect of carrier transport on the dynamic performance of gain-saturation wavelength conversion on MQW semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. |

**OCIS Codes**

(140.4480) Lasers and laser optics : Optical amplifiers

(140.5960) Lasers and laser optics : Semiconductor lasers

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 7, 2003

Revised Manuscript: June 9, 2003

Published: July 14, 2003

**Citation**

H. Liu, P. Shum, and M. Kao, "Design and analysis of VCSEL based twodimension wavelength converter," Opt. Express **11**, 1659-1668 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-14-1659

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### References

- T. Durhuus, B. Mikkesen, C. Joergensen, S. L. Danieselen, and K. E. Stubjkaer, �??All-optical wavelength conversion by semiconductor optical amplifiers,�?? J. Lightwave Technol. 14, 943-954 (1996). [CrossRef]
- S.L. Danielsen, P.B.Hansen, and K.E. Stubjær, �??Wavelength conversion in optical packet switching,�?? J. Lightwave Technol. 16, 2095-2108 (1998). [CrossRef]
- K. Obermann, S. Kindt, D. Breuer, and K. Petermann, �?? Performance analysis of wavelength converters based on cross-gain modulation in semiconductor-optical amplifiers,�?? J. Lightwave Technol. 16, 78-85 (1998). [CrossRef]
- K. Nonaka, H. Tsuda, H. Uenohara, H. Iwamura and T. Kurokawa, �??Optical nonlinear characteristics of a side-injection light-controlled laser diode with a multiple-quantum-well saturable absorption region,�?? IEEE Photon. Technol. Lett. 5, 139-141 (1993). [CrossRef]
- K. Nonaka, F. Kobayashi, K. Kishi, T. Tadokoro,Y. Itoh, C. Amano, and T. Kurokawa, �??Direct Time Domain Optical Demultiplexing of 10-Gb/s NRZ signals using side-injection light-controlled bistable laser diode,�?? IEEE Photon. Tech. Lett. 10, 1484-1486 (1998). [CrossRef]
- E. Höfling, R. Werner, F. Schäfer, J.P. Reithmaier and A. Forchel, �??Short-cavity edge-emitting lasers with deeply etched distributed Bragg mirrors,�?? Electron. Lett. 35, 154-155 (1999). [CrossRef]
- K. Iga, �??Surface-emitting laser-its birth and generation of new optoelectronics field,�?? IEEE J. Select. Topics Quantum Electron. 6, 1201-1215 (2000). [CrossRef]
- J. Cheng and N. K.Dutta, Verical-cavity surface-emitting lasers: technology and applications, (Gordon and Breach Science Publishers, 2000), Chap 1.
- S.F.Yu, �??Dynamic behavior of vertical-cavity surface-emitting lasers,�?? IEEE J. Quantum Electron. 32, 1168-1179 (1996). [CrossRef]
- S.F.Yu, �??An improved Time-Domain Travelling-Wave model for vertical-cavity surface-Emitting lasers,�?? IEEE J. Quantum Electron. 34, 1938-1948 (1998). [CrossRef]
- A. J. Lowery, �??Transmission-line modeling of semiconductor lasers: the transmission-line laser model�??, International Journal of numerical modeling: Electronic Networks, Devices and Fields, 2, 249-265 (1989). [CrossRef]
- H. Lee, H. Yoon, Y. Kim, and J. Jeong, �??Theoretical study of frequency chirping and extinction ration of wavelength-converted optical signals by XGM and XPM using SOA�??s,�?? IEEE J. Quantum Electron. 35, 1213-1219 (1999). [CrossRef]
- A.J.Lowery, �??Dynamic modeling of distributed-feedback lasers using scattering matrices,�?? Electron. Lett. 25, 1307-1308 (1989). [CrossRef]
- L.V.T. Nguyen, A.J. Lowey, P.C.R. Gurney, and D.Novak, �??A time domain model for high speed quantum well lasers including carrier transport effects,�?? IEEE J. Sel. Top. Quantum Electron. 1, 494-504 (1995). [CrossRef]
- P.J. Annets, M.Asghari and I.H. White, �??The effect of carrier transport on the dynamic performance of gain-saturation wavelength conversion on MQW semiconductor optical amplifiers,�?? IEEE J. Sel. Top. Quantum Electron. 3, 320-329 (1997). [CrossRef]

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