## XOR performance of a quantum dot semiconductor optical amplifier based Mach-Zehnder interferometer

Optics Express, Vol. 13, Issue 6, pp. 1892-1899 (2005)

http://dx.doi.org/10.1364/OPEX.13.001892

Acrobat PDF (157 KB)

### Abstract

The performance of all-optical XOR gate based on quantum-dot (QD) SOA MZI has been simulated. The saturation power, optical gain and phase response of a QD SOA has been analyzed numerically using a rate equation model of quantum dots embedded in a wetting layer. The calculated response is used to model the XOR performance. For the parameters used here, XOR operation at ~250 Gb/s is feasible using QD based Mach-Zehnder interferometers. The speed is limited by the relaxation time from wetting layer to the quantum dots.

© 2005 Optical Society of America

## 1. Introduction

1. K. L. Hall and K. A. Rauschenbach, “All-optical bit pattern generation and matching,” Electron. Lett. **32**, 1214–1215 (1996) [CrossRef]

2. A. J. Poustie, K. J. Blow, R. J. Manning, and A. E. Kelly, “All-optical pseudorandom number generator,” Opt. Commun. **159**, 208–214 (1999) [CrossRef]

3. T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,” IEEE Photon. Technol. Lett. **13**, 750–752 (2001) [CrossRef]

4. N. S. Patel, K. L. Hall, and K. A. Rauschenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. **37**, 2831–2842 (1998) [CrossRef]

1. K. L. Hall and K. A. Rauschenbach, “All-optical bit pattern generation and matching,” Electron. Lett. **32**, 1214–1215 (1996) [CrossRef]

5. M. Jinno and T. Matsumoto, “Ultrafast all-optical logic operations in a nonlinear sagnac interferometer with two control beams,” Opt. Lett. **16**, 220–222 (1991) [CrossRef] [PubMed]

6. T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, and R. Dall’Ara, “10 Gbit/s all-optical Boolean XOR with SOA fiber Sagnac gate,” Electron. Lett. **35**, 1650–1652 (1999) [CrossRef]

7. C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, and R. Dall’Ara, “20 Gb/s all-optical XOR with UNI gate,” IEEE Photon. Technol. Lett. **12**, 834–836 (2000) [CrossRef]

8. T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOA-based interferometric wavelength converter,” Electron. Lett. **36 (22)**, 1863–1864 (2000) [CrossRef]

6. T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, and R. Dall’Ara, “10 Gbit/s all-optical Boolean XOR with SOA fiber Sagnac gate,” Electron. Lett. **35**, 1650–1652 (1999) [CrossRef]

7. C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, and R. Dall’Ara, “20 Gb/s all-optical XOR with UNI gate,” IEEE Photon. Technol. Lett. **12**, 834–836 (2000) [CrossRef]

8. T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOA-based interferometric wavelength converter,” Electron. Lett. **36 (22)**, 1863–1864 (2000) [CrossRef]

9. Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. B. Piccirilli, and N. K. Dutta, “Study of all-optical XOR using Mach-Zehnder interferometer and differential scheme,” IEEE J.Quantum Electron. , **Vol.40**, pp.703–710,2004 [CrossRef]

11. H. Chen, G. Zhu, J. Jaques, J. Leuthold, A.B. Piccirilli, and N.K. Dutta, “All-optical logic XOR using a differential scheme and Mach-Zehnder interferometer,” Electron. Lett. **38**, 1271–1273 (2002) [CrossRef]

## 2. Principle of operation

_{1}and λ

_{2}are sent into port A and B of the MZI separately. The wavelengths of the two data signals can also be same. The signal, a clock stream of continuous series of “1”s̀ or a CW beam is split into two equal parts and injected into the two SOAs. Initially the MZI is unbalanced i.e. when A=0 and B=0, the signal at port C traveling through the two arms of the SOA acquires a phase difference of π when it recombines at the output port, thus the output is “0”. When A=1, B=0, the signal traveling through the arm with signal A acquires a phase change due to the cross phase modulation (XPM) between the pulse train A and signal and the signal traveling through the lower arm does not have this additional phase change. This results in an output “1”. The same phenomenon happens if A=0 and B=1. However, when A=1 and B=1 the phase change for the signal traveling both arms are equal, hence the output is “0”. When the phase shift is optimum, the best contrast ratio is achieved at the output port.

## 3. Quantum dot model

12. M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B **69**, 235332-1-39 (2004) [CrossRef]

*N*

_{w}in wetting layer,

*N*

_{id}in the

^{i}th quantum dot, and

*N*

_{imax}as the maximum carrier density that

*i*th quantum-dot can sustain. The rate equations for carrier density are given as follows:

*J*is the injection current density,

*d*is the total wetting layer thickness,

13. J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers; Experiment and theory,” Appl. Phys. Lett. **61**, 2281–2283 (1992) [CrossRef]

*ε*

_{SHB}and

*ε*

_{CH}are the nonlinear gain suppression factors due to carrier heating and spectral hole burning [14], and

*g*

_{i}is the gain in the for the quantum dot transition. The total gain is given by:

*G*(

*t, z*)=

*Exp*[

*h*(

*t*)] and

*h*(

*t*)=∫z0

*g*(

*t,z*)

*dz*

*h*

_{max}=

*a*(

*N*

_{max}-

*N*

_{tr})

*dz*′,

*N*

_{tr}is the carrier density at transparency,

*a*is the differential gain of SOA,

*ε*

_{SHB}and

*ε*

_{CH}are the gain suppression factors owing to spectral hole burning and carrier heating effect respectively. The phase change equation is given by:

*α*is the usual linewidth enhancement factor associated with the interband transitions and

*α*

_{CH}is the linewidth enhancement factor for carrier heating. The linwidth enhancement factor for spectral hole burning (SHB) process,

*α*

_{SHB}~0 [14]. Typical α values are in the 2 to 7 range and

*α*

_{CH}~1 [15

15. J. M. Tang and K. A. Shore, “Characteristic of Optical Phase Conjugation of Picosecond Pulses in Semiconductor Optical Amplifiers,” IEEE J. Quantum Electron. **35–7**, 1032–1040 (1999) [CrossRef]

16. M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikawa, “Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160Gbs-1 and a new scheme of 3R regenerators,” Meas. Sci. Technol. **13**, 1683–1691 (2002) [CrossRef]

16. M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikawa, “Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160Gbs-1 and a new scheme of 3R regenerators,” Meas. Sci. Technol. **13**, 1683–1691 (2002) [CrossRef]

*τ*

_{w→d}=6ps,

*τ*

_{wr}=0.2ns,

*τ*

_{dr}=0.4ns,

*τ*

_{d→w}=10ns,

*τ*

_{SHB}=100fs,

*τ*

_{CH}=300fs,

*ε*

_{SHB}

*=ε*

_{CH}=0.08ps, and, Γ=0.15.

## 4. Simulation of Mach-Zehnder interferometer and XOR operation

_{3}(see Fig. 1) depends on the phase changes the CW signal undergoes at the two arms of the MZI due to the co-propagating data signals. At the output of the MZI, the light at wavelength λ

_{3}propagating through the two arms interfere and the time dependent XOR output intensity is described by the following basic interferometer equations:

16. M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikawa, “Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160Gbs-1 and a new scheme of 3R regenerators,” Meas. Sci. Technol. **13**, 1683–1691 (2002) [CrossRef]

*τ*

_{w→d}=6ps,

*τ*

_{wr}=0.2ns,

*τ*

_{dr}=0.4ns,

*τ*

_{d→w}=10ns,

*τ*

_{SHB}=100fs,

*τ*

_{CH}=300fs,

*ε*

_{SHB}=

*ε*

_{CH}=0.08ps, Γ=0.15, line width enhancement factor

*α*=5,

*α*

_{CH}=1 amplifier maximum gain=20dB, injected current density=4kA/cm

^{2}.

*Q*is widely used to characterize the signal quality for pseudo-random signals[17]. Q -factor is defined as:

*“*

_{1}”, σ1 is the standard deviation of all “1”.

*σ*

_{0}are defined analogously for output signal “0”. Here we utilize “pseudo-eye-diagrams” (PED) [18

18. R. Gutierrez-Castrejon, L. Occhi, L. Schares, and G. Guekos, “Recovery dynamics of cross-modulated beam phase in semiconductor amplifiers and applications to all-optical signal processing,” Opt. Commun. **195**, 167–177 (2001) [CrossRef]

^{7}-1 pseudo-random input bit pattern is shown in Fig. 6. The two Fig.s are for data rates of 80 Gb/s, 160 Gb/s and 250 Gb/s are generated at

*τ*

_{w→d}=6ps and

*τ*

_{w→d}=1ps respectively. The full width at half maximum of the Gaussian pulse used in the calculation is 1/5 th of the pulse period. The calculated Q-values are shown. The Q-value decreases as the data rate is increased.

^{2}, however, Q saturates. The saturated Q factor for 250Gb/s is ~6 for the parameters [15

15. J. M. Tang and K. A. Shore, “Characteristic of Optical Phase Conjugation of Picosecond Pulses in Semiconductor Optical Amplifiers,” IEEE J. Quantum Electron. **35–7**, 1032–1040 (1999) [CrossRef]

**13**, 1683–1691 (2002) [CrossRef]

^{-9}[19]. Hence, we conclude that ~250Gb/s is the speed limit for the parameters used here. Higher speed of operation is feasible for shorter relaxation time from the wetting layer to the QD level.

## 5. Summary and discussion

**13**, 1683–1691 (2002) [CrossRef]

## References and links

1. | K. L. Hall and K. A. Rauschenbach, “All-optical bit pattern generation and matching,” Electron. Lett. |

2. | A. J. Poustie, K. J. Blow, R. J. Manning, and A. E. Kelly, “All-optical pseudorandom number generator,” Opt. Commun. |

3. | T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,” IEEE Photon. Technol. Lett. |

4. | N. S. Patel, K. L. Hall, and K. A. Rauschenbach, “Interferometric all-optical switches for ultrafast signal processing,” Appl. Opt. |

5. | M. Jinno and T. Matsumoto, “Ultrafast all-optical logic operations in a nonlinear sagnac interferometer with two control beams,” Opt. Lett. |

6. | T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, and R. Dall’Ara, “10 Gbit/s all-optical Boolean XOR with SOA fiber Sagnac gate,” Electron. Lett. |

7. | C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, and R. Dall’Ara, “20 Gb/s all-optical XOR with UNI gate,” IEEE Photon. Technol. Lett. |

8. | T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOA-based interferometric wavelength converter,” Electron. Lett. |

9. | Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. B. Piccirilli, and N. K. Dutta, “Study of all-optical XOR using Mach-Zehnder interferometer and differential scheme,” IEEE J.Quantum Electron. , |

10. | G. Agrawal and N. Olsson, “Self-Phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,” IEEE, J. Quantum Electron. |

11. | H. Chen, G. Zhu, J. Jaques, J. Leuthold, A.B. Piccirilli, and N.K. Dutta, “All-optical logic XOR using a differential scheme and Mach-Zehnder interferometer,” Electron. Lett. |

12. | M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,” Phys. Rev. B |

13. | J. Mark and J. Mørk, “Subpicosecond gain dynamics in InGaAsP optical amplifiers; Experiment and theory,” Appl. Phys. Lett. |

14. | A. Mecozzi and J. Mørk, “Saturation effect in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifier,” IEEE J. Sel. Top. Quantum Electron. |

15. | J. M. Tang and K. A. Shore, “Characteristic of Optical Phase Conjugation of Picosecond Pulses in Semiconductor Optical Amplifiers,” IEEE J. Quantum Electron. |

16. | M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikawa, “Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160Gbs-1 and a new scheme of 3R regenerators,” Meas. Sci. Technol. |

17. | A. Sakamoto and M. Sugawara “Theoretical calculation of lasing spectra of quantum-dot lasers: Effect of homogeneous broadening of optical gain,” IEEE Photon. Technol. Lett.12–2, (2000) |

18. | R. Gutierrez-Castrejon, L. Occhi, L. Schares, and G. Guekos, “Recovery dynamics of cross-modulated beam phase in semiconductor amplifiers and applications to all-optical signal processing,” Opt. Commun. |

19. | G. P. Agrawal, |

**OCIS Codes**

(200.4660) Optics in computing : Optical logic

(250.5980) Optoelectronics : Semiconductor optical amplifiers

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 25, 2005

Revised Manuscript: February 24, 2005

Published: March 21, 2005

**Citation**

H. Sun, Q. Wang, H. Dong, and N. Dutta, "XOR performance of a quantum dot semiconductor optical amplifier based Mach-Zehnder interferometer," Opt. Express **13**, 1892-1899 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1892

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### References

- K. L. Hall and K. A. Rauschenbach, �??All-optical bit pattern generation and matching,�?? Electron. Lett. 32, 1214-1215 (1996). [CrossRef]
- A. J. Poustie, K. J. Blow, R. J. Manning, and A. E. Kelly, �??All-optical pseudorandom number generator,�?? Opt. Commun. 159, 208-214 (1999). [CrossRef]
- T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, M. Renaud, �??Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,�?? IEEE Photon. Technol. Lett. 13, 750-752 (2001). [CrossRef]
- N. S. Patel, K. L. Hall, and K. A. Rauschenbach, �??Interferometric all-optical switches for ultrafast signal processing,�?? Appl. Opt. 37, 2831-2842 (1998). [CrossRef]
- M. Jinno, and T. Matsumoto, �??Ultrafast all-optical logic operations in a nonlinear sagnac interferometer with two control beams,�?? Opt. Lett. 16, 220-222 (1991). [CrossRef] [PubMed]
- T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard and R. Dall�??Ara, �??10 Gbit/s all-optical Boolean XOR with SOA fiber Sagnac gate,�?? Electron. Lett. 35, 1650-1652 (1999). [CrossRef]
- C. Bintjas, M. Kalyvas, G. Theophilopoulos, T. Stathopoulos, H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, and R. Dall�??Ara, �??20 Gb/s all-optical XOR with UNI gate,�?? IEEE Photon. Technol. Lett. 12, 834-836 (2000). [CrossRef]
- T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, �??Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOA-based interferometric wavelength converter,�?? Electron. Lett. 36 (22), 1863-1864 (2000). [CrossRef]
- Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. B. Piccirilli, and N. K. Dutta, �??Study of all-optical XOR using Mach-Zehnder interferometer and differential scheme,�?? IEEE J. Quantum Electron., Vol.40, pp.703-710,2004. [CrossRef]
- G. Agrawal and N. Olsson, �??Self-Phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers,�?? IEEE J. Quantum Electron. 25-11, 2297-2306 (1989). [CrossRef]
- H.Chen, G.Zhu, J.Jaques, J.Leuthold, A.B.Piccirilli, and N.K.Dutta, �??All-optical logic XOR using a differential scheme and Mach-Zehnder interferometer,�?? Electron. Lett. 38, 1271-1273 (2002). [CrossRef]
- M. Sugawara, H. Ebe, N. Hatori, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, �??Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers,�?? Phys. Rev. B 69, 235332-1-39 (2004). [CrossRef]
- J. Mark and J. Mørk, �??Subpicosecond gain dynamics in InGaAsP optical amplifiers; Experiment and theory,�?? Appl. Phys. Lett. 61, 2281-2283 (1992). [CrossRef]
- A. Mecozzi and J. Mørk, �??Saturation effect in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifier,�?? IEEE J. Sel. Top. Quantum Electron. 3-5, 1190-1207 (1997).
- J. M. Tang and K. A. Shore,"Characteristic of Optical Phase Conjugation of Picosecond Pulses in Semiconductor Optical Amplifiers," IEEE J. Quantum Electron. 35-7, 1032-1040 (1999). [CrossRef]
- M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe and H. Ishikawa, �??Quantum-dot semiconductor optical amplifiers for high-bit-rate signal processing up to 160Gbs-1 and a new scheme of 3R regenerators,�?? Meas. Sci. Technol. 13, 1683-1691 (2002). [CrossRef]
- A. Sakamoto and M. Sugawara �??Theoretical calculation of lasing spectra of quantum-dot lasers: Effect of homogeneous broadening of optical gain,�?? IEEE Photon. Technol. Lett. 12-2, (2000).
- R. Gutierrez-Castrejon, L. Occhi, L. Schares, and G. Guekos, �??Recovery dynamics of cross-modulated beam phase in semiconductor amplifiers and applications to all-optical signal processing,�?? Opt. Commun. 195, 167-177 (2001). [CrossRef]
- G. P. Agrawal, Fiber Optic Communication systems, (John Wiley, 1997) Section 4.5.

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