## High speed all optical logic gates based on quantum dot semiconductor optical amplifiers

Optics Express, Vol. 18, Issue 7, pp. 6417-6422 (2010)

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### Abstract

A scheme to realize all-optical Boolean logic functions AND, XOR and NOT using semiconductor optical amplifiers with quantum-dot active layers is studied. nonlinear dynamics including carrier heating and spectral hole-burning are taken into account together with the rate equations scheme. Results show with QD excited state and wetting layer serving as dual-reservoir of carriers, as well as the ultra fast carrier relaxation of the QD device, this scheme is suitable for high speed Boolean logic operations. Logic operation can be carried out up to speed of 250 Gb/s.

© 2010 OSA

## 1. Introduction

8. T. Akiyama, M. Sugawara, and Y. Arakawa, “Quantum-dot semiconductor optical amplifiers,” Proc. IEEE **95**(9), 1757–1766 (2007). [CrossRef]

9. T. Berg and J. Mork, “Saturation and noise properties of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. **40**(11), 1527–1539 (2004). [CrossRef]

10. P. Reithmaier, and G. Eisenstein, “Semiconductor optical amplifiers with nanostructured gain material,” in *Frontiers in Optics*, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FTuN1. http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2008-FTuN1

12. P. Borri, W. Langbein, J. M. Hvam, F. Heirichsdorff, M. Mao, and D. Bimberg, “Spectral hole-burning and carrier-heating dynamics in quantum-dot amplifiers: comparison with bulk amplifiers,” Phys. Stat. Solidi. B **224**(2), 419–423 (2001). [CrossRef]

13. Y. B. Ezra, B. I. Lembrikov, and M. Haridim, “Ultrafast all-optical processor based on quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. **45**(1), 34–41 (2009). [CrossRef]

13. Y. B. Ezra, B. I. Lembrikov, and M. Haridim, “Ultrafast all-optical processor based on quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. **45**(1), 34–41 (2009). [CrossRef]

^{2}(compared to Q factor ~4.8 under the same operating condition as reported in [13

13. Y. B. Ezra, B. I. Lembrikov, and M. Haridim, “Ultrafast all-optical processor based on quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. **45**(1), 34–41 (2009). [CrossRef]

## 2. QD-SOA structures and rate equations

14. K. Mukai, Y. Nakata, H. Shoji, M. Sugawara, K. Ohtsubo, N. Yokoyama, and H. Ishikawa, “Lasing with low threshold current and high output power from columnar-shaped InAs-GaAs quantum dots,” Electron. Lett. **34**(16), 1588 (1998). [CrossRef]

15. T. Akiyama, O. Wada, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, and H. Ishikawa, “Nonlinear processes responsible for non-degenerate four-wave mixing in quantum dot optical amplifiers,” Appl. Phys. Lett. **77**(12), 1753 (2000). [CrossRef]

9. T. Berg and J. Mork, “Saturation and noise properties of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. **40**(11), 1527–1539 (2004). [CrossRef]

14. K. Mukai, Y. Nakata, H. Shoji, M. Sugawara, K. Ohtsubo, N. Yokoyama, and H. Ishikawa, “Lasing with low threshold current and high output power from columnar-shaped InAs-GaAs quantum dots,” Electron. Lett. **34**(16), 1588 (1998). [CrossRef]

16. P. Ridha, L. Li, M. Rossetti, G. Patriarche, and A. Fiore, “Polarization dependence of electroluminescence from closely-stacked and columnar quantum dots,” Opt. Quantum Electron. **40**(2-4), 239–248 (2008). [CrossRef]

17. T. Berg, S. Bischoff, I. Magnusdottir, and J. Mork, “Ultrafast gain recovery and modulation limitations in self-assembled quantum-dot devices,” IEEE Photon. Technol. Lett. **13**(6), 541–543 (2001). [CrossRef]

19. T. Berg and J. Mork, “Quantum dot amplifiers with high output power and low noise,” Appl. Phys. Lett. **82**(18), 3083 (2003). [CrossRef]

20. S. Ma, H. Sun, Z. Chen, and N. K. Dutta, “High speed all-optical PRBS generation based on quantum-dot semiconductor optical amplifiers,” Opt. Express **17**(21), 18469–18477 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-18469. [CrossRef]

*w*,

*h*and

*f*are the occupation probabilities of the wetting layer, the QD excited state and ground state, respectively;

*N*,

_{wm}*N*and

_{esm}*N*are the maximum possible carrier densities of each state;

_{gsm}*Г*is the active layer confinement factor,

_{d}*I*is the injected current,

*V*is the effective volume of the active layer,

*a*is differential gain,

*S*(t) is photon density in the active region.

12. P. Borri, W. Langbein, J. M. Hvam, F. Heirichsdorff, M. Mao, and D. Bimberg, “Spectral hole-burning and carrier-heating dynamics in quantum-dot amplifiers: comparison with bulk amplifiers,” Phys. Stat. Solidi. B **224**(2), 419–423 (2001). [CrossRef]

21. T. Akiyama, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, O. Wada, and H. Ishikawa, “Application of spectral-hole burning in the inhomogeneous broadened gain of self-assembled quantum dots to a multi-wavelength channel nonlinear optical device,” IEEE Photon. Technol. Lett. **12**(10), 1301–1303 (2000). [CrossRef]

*ε*and

_{CH}*ε*are the gain suppression factors of carrier heating and spectral hole burning effects, respectively.

_{SHB}20. S. Ma, H. Sun, Z. Chen, and N. K. Dutta, “High speed all-optical PRBS generation based on quantum-dot semiconductor optical amplifiers,” Opt. Express **17**(21), 18469–18477 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-18469. [CrossRef]

*G*is the gain factor of the device with

_{l}(t)=exp[g(t)l]*l*being the effective length of the active layer,

*α*and

*α*are the linewidth enhancement factors of the waveguide and carrier heating process, respectively.

_{CH}## 3. Operation Principles of all-optical logic gates using QD-SOA-MZI

*λ*is evenly split into two branches at port 3 and guided into the two QD-SOAs respectively. The two branches each interact with data stream A or B in QD-SOA and experience modulated gain and phase due to XGM and XPM processes.

_{3}*λ*and

_{1}*λ*, the interference result (at

_{2}*λ*) can be expressed as [3

_{3}3. 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. **40**(6), 703–710 (2004). [CrossRef]

*P*(

_{cb}*t*) is the time-dependent power of control beam.

*ϕ*and

_{1}*ϕ*are phases experienced by control beam in each arm expressed in (5).

_{1}3. 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. **40**(6), 703–710 (2004). [CrossRef]

*A=B*, then

*G*,

_{1}=G_{2}*ϕ*, output will be 0 according to (6); if

_{1}=ϕ_{2}*A≠B*,

*P*, and its temporal shape similar to the input control beam pulse as a result of fast gain response.

_{out}(t)≠022. H. Dong, H. Sun, Q. Wang, N. K. Dutta, and J. Jaques, “All-optical logic AND operation at 80 Gb/s using semiconductor optical amplifier based on the Mach-Zehnder interferometer,” Microw. Opt. Technol. Lett. **48**(8), 1672–1675 (2006). [CrossRef]

*SNR*, where

_{in}=F∙SNR_{out}*F*is the device’s noise figure. For QD-SOA with short active region (~1mm), the ASE produced are usually much smaller compared to the saturation output power [11], so it’s impact on SOA’s XGM and XPM processes are totally negligible. For this reason, we only added an additional gain factor of

*F*to the control beam’s input noise power through the device amplification.

## 4. Simulation results and output quality evaluation

*1.55μm*:

*τ*=

_{wr}*τ*,

_{esr}=200ps*τ*,

_{gsr}=50ps*τ*,

_{w-e}=3ps*τ*[20

_{e-w}=300ps20. S. Ma, H. Sun, Z. Chen, and N. K. Dutta, “High speed all-optical PRBS generation based on quantum-dot semiconductor optical amplifiers,” Opt. Express **17**(21), 18469–18477 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-18469. [CrossRef]

*τ*,

_{g-e}=10ps*Г*, linewidth enhancement factors

_{d}=10%*α=4*,

*α*[23

_{CH}=0.223. J. M. Vazquez, H. H. Nilsson, J. Zhang, and I. Galbraith, “Linewidth enhancement factor of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. **42**(10), 986–993 (2006). [CrossRef]

24. O. Qasaimeh, “Linewidth enhancement factor of quantum-dot lasers,” Opt. Quantum Electron. **37**(5), 495–507 (2005). [CrossRef]

*n*,

_{w}=5.4×10^{17}cm^{−3}*n*[18], QD areal density is

_{w}:n_{e}:n_{g}≈15:2:1*7.5×10*, saturated output power is

^{10}cm^{−2}*18dBm*at

*1.55μm*wavelength[8

8. T. Akiyama, M. Sugawara, and Y. Arakawa, “Quantum-dot semiconductor optical amplifiers,” Proc. IEEE **95**(9), 1757–1766 (2007). [CrossRef]

*a=8.6×10*[15

^{−15}cm^{2}15. T. Akiyama, O. Wada, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, and H. Ishikawa, “Nonlinear processes responsible for non-degenerate four-wave mixing in quantum dot optical amplifiers,” Appl. Phys. Lett. **77**(12), 1753 (2000). [CrossRef]

*l*=1.0mm, noise figure

*F=7dB*[8

8. T. Akiyama, M. Sugawara, and Y. Arakawa, “Quantum-dot semiconductor optical amplifiers,” Proc. IEEE **95**(9), 1757–1766 (2007). [CrossRef]

*~0.2kA/cm*[12

^{2}12. P. Borri, W. Langbein, J. M. Hvam, F. Heirichsdorff, M. Mao, and D. Bimberg, “Spectral hole-burning and carrier-heating dynamics in quantum-dot amplifiers: comparison with bulk amplifiers,” Phys. Stat. Solidi. B **224**(2), 419–423 (2001). [CrossRef]

*ε*,

_{CH}=0.5×10^{−23}m^{3}*ε*[25

_{SHB}=7.5×10^{−23}m^{3}25. A. Uskov, E. O’Reilly, M. Laemmlin, N. Ledentsov, and D. Bimberg, “On gain saturation in quantum dot semiconductor optical amplifiers,” Opt. Commun. **248**(1-3), 211–219 (2005). [CrossRef]

*τ*has been measured in many experiments, the smallest reported value is ~0.1ps [12

_{e-g}**224**(2), 419–423 (2001). [CrossRef]

*τ*and single pulse energy. Figure 5 shows the output quality’s dependence on injected current density and input pulse width. From the results we find that at low injected current density level (J<1.8 kA/cm

_{e-g}^{2}), the Q factor is lower and increases as current density increases. This can be explained as: with increased current density, more carriers are fed to the wetting layer, each QD energy level can recover faster to initial carrier density level after depletion following pulse injection and amplification. This reduces the pattern effect considerably. For higher current density (J>1.8 kA/cm

^{2}), the increase in J will have a smaller impact on the gain recovery process because of carrier saturation. Also, narrower the input pulse (less energy and hence less carrier depletion) also results in better performance (higher Q).

*τ*. As single pulse energy increases, the carrier density of the active region of the device is depleted more and takes longer time to recover to initial level, thus lead to bigger patterning effect and degrade the quality. The transition lifetime

_{e-g}*τ*determines the speed of gain and phase recovery in the active region, thus Q-factor is higher for shorter transition times at high operation speed.

_{e-g}## 5. Conclusion

*τ*, input pulse width and single pulse energy, are also studied and discussed. Results show that for operation speed as high as 250 Gb/s, the Q factor is typically above 7 and can reach 11 under best conditions. For best output quality, the logic system requires injected current to be sufficiently high (>1.8 kA/cm

_{e-g}^{2}) and single pulse energy not be too big (<1.0 pJ), narrower input pulse width (FWHM ~1.0ps) can also lead to better output quality.

## References and links

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7. | Z. Li, Y. Liu, S. Zhang, H. Ju, H. de Waardt, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “All-optical logic gates using semiconductor optical amplifier assisted by optical filter,” Electron. Lett. |

8. | T. Akiyama, M. Sugawara, and Y. Arakawa, “Quantum-dot semiconductor optical amplifiers,” Proc. IEEE |

9. | T. Berg and J. Mork, “Saturation and noise properties of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. |

10. | P. Reithmaier, and G. Eisenstein, “Semiconductor optical amplifiers with nanostructured gain material,” in |

11. | P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff, M. H. Mao, and D. Bimberg, “Ultrafast gain dynamics in InAs-InGaAs quantum-dot amplifiers,” IEEE J. Quantum Electron. |

12. | P. Borri, W. Langbein, J. M. Hvam, F. Heirichsdorff, M. Mao, and D. Bimberg, “Spectral hole-burning and carrier-heating dynamics in quantum-dot amplifiers: comparison with bulk amplifiers,” Phys. Stat. Solidi. B |

13. | Y. B. Ezra, B. I. Lembrikov, and M. Haridim, “Ultrafast all-optical processor based on quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. |

14. | K. Mukai, Y. Nakata, H. Shoji, M. Sugawara, K. Ohtsubo, N. Yokoyama, and H. Ishikawa, “Lasing with low threshold current and high output power from columnar-shaped InAs-GaAs quantum dots,” Electron. Lett. |

15. | T. Akiyama, O. Wada, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, and H. Ishikawa, “Nonlinear processes responsible for non-degenerate four-wave mixing in quantum dot optical amplifiers,” Appl. Phys. Lett. |

16. | P. Ridha, L. Li, M. Rossetti, G. Patriarche, and A. Fiore, “Polarization dependence of electroluminescence from closely-stacked and columnar quantum dots,” Opt. Quantum Electron. |

17. | T. Berg, S. Bischoff, I. Magnusdottir, and J. Mork, “Ultrafast gain recovery and modulation limitations in self-assembled quantum-dot devices,” IEEE Photon. Technol. Lett. |

18. | J. Kim and S. Chuang, “Small-signal cross-gain modulation of quantum-dot semiconductor optical amplifiers,” IEEE J. Quantum Electron. |

19. | T. Berg and J. Mork, “Quantum dot amplifiers with high output power and low noise,” Appl. Phys. Lett. |

20. | S. Ma, H. Sun, Z. Chen, and N. K. Dutta, “High speed all-optical PRBS generation based on quantum-dot semiconductor optical amplifiers,” Opt. Express |

21. | T. Akiyama, H. Kuwatsuka, T. Simoyama, Y. Nakata, K. Mukai, M. Sugawara, O. Wada, and H. Ishikawa, “Application of spectral-hole burning in the inhomogeneous broadened gain of self-assembled quantum dots to a multi-wavelength channel nonlinear optical device,” IEEE Photon. Technol. Lett. |

22. | H. Dong, H. Sun, Q. Wang, N. K. Dutta, and J. Jaques, “All-optical logic AND operation at 80 Gb/s using semiconductor optical amplifier based on the Mach-Zehnder interferometer,” Microw. Opt. Technol. Lett. |

23. | J. M. Vazquez, H. H. Nilsson, J. Zhang, and I. Galbraith, “Linewidth enhancement factor of quantum-dot optical amplifiers,” IEEE J. Quantum Electron. |

24. | O. Qasaimeh, “Linewidth enhancement factor of quantum-dot lasers,” Opt. Quantum Electron. |

25. | A. Uskov, E. O’Reilly, M. Laemmlin, N. Ledentsov, and D. Bimberg, “On gain saturation in quantum dot semiconductor optical amplifiers,” Opt. Commun. |

**OCIS Codes**

(230.5590) Optical devices : Quantum-well, -wire and -dot devices

(230.3750) Optical devices : Optical logic devices

**ToC Category:**

Optical Devices

**History**

Original Manuscript: April 22, 2009

Revised Manuscript: December 4, 2009

Manuscript Accepted: January 5, 2010

Published: March 15, 2010

**Citation**

, "High speed all optical logic gates based on quantum dot semiconductor optical amplifiers," Opt. Express **18**, 6417-6422 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-6417

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