## Time-domain models for the performance simulation of semiconductor optical amplifiers

Optics Express, Vol. 14, Issue 7, pp. 2956-2968 (2006)

http://dx.doi.org/10.1364/OE.14.002956

Acrobat PDF (1970 KB)

### Abstract

In this paper, we have implemented and compared two complementary time-domain models that have been widely used for the simulation of SOAs. One of the key differences between them lies in their treatment of the material (gain and refractive index) dispersion. One model named as a spectrum slicing model (SSM) is desirable for the simulation of broadband behaviours of SOAs, but not for the nonlinear effect such as the intermodulation distortion, since the gain dispersion is considered by slicing the entire spontaneous emission spectrum into many stripes. The other model based on effective Bloch equations (EBE’s) is capable of dealing with the SOA nonlinear effects with the material dispersion incorporated explicitly through the susceptibility, but can’t capture the broadband behaviours. Both of them, however, can readily handle the SOA characteristics such as the fibre-to-fibre gain, noise, and crosstalk. Through a direct comparison between them, we have shown that they are in generally good agreement. A discussion on detailed implementations and each model’s salient features is also presented.

© 2006 Optical Society of America

## 1. Introduction

1. T. J. Menne, “Analysis of the uniform rate equation model of laser dynamics,” IEEE J. Quantum Electron. **2**, 38–44 (1966). [CrossRef]

2. C. Tombling, T. Saitoh, and T. Mukai, “Performance predictions for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. **30**, 2491–2499 (1994). [CrossRef]

3. J. Piprek, S. BjÖrlin, and J. E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. **37**, 127–134 (2001). [CrossRef]

4. W. Li, W.-P. Huang, X. Li, and J. Hong, “Multiwavelength gain-coupled DFB laser cascade: design modeling and simulation,” IEEE J. Quantum Electron. **36**, 1110–1116 (2000). [CrossRef]

5. L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. **30**, 1389–1395 (1994). [CrossRef]

7. E. Gehrig, O. Hess, and R. Wallenstein, “Modeling of the performance of high-power diode amplifier systems with an optothermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. **35**, 320–331 (1999). [CrossRef]

8. M. Kolesik and J. V. Moloney, “A spatial digital filter method for broadband simulation of semiconductor lasers,” IEEE J. Quantum Electron. **37**, 936–944 (2001). [CrossRef]

9. G. P. Agrawal, “Effect of gain dispersion on ultrashort pulse amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. **27**, 1843–1849 (1991). [CrossRef]

14. A. Mecozzi and J. Mork, “Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers,” IEEE J. Sel. Top. Quantum Electron. **3**, 1190–1207 (1997). [CrossRef]

15. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. **33**, 1543–1550 (1997). [CrossRef]

16. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principle fully space-time resolved model of a semiconductor laser,” Quantum Semiclassic. Opt. **9**, 681–691 (1997). [CrossRef]

15. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. **33**, 1543–1550 (1997). [CrossRef]

18. M. Bahl, H. Rao, N. C. Panoiu, and R. M. Osgood, Jr, “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. **29**, 1689–1691 (2004). [CrossRef] [PubMed]

19. M. A. Summerfield and R. S. Tucker, “Frequency-domain model of multiwave mixing in bulk semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. **5**, 839–850 (1999). [CrossRef]

21. M. J. Connelly, “Wideband dynamic numerical model of a tapered buried ridge stripe semiconductor optical amplifier gate,” IEE Proc.: Circuits Devices Syst. **149**, 173–178 (2002). [CrossRef]

22. J. W. Park, X. Li, and W. P. Huang, “Comparative study on mixed frequency-time-domain models of semiconductor laser optical amplifiers,” IEE Proc.: Optoelectron. **152**, 151–159 (2005). [CrossRef]

7. E. Gehrig, O. Hess, and R. Wallenstein, “Modeling of the performance of high-power diode amplifier systems with an optothermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. **35**, 320–331 (1999). [CrossRef]

22. J. W. Park, X. Li, and W. P. Huang, “Comparative study on mixed frequency-time-domain models of semiconductor laser optical amplifiers,” IEE Proc.: Optoelectron. **152**, 151–159 (2005). [CrossRef]

22. J. W. Park, X. Li, and W. P. Huang, “Comparative study on mixed frequency-time-domain models of semiconductor laser optical amplifiers,” IEE Proc.: Optoelectron. **152**, 151–159 (2005). [CrossRef]

## 2. Models

### 2.1 Effective Bloch equations (EBE’s)

*ε*

_{o,r}are the permittivity in free space and the average relative permittivity of the optical waveguide, respectively.

*ν*

_{g}is the group velocity,

*α*

_{s}is the modal loss, Γ is the confinement factor,

*β*is the propagation constant, and

*E*

_{(f,r)}are the forward and backward traveling optical waves, respectively. The material dispersion is considered through the frequency-domain susceptibility

*χ*given as [15

15. C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. **33**, 1543–1550 (1997). [CrossRef]

16. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principle fully space-time resolved model of a semiconductor laser,” Quantum Semiclassic. Opt. **9**, 681–691 (1997). [CrossRef]

**152**, 151–159 (2005). [CrossRef]

*q*defined as the magnitude of the electron charge,

*h*the Planck constant,

*μ*¯ the refractive index of the medium, and

*m*

_{0}the free-electron mass.

*M*

_{if}represents the momentum matrix element that links the transition between the initial and final states. The variables

*ρ*

_{c}and

*ρ*

_{ν}are the densities of states per unit volume per unit energy for the conduction and valence bands, respectively.

*f*

_{c}and

*f*

_{ν}are the Fermi factors for electrons and holes, respectively. The carrier-induced refractive index change

*δ*

*n*is computed by [24

24. C. H. Henry, R. A. Logan, and K. A. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. **52**, 4457–4461 (1981). [CrossRef]

*P*indicates taking the principal value integral.

**33**, 1543–1550 (1997). [CrossRef]

16. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principle fully space-time resolved model of a semiconductor laser,” Quantum Semiclassic. Opt. **9**, 681–691 (1997). [CrossRef]

*χ*

_{o}denotes the frequency-independent (background) susceptibility,

*δn*

_{0}the frequency-independent (background) carrier-induced index change,

*g*

_{o}the frequency-independent (background) material gain,

*ω*

_{o}the reference angular frequency, and

*ω*

_{p}the material gain peak position. The mapping is realized by searching for the best fitting between Eq. (2) and Eq. (5a) with

*A*

_{i},

*δ*

_{i}, and Γ

_{i}taken as the carrier-dependent Lorentzian fitting parameters. Only one Lorentzian oscillator (

*T*=1) is enough to approximate the material dispersion of SOAs [15

**33**, 1543–1550 (1997). [CrossRef]

**9**, 681–691 (1997). [CrossRef]

**33**, 1543–1550 (1997). [CrossRef]

**9**, 681–691 (1997). [CrossRef]

*i*=1, 2,… ,

*T*. It is noted that in obtaining Eq. (6) by taking the Fourier transformation of Eq. (5), those Lorentzian fitting parameters are assumed to be independent of time. Such an assumption may be valid as long as the time marching step is so small that the carrier density varies much more slowly compared to the inverse gain bandwidth [15

**33**, 1543–1550 (1997). [CrossRef]

**9**, 681–691 (1997). [CrossRef]

**152**, 151–159 (2005). [CrossRef]

*d*

_{z}indicates the length of a subsection introduced by the spatial discretization of the active region along the wave propagation direction and

*γ*the coupling coefficient of the spontaneous emission rate

*R*

_{sp}into the waveguide. δ() denotes the Dirac-function.

*η*denotes the current injection efficiency,

*A*the non-radiative (Shockley-Reed-Hall and surface) recombination coefficient,

*B*the bimolecular recombination coefficient, and

*C*the Auger recombination coefficient.

### 2.2 Spectrum slicing model (SSM)

*N*

_{d}narrow segments with equal width that cover the whole ASE spectrum (1.2μm~1.65μm). Since it is sliced in the frequency domain, the model is also named as the mixed frequency-time-domain traveling-wave model [22

**152**, 151–159 (2005). [CrossRef]

*k*=1, 2,… ,

*N*

_{d}.

**152**, 151–159 (2005). [CrossRef]

*ν*

_{L}is the subsection width (measured in frequency) sliced in the ASE spectrum. It is shown in Ref. [22

**152**, 151–159 (2005). [CrossRef]

*ν*

_{L}is a tradeoff between the accuracy and computation efficiency. However, the total noise contribution to the gain saturation won’t be affected by the selection of Δ

*ν*

_{L}.

## 3. Numerical implementation

*M*(=61) subsections. The longitudinal variation of carrier density and optical intensity is thus taken into account. The structural and material parameter values used in the simulations are summarized in Table 1.

**152**, 151–159 (2005). [CrossRef]

*ν*

_{L}for low input signal powers. In fact, the device gain is overestimated for larger Δ

*ν*

_{L}(coarse discretization), as more spontaneous emission noise is coupled into the low input signal power. Therefore, one needs an adaptive discretization scheme; namely, Δ

_{νL}is kept reducing for low input signal powers until a certain convergence is reached.

**33**, 1543–1550 (1997). [CrossRef]

**9**, 681–691 (1997). [CrossRef]

*dt*) is infinitely small. To minimize and possibly ignore such a numerical error, therefore, one has to use a very small time step. As demonstrated in Fig. 1, showing the dependence of the numerical result on a time step, the output power converges into some value as

*dt*decreases and thus the numerical error may become negligibly small as long as

*dt*is small enough (<0.13ps).

*ν*

_{L}and

*dt*, respectively.

## 4. Results and discussions

### 4.1 Unique feature of SSM: broadband behaviours

^{-1}. The ASE noise is shown to be considerably suppressed by the internal lasing mode. In addition, the ASE peak is red-shifted. In typical GC-SOAs, the lasing mode is normally positioned far away (more than 20nm blue-shift) from the signal band (near gain peak). In such a case, it is not feasible to capture the interaction between the lasing mode and signals with the EBE, unless additional Bloch equations are introduced at the lasing wavelength.

### 4.2 Salient features of EBE: pulse propagation and intermodulation distortion

*τ*

_{0}). It is evident that pulses with a width shorter than the carrier lifetime (≈1/

*A*) are distorted the most [23].

26. G. P. Agrawal, “*Fiber-optic communication systems*,” 3rd edition, (Wiley-Interscience, 2002). [CrossRef]

13. T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and inter-modulation distortion,” J. Lightwave Technol. **10**, 1056–1065 (1992). [CrossRef]

### 4.3 Comparison: gain and noise figure

### 4.4 Comparison: crosstalk

13. T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and inter-modulation distortion,” J. Lightwave Technol. **10**, 1056–1065 (1992). [CrossRef]

27. J. Sun, G. Morthier, and R. Baets, “Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. **3**, 1162–1167 (1997). [CrossRef]

28. H. E. Lassen, P. B. Hansen, and K. E. Stubkjaer, “Crosstalk in 1.5μm InGaAsP optical amplifiers,” J. Lightwave Technol. **6**, 1559–1565 (1988). [CrossRef]

27. J. Sun, G. Morthier, and R. Baets, “Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. **3**, 1162–1167 (1997). [CrossRef]

*ε*

_{1}

*S*) [23] where ε

_{1}is the gain compression coefficient and

*S*the total photon density inside the cavity. Shown in Fig. 10(a) is the crosstalk versus the Ch2 input power at 1535.7nm when the Ch1 input power at 1538.9nm is -23dBm and

*I*=140mA. The crosstalk increases with increasing Ch2 input power and reaches saturation at about -5dBm. A small discrepancy between the models may come from the different way of treating the material dispersion or slightly different way of calculating the crosstalk. The calculation of the crosstalk with the SSM is done directly from the time-domain output envelope, while its calculation with the EBE requires one more step, an inverse Fourier transform, to get the envelope. Another finding is that, although the effect of the nonlinear gain is not so remarkable, it indeed causes more crosstalk. Figure 10(b) is the crosstalk as a function of the detuning frequency (channel spacing) when the input power at each channel is -10dBm. Both models show that the crosstalk keeps unchanged as the detuning frequency increases, indicating that the channel crosstalk is attributed to the cross-gain saturation, a nonlinear phenomenon that doesn’t depend on the beating frequency (i.e., the channel spacing) explicitly [26

26. G. P. Agrawal, “*Fiber-optic communication systems*,” 3rd edition, (Wiley-Interscience, 2002). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | T. J. Menne, “Analysis of the uniform rate equation model of laser dynamics,” IEEE J. Quantum Electron. |

2. | C. Tombling, T. Saitoh, and T. Mukai, “Performance predictions for vertical-cavity semiconductor laser amplifiers,” IEEE J. Quantum Electron. |

3. | J. Piprek, S. BjÖrlin, and J. E. Bowers, “Design and analysis of vertical-cavity semiconductor optical amplifiers,” IEEE J. Quantum Electron. |

4. | W. Li, W.-P. Huang, X. Li, and J. Hong, “Multiwavelength gain-coupled DFB laser cascade: design modeling and simulation,” IEEE J. Quantum Electron. |

5. | L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. |

6. | A. J. Lowery, “New dynamic semiconductor laser model based on the transmission line modeling method,” IEE Proc. J. |

7. | E. Gehrig, O. Hess, and R. Wallenstein, “Modeling of the performance of high-power diode amplifier systems with an optothermal microscopic spatio-temporal theory,” IEEE J. Quantum Electron. |

8. | M. Kolesik and J. V. Moloney, “A spatial digital filter method for broadband simulation of semiconductor lasers,” IEEE J. Quantum Electron. |

9. | G. P. Agrawal, “Effect of gain dispersion on ultrashort pulse amplification in semiconductor laser amplifiers,” IEEE J. Quantum Electron. |

10. | C. Bowden and G. P. Agrawal, “Maxwell-Bloch formulation for semiconductors: Effects of coherent Coulomb exchange,” Phys. Rev. A |

11. | M. Homar, J. V. Moloney, and M. San Miguel, “Traveling wave model of a multimode Fabry-Perot laser in free running and external cavity configurations,” IEEE J. Quantum Electron. |

12. | G. C. Dente and M. L. Tilton, “Modeling multiple-longitudinal-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. |

13. | T. Durhuus, B. Mikkelsen, and K. E. Stubkjaer, “Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and inter-modulation distortion,” J. Lightwave Technol. |

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

15. | C. Z. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. |

16. | C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, “A first-principle fully space-time resolved model of a semiconductor laser,” Quantum Semiclassic. Opt. |

17. | U. Bandelow, M. Radziunas, J. Sieber, and M. Wolfrum, “Impact of gain dispersion on the Spatio-temperal dynamics of multisection lasers,” IEEE J. Quantum Electron. |

18. | M. Bahl, H. Rao, N. C. Panoiu, and R. M. Osgood, Jr, “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. |

19. | M. A. Summerfield and R. S. Tucker, “Frequency-domain model of multiwave mixing in bulk semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. |

20. | M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron. |

21. | M. J. Connelly, “Wideband dynamic numerical model of a tapered buried ridge stripe semiconductor optical amplifier gate,” IEE Proc.: Circuits Devices Syst. |

22. | J. W. Park, X. Li, and W. P. Huang, “Comparative study on mixed frequency-time-domain models of semiconductor laser optical amplifiers,” IEE Proc.: Optoelectron. |

23. | G. P. Agrawal and N. K. Dutta, “ |

24. | C. H. Henry, R. A. Logan, and K. A. Bertness, “Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers,” J. Appl. Phys. |

25. | W. H. Press, B. P. Flannery, S. A. Teukolssy, and W. T. Vetterling, “ |

26. | G. P. Agrawal, “ |

27. | J. Sun, G. Morthier, and R. Baets, “Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers,” IEEE J. Sel. Top. Quantum Electron. |

28. | H. E. Lassen, P. B. Hansen, and K. E. Stubkjaer, “Crosstalk in 1.5μm InGaAsP optical amplifiers,” J. Lightwave Technol. |

**OCIS Codes**

(250.0250) Optoelectronics : Optoelectronics

(250.5980) Optoelectronics : Semiconductor optical amplifiers

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: January 10, 2006

Revised Manuscript: March 17, 2006

Manuscript Accepted: March 17, 2006

Published: April 3, 2006

**Citation**

Jongwoon Park and Yoichi Kawakami, "Time-domain models for the performance simulation of semiconductor optical amplifiers," Opt. Express **14**, 2956-2968 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2956

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### References

- T. J. Menne, "Analysis of the uniform rate equation model of laser dynamics," IEEE J. Quantum Electron. 2, 38-44 (1966). [CrossRef]
- C. Tombling, T. Saitoh and T. Mukai, "Performance predictions for vertical-cavity semiconductor laser amplifiers," IEEE J. Quantum Electron. 30, 2491-2499 (1994). [CrossRef]
- J. Piprek, S. Björlin and J. E. Bowers, "Design and analysis of vertical-cavity semiconductor optical amplifiers," IEEE J. Quantum Electron. 37, 127-134 (2001). [CrossRef]
- W. Li, W.-P. Huang, X. Li, and J. Hong, "Multiwavelength gain-coupled DFB laser cascade: design modeling and simulation," IEEE J. Quantum Electron. 36, 1110-1116 (2000). [CrossRef]
- L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, "Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model," IEEE J. Quantum Electron. 30, 1389-1395 (1994). [CrossRef]
- A. J. Lowery, "New dynamic semiconductor laser model based on the transmission line modeling method," IEE Proc. J. 134, 281-289 (1987).
- E. Gehrig, O. Hess and R. Wallenstein, "Modeling of the performance of high-power diode amplifier systems with an optothermal microscopic spatio-temporal theory," IEEE J. Quantum Electron. 35, 320-331 (1999). [CrossRef]
- M. Kolesik and J. V. Moloney, "A spatial digital filter method for broadband simulation of semiconductor lasers," IEEE J. Quantum Electron. 37, 936-944 (2001). [CrossRef]
- G. P. Agrawal, "Effect of gain dispersion on ultrashort pulse amplification in semiconductor laser amplifiers," IEEE J. Quantum Electron. 27, 1843-1849 (1991). [CrossRef]
- C. Bowden and G. P. Agrawal, "Maxwell-Bloch formulation for semiconductors: Effects of coherent Coulomb exchange," Phys. Rev. A 51, 4132-4139 (1995). [CrossRef] [PubMed]
- M. Homar, J. V. Moloney and M. San Miguel, "Traveling wave model of a multimode Fabry-Perot laser in free running and external cavity configurations," IEEE J. Quantum Electron. 32, 553-566 (1996). [CrossRef]
- G. C. Dente and M. L. Tilton, "Modeling multiple-longitudinal-mode dynamics in semiconductor lasers," IEEE J. Quantum Electron. 34, 325-335 (1998). [CrossRef]
- T. Durhuus, B. Mikkelsen and K. E. Stubkjaer, "Detailed dynamic model for semiconductor optical amplifiers and their crosstalk and inter-modulation distortion," J. Lightwave Technol. 10, 1056-1065 (1992). [CrossRef]
- A. Mecozzi and J. Mork, "Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers," IEEE J. Sel. Top. Quantum Electron. 3, 1190-1207 (1997). [CrossRef]
- C. Z. Ning, R. A. Indik and J. V. Moloney, "Effective Bloch equations for semiconductor lasers and amplifiers," IEEE J. Quantum Electron. 33, 1543-1550 (1997). [CrossRef]
- C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, "A first-principle fully space-time resolved model of a semiconductor laser," Quantum Semiclassic. Opt. 9, 681-691 (1997). [CrossRef]
- U. Bandelow, M. Radziunas, J. Sieber, and M. Wolfrum, "Impact of gain dispersion on the Spatio-temperal dynamics of multisection lasers," IEEE J. Quantum Electron. 37, 183-188 (2001). [CrossRef]
- M. Bahl, H. Rao, N. C. Panoiu, and R. M. Osgood, Jr, "Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm," Opt. Lett. 29, 1689-1691 (2004). [CrossRef] [PubMed]
- M. A. Summerfield and R. S. Tucker, "Frequency-domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999). [CrossRef]
- M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-1103 (2001). [CrossRef]
- M. J. Connelly, "Wideband dynamic numerical model of a tapered buried ridge stripe semiconductor optical amplifier gate," IEE Proc.: Circuits Devices Syst. 149, 173-178 (2002). [CrossRef]
- J. W. Park, X. Li, and W. P. Huang, "Comparative study on mixed frequency-time-domain models of semiconductor laser optical amplifiers," IEE Proc.: Optoelectron. 152, 151-159 (2005). [CrossRef]
- G. P. Agrawal and N. K. Dutta, "Semiconductor Lasers," (Van Nostrand Reinhold, New York, 1993).
- C. H. Henry, R. A. Logan, and K. A. Bertness, "Spectral dependence of the change in refractive index due to carrier injection in GaAs lasers," J. Appl. Phys. 52, 4457-4461 (1981). [CrossRef]
- W. H. Press, B. P. Flannery, S. A. Teukolssy and W. T. Vetterling, "Numerical Recipes: The art of Scientific Computing," (Cambridge Univ. Press, Cambridge, MA, 1986).
- G. P. Agrawal, "Fiber-optic communication systems," 3rd edition, (Wiley-Interscience, 2002). [CrossRef]
- J. Sun, G. Morthier, and R. Baets, "Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 3, 1162-1167 (1997). [CrossRef]
- H. E. Lassen, P. B. Hansen, and K. E. Stubkjaer, "Crosstalk in 1.5μm InGaAsP optical amplifiers," J. Lightwave Technol. 6, 1559-1565 (1988). [CrossRef]

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