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

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  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]
  6. A. J. Lowery, "New dynamic semiconductor laser model based on the transmission line modeling method," IEE Proc. J. 134, 281-289 (1987).
  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).
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  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).
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  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).
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  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]

2005

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]

2004

2002

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]

2001

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-1103 (2001).
[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]

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]

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]

2000

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]

1999

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. 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]

1998

G. C. Dente and M. L. Tilton, "Modeling multiple-longitudinal-mode dynamics in semiconductor lasers," IEEE J. Quantum Electron. 34, 325-335 (1998).
[CrossRef]

1997

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]

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]

1996

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]

1995

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]

1994

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]

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

1992

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]

1991

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

1988

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]

1987

A. J. Lowery, "New dynamic semiconductor laser model based on the transmission line modeling method," IEE Proc. J. 134, 281-289 (1987).

1981

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]

1966

T. J. Menne, "Analysis of the uniform rate equation model of laser dynamics," IEEE J. Quantum Electron. 2, 38-44 (1966).
[CrossRef]

Agrawal, G. P.

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]

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

Baets, R.

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]

Bahl, M.

Bandelow, U.

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]

Bertness, K. A.

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]

Björlin, S.

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]

Bowden, C.

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]

Bowers, J. E.

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]

Carroll, J. E.

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]

Connelly, M. J.

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]

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-1103 (2001).
[CrossRef]

Dente, G. C.

G. C. Dente and M. L. Tilton, "Modeling multiple-longitudinal-mode dynamics in semiconductor lasers," IEEE J. Quantum Electron. 34, 325-335 (1998).
[CrossRef]

Durhuus, T.

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]

Egan, A.

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]

Gehrig, E.

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]

Hansen, P. B.

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]

Henry, C. H.

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]

Hess, O.

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]

Homar, M.

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]

Hong, J.

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]

Huang, W. P.

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]

Huang, W.-P.

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]

Indik, R. A.

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]

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]

Kolesik, M.

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]

Lassen, H. E.

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]

Li, W.

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]

Li, X.

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]

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]

Logan, R. A.

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]

Lowery, A. J.

A. J. Lowery, "New dynamic semiconductor laser model based on the transmission line modeling method," IEE Proc. J. 134, 281-289 (1987).

Marcenac, D. D.

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]

Mecozzi, A.

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]

Menne, T. J.

T. J. Menne, "Analysis of the uniform rate equation model of laser dynamics," IEEE J. Quantum Electron. 2, 38-44 (1966).
[CrossRef]

Mikkelsen, B.

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]

Moloney, J. V.

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]

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]

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]

Mork, J.

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]

Morthier, G.

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]

Mukai, T.

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

Ning, C. Z.

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]

Nowell, M.

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]

Osgood, R. M.

Panoiu, N. C.

Park, J. W.

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]

Piprek, J.

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]

Radziunas, M.

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]

Rao, H.

Saitoh, T.

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

San Miguel, M.

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]

Sieber, J.

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]

Stubkjaer, K. E.

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]

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]

Summerfield, M. A.

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]

Sun, J.

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]

Tilton, M. L.

G. C. Dente and M. L. Tilton, "Modeling multiple-longitudinal-mode dynamics in semiconductor lasers," IEEE J. Quantum Electron. 34, 325-335 (1998).
[CrossRef]

Tombling, C.

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

Tucker, R. S.

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]

Wallenstein, R.

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]

Wolfrum, M.

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]

Yu, S. F.

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]

Zhang, L. M.

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]

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Figures (10)

Fig. 1.
Fig. 1.

Average output power as a function of the time step dt at I=140mA when the input Gaussian-pulse power with 10ns 1/e-width at 1538.9nm is -17dBm and L=700μm.

Fig. 2.
Fig. 2.

Waveform of the input envelope for the channel spacing of (a) 400MHz and (b) 2GHz when the input signal envelope consists of identical Gaussian pulses with 10ns 1/e-width in two different channels; Ch1 at 1538.9nm (reference channel) and Ch2 at 1538.89684nm.

Fig. 3.
Fig. 3.

Average output envelope power as a function of the channel spacing at I=140mA when the average input envelope power [Fig. 2(a)] is -13.63dBm and L=700μm.

Fig. 4.
Fig. 4.

ASE spectra of SOA and GC-SOA with a lasing mode at 1514nm, both simulated with the SSM at I=140mA when the resolution bandwidth is 51GHz and L=700μm. The grating coupling coefficient is 6cm-1 and the length of the DBR sections is 200μm under no current injection.

Fig. 5.
Fig. 5.

Gaussian-pulse propagation through the SOA for different pulse width (τ0 ) when the input power is 0dBm. Gaussian pulse is excited at 1538.9nm when I=160mA and L=700μm.

Fig. 6.
Fig. 6.

Input and output signal spectra of the SOA under the bias current of 140mA when the input signal envelope consists of identical Gaussian pulses with 4.5ns 1/e-width and peak power of -20dBm in two different channels (Ch1: 1538.9nm and Ch2: 1538.89684nm, channel spacing =400MHz).

Fig. 7.
Fig. 7.

(a) Input and output signal spectra of the SOA under the bias current of 140mA when the input signal envelope consists of identical Gaussian pulses with 10ns 1/e-width and peak power of -15dBm in two different channels (Ch1: 1538.9nm and Ch2: 1538.89684nm) and (b) relative intermodulation distortion (IMD) as a function of the Ch2 input power when the Ch1 input power is -20dBm.

Fig. 8.
Fig. 8.

Fibre-to-fibre gain and noise figure as a function of the input signal power at 1538.9nm under the bias current of 140mA for L=700μm.

Fig. 9.
Fig. 9.

Output signal spectra of the SOA for different input powers of each channel under the bias current of 140mA when the channel spacing is 400MHz.

Fig. 10.
Fig. 10.

(a) Crosstalk versus the Ch2 input power at 1535.7nm when the Ch1 input power at 1538.9nm is -23dBm and I=140mA and (b) crosstalk as a function of the detuning frequency when the input power of each channel is -10dBm. The gain compression coefficient (ε 1) is 3×10-18cm3.

Tables (1)

Tables Icon

Table 1. Material and structural parameter values

Equations (16)

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( 1 ν g t ± z ) E ( f , r ) ( z , t ) = α s 2 E ( f , r ) ( z , t ) + j Γ β 2 ε o ε r [ P o ( f , r ) ( z , t ) + i P i ( f , r ) ( z , t ) ]
χ ( N , ω ) 2 ε r 1 / 2 δn ( N , ω ) j 1 β g ( N , ω )
g ( E ) = q 2 h 2 ε 0 m 0 2 c μ ̅ E ρ c ( E′ ) ρ ν ( E′ E ) M if 2 [ f c ( E′ ) + f ν ( E′ E ) 1 ] dE′
δn ( E ) = 1 2 π 2 P 0 1 E + E ( Δ g ( E′ ) Δ g ( E ) E′ E ) dE′ Δ g ( E ) 2 π 2 P 0 dE E 2 E 2
χ ( N , ω ) χ o ( N ) + i = 1 T A i ( N ) ω + ω o ω p ( N ) δ i ( N ) + j Γ i ( N )
χ o ( N ) = 2 ε r 1 / 2 δn o ( N ) j 1 β g o ( N )
P o ( f , r ) ( z , t ) = ε o ε r χ o ( N ) [ E ( f , r ) ( z , t ) + s ˜ ( f , r ) ( z , t ) ]
t P i ( f , r ) ( z , t ) = { Γ i ( N ) + j [ ω o ω p δ i ( N ) ] } P i ( f , r ) ( z , t ) j ε o ε r A i ( N ) E ( f , r ) ( z , t )
s ˜ ( f , , r ) ( z , t , λ o ) s ˜ * ( f , r ) ( z , t , λ o , ) = γ R sp ( z , t , λ o ) d z ν g δ ( z z′ ) δ ( t t′ ) δ ( λ o λ o′ )
N ( z , t ) t = η J qd [ A + BN ( z , t ) + C N 2 ( z , t ) ] N ( z , t )
+ j 4 ħ ω o ε o ε r [ P o f ( z , t ) + i = 1 T P i f ( z , t ) ] * E f ( z , t ) [ P o f ( z , t ) + i = 1 T P i f ( z , t ) ] E f * z t + [ P o r ( z , t ) + i = 1 T P i r ( z , t ) ] * E r ( z , t ) [ P o r ( z , t ) + i = 1 T P i r ( z , t ) ] E r * z t
1 ν g E ( f , r ) ( z , t , λ k ) t ± E ( f , r ) ( z , t , λ k ) z
= { j ( β ( λ k ) + 1 2 Γ α m g ( z , t , λ k ) ) + 1 2 ( Γ g ( z , t , λ k ) α s ) } E ( f , r ) ( z , t , λ k ) + s ˜ ( f , r ) ( z , t , λ k )
R sp ( E ) = Δ ν L 4 πq μ ̅ E ε 0 m 0 2 c 3 h ρ c ( E′ ) ρ ν ( E′ E ) M if 2 f c ( E′ ) f ν ( E′ E ) dE′
N ( z , t ) t = η J qd [ A + BN ( z , t ) + C N 2 ( z , t ) ] N ( z , t )
k = 1 N d Γ ν g g ( z , t , λ k ) E f ( z , t , λ k ) + E r ( z , t , λ k ) 2 .

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