In this paper, the effects of homogeneous and inhomogeneous broadenings on the response of quantum-dot semiconductor optical amplifier (QD-SOAs) are investigated. For the first time, the state space model is used to simulate static and dynamic characteristics of the QD-SOA. It is found that with decreasing the homogeneous and inhomogeneous broadenings, the saturation power of the QD-SOA decreases and the optical gain and the ultrafast gain compression increase. Simulation results show that with decreasing the homogeneous broadening from 20 to 1 meV, the gain compression increases from 40% to 90%, the unsaturated optical gain becomes approximately tripled, and the saturation power becomes two times less. Also, simulations demonstrate that with decreasing the inhomogeneous broadening from 50 to 25 meV, the gain compression increases from less than 50% to more than 90%, the unsaturated optical gain becomes approximately 10-fold, and the saturation power becomes three times less. In addition, it is found that the homogeneous and inhomogeneous linewidths should be small for nonlinear applications. The homogeneous and inhomogeneous broadenings need to be large enough for linear applications.

Hussein TALEB,Kambiz ABEDI. Homogeneous and inhomogeneous broadening effects on static and dynamic responses of quantum-dot semiconductor optical amplifiers[J]. Front Optoelec,
2012, 5(4): 445-456.

Fig.1 Energy band diagram of QD group. Relative energies of 91-th QD group are indicated in the figure. QW: quantum well, ES: excited state, GS: ground state

symbol

value

symbol

value

Lca

2 mm

Ep

22.2 /eV

W

4 μm

Γihc(v)

40(10) meV

A

8 × 10^{-5} cm^{2}

Γih

50 meV

LH

5 nm

Γh

10 meV

lD

10

Γ

0.025

αi

5 cm^{-1}

τ^egc(v)

0.5(0.075) ps

T

300 K

τ^ugc(v)

0.33(0.022) ps

nD

5 × 10^{10} cm^{-2}

τ^uec(v)

0.66(0.043) ps

Dgc,v

2

τ^wuc(v)

1.8(0.078) ps

Dec,v

4

τ^dr

1 ns

Duc(v)

10(20)

τ^wrc(v)

0.14(0.28) ns

Dwc(v)

100(200)

τ^urc(v)

0.71(1.42) ns

|Menv|2

0.88

rc(v)

0.8(0.2)

?|e^.pcv|2?

3.37 × 10^{-30} kg·eV

2M+1

181

fD

6

nr

3.51

ND

10^{23} m^{-3}

Vd

4 × 10^{-10} cm^{3}

Tab.1 Parameters used in numerical simulations

Fig.2 Temperature dependence of homogeneous linewidth

Fig.3 (a) Homogenous broadening function calculated for different homogeneous linewidths. The product of homogeneous and inhomogeneous functions () for different homogeneous linewidths, (b) , (c) and (d) . The inhomogeneous linewidth is

Fig.4 Absorption/gain spectra of QD-SOA under different values of homogeneous linewidth: (a) G = 1 meV, (b) G = 5 meV, and (c) G = 20 meV. (Injection current density: = 12 kA/cm, inhomogeneous broadening : G = 50 meV). At = 100 ps, a CW optical signal corresponding to the GS transition is injected into the active region. Simulations are terminated at = 200 ps, and the time interval between consecutive plots in the time axes is 6 ps

Fig.5 Optical gain response of QD-SOA under different values of homogeneous linewidth: (a) G = 1 meV; and (b) G = 20 meV; (c) percentage of ultra-fast gain compression as function of current density for three different homogeneous linewidths. (Inhomogeneous linewidth:G = 50 meV; pulse is injected at = 3 ps; simulations are terminated at = 15 ps)

Fig.6 Gain saturation curves of QD-SOA under different values of homogeneous linewidth (G = 1, 5, 10, 20 meV) and different current densities ( = 2, 6 kA/cm). Iinhomogeneous linewidth is G = 50 meV in all curves

Fig.7 (a) Homogenous and inhomogeneous broadening functions. The product of homogeneous and inhomogeneous functions () for different inhomogeneous linewidths, (b); (c); and (d). Homogeneous linewidth is in all figures

Fig.8 Absorption/gain spectra of QD-SOA under three different inhomogeneous linewidths (a) G = 25 meV; (b) G = 50 meV; (c) G = 75 meV. Pump current density is = 12 kA/cm, and homogeneous broadening is G = 10 meV. At = 100 ps, CW optical signal with photons energy corresponding to GS transition is injected into QD-SOA. Simulations are terminated at = 200 ps, and the time interval between consecutive plots in the time axis is 6 ps

Fig.9 Gain response of QD-SOA under different values of inhomogeneous linewidth and current density, (a) G = 25 meV; and (b) G = 75 meV; (c) percentage of ultra-fast gain compression as function of current density for different inhomogeneous linewidths. Homogeneous linewidth is G = 10 meV. Optical pulse is injected at = 3 ps and simulations are terminated at = 15 ps

Fig.10 Gain saturation curves of QD-SOA under different values of inhomogeneous broadening (G = 25, 50, 75 meV) and different current densities ( = 2, 6, and 12 kA/cm). In all curves, the homogeneous linewidth is G = 10 meV

1

Borri P, Langbein W, Hvam J M, Heinrichsdorff F, Mao H M, Bimberg D. Spectral hole-burning and carrier-heating dynamics in InGaAs quantum-dot amplifiers. IEEE Journal on Selected Topics in Quantum Electronics , 2000, 6(3): 544–551 doi: 10.1109/2944.865110

2

Sugawara M, Ebe H, Hatori N, Ishida M, Arakawa Y, Akiyama T, Otsubo K, Nakata Y. Theory of optical signal amplification and processing by quantum-dot semiconductor optical amplifiers. Physical Review B: Condensed Matter and Materials Physics , 2004, 69(23): 235332 doi: 10.1103/PhysRevB.69.235332

3

van der Poel M, Gehrig E, Hess O, Birkedal D, Hvam J M. Ultrafast gain dynamics in quantum-dot amplifiers: theoretical analysis and experimental investigations. IEEE Journal of Quantum Electronics , 2005, 41(9): 1115–1123 doi: 10.1109/JQE.2005.852795

4

Kim J, Laemmlin M, Meuer C, Bimberg D, Eisenstein G. Theoretical and experimental study of high-speed small-signal cross-gain modulation of quantum-dot semiconductor optical amplifiers. IEEE Journal of Quantum Electronics , 2009, 45(3): 240–248 doi: 10.1109/JQE.2008.2010881

5

Bilenca A, Eisenstein G. On the noise properties of linear and nonlinear quantum-dot semiconductor optical amplifiers: the impact of inhomogeneously broadened gain and fast carrier dynamics. IEEE Journal of Quantum Electronics , 2004, 40(6): 690–702 doi: 10.1109/JQE.2004.828260

6

Berg T W, M?rk J. Saturation and noise properties of quantum-dot optical amplifiers. IEEE Journal of Quantum Electronics , 2004, 40(11): 1527–1539 doi: 10.1109/JQE.2004.835114

7

Akiyama T, Ekawa M, Sugawara M, Kawaguchi K, Sudo H, Kuramata A, Ebe H, Arakawa Y. An ultrawide-band semiconductor optical amplifier having an extremely high penalty-free output power of 23 dBm achieved with quantum dots. IEEE Photonics Technology Letters , 2005, 17(8): 1614–1616 doi: 10.1109/LPT.2005.851884

8

Meuer C, Schmeckebier H, Fiol G, Arsenijevi’c D, Kim J, Eisenstein G, Bimberg D. Cross-gain modulation and four-wave mixing for wavelength conversion in undoped and p-doped 1.3-m quantum dot semiconductor optical amplifiers. IEEE Journal of Photonics , 2010, 2(2): 141–151 doi: 10.1109/JPHOT.2010.2044568

9

Sugawara M, Hatori N, Ishida M, Ebe H, Arakawa Y, Akiyama T, Otsubo K, Yamamoto Y, Nakata Y. Recent progress in self-assembled quantum-dot optical devices for optical telecommunication: temperature-insensitive 10 Gb·s^{-1} directly modulated lasers and 40 Gb·s^{-1} signal-regenerative amplifiers. Journal of Physics D: Applied Physics , 2005, 38(13): 2126–2134 doi: 10.1088/0022-3727/38/13/008

10

Rostami A, Nejad H B A, Qartavol R M, Saghai H R. Tb/s optical logic gates based on quantum-dot semiconductor optical amplifiers. IEEE Journal of Quantum Electronics , 2010, 46(3): 354–360 doi: 10.1109/JQE.2009.2033253

11

Meuer C, Kim J, Laemmlin M, Liebich S, Eisenstein G, Bonk R, Vallaitis T, Leuthold J, Kovsh A, Krestnikov I, Bimberg D. High-speed small-signal cross-gain modulation in quantum-dot semiconductor optical amplifiers at 1.3 μm. IEEE Journal on Selected Topics in Quantum Electronics , 2009, 15(3): 749–756 doi: 10.1109/JSTQE.2009.2012395

12

Kim J, Laemmlin M, Meuer C, Bimberg D, Eisenstein G. Effect of inhomogeneous broadening on gain and phase recovery of quantum-dot semiconductor optical amplifiers. IEEE Journal of Quantum Electronics , 2010, 46(11): 1670–1680

13

Kuntze S B, Zilkie A J, Pavel L, Aitchison J S. Nonlinear state-space model of semiconductor optical amplifiers with gain compression for system design and analysis. Journal of Lightwave Technology , 2008, 26(14): 2274–2281 doi: 10.1109/JLT.2008.922212

14

Taleb H, Abedi K, Golmohammadi S. Operation of quantum-dot semiconductor optical amplifiers under nonuniform current injection. Applied Optics , 2011, 50(5): 608–617 doi: 10.1364/AO.50.000608 pmid:21343980

15

Meuer C, Kim J, Laemmlin M, Liebich S, Capua A, Eisenstein G, Kovsh A R, Mikhrin S S, Krestnikov I L, Bimberg D. Static gain saturation in quantum dot semiconductor optical amplifiers. Optics Express , 2008, 16(11): 8269–8279 doi: 10.1364/OE.16.008269 pmid:18545539

16

Xiao J L, Yang Y D, Huang Y Z. Investigation of gain recovery for InAs/GaAs quantum dot semiconductor optical amplifiers by rate equation simulation. Optical and Quantum Electronics , 2009, 41(8): 613–626 doi: 10.1007/s11082-010-9368-0

17

Vasileiadis M, Alexandropoulos D, Adams M J, Simos H, Syvridis D. Potential of InGaAs/GaAs quantum dots for applications in vertical cavity semiconductor optical amplifiers. IEEE Journal on Selected Topics in Quantum Electronics , 2008, 14(4): 1180–1187 doi: 10.1109/JSTQE.2007.915517

18

Blood P. Gain and recombination in quantum dot lasers. IEEE Journal on Selected Topics in Quantum Electronics , 2009, 15(3): 808–818 doi: 10.1109/JSTQE.2008.2011998

19

Kim J, Laemmlin M, Meuer C, Bimberg D, Eisenstein G. Static gain saturation model of quantum-dot semiconductor optical amplifiers. IEEE Journal of Quantum Electronics , 2008, 44(7): 658–666 doi: 10.1109/JQE.2008.922325

20

Ozgur G, Demir A, Deppe D G. Threshold temperature dependence of a quantum-dot laser diode with and without p-doping. IEEE Journal of Quantum Electronics , 2009, 45(10): 1265–1272 doi: 10.1109/JQE.2009.2025660

21

Wong H C, Ren G B, Rorison J M. Mode amplification in inhomogeneous QD semiconductor optical amplifiers. Optical and Quantum Electronics , 2006, 38(4–6): 395–409 doi: 10.1007/s11082-006-0039-0

22

Qasaimeh O. Optical gain and saturation characteristics of quantum-dot semiconductor optical amplifiers. IEEE Journal of Quantum Electronics , 2003, 39(6): 793–798 doi: 10.1109/JQE.2003.810770