Bandelow, U

Gehrig, E

Hess, O

Piprek, J

Reschner, DW

Wenzel, H

Wunsche, HJ

Surrey Research Insight

Theory and simulation of ultrafast carrier dynamics and nonlinear pulse propagation in quantum dot semiconductor optical amplifiers

Reschner, DW

Gehrig, E

Hess, O

Wunsche, HJ

Piprek, J

Bandelow, U

Wenzel, H

University of Surrey

Theory and Simulation of Ultrafast CarrierDynamics and Nonlinear Pulse Propagation inQuantum Dot Semiconductor Optical AmplifiersDietmar W. Reschner, Edeltraud Gehrig, and Ortwin HessAdvanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, GuildfordSurrey, GU2 7XH United KingdomAbstract— We investigate the propagation of an ultra-fast lightpulse dynamically interacting with the charge carrier plasma inthe active area of a quantum dot semiconductor optical amplifier(QD-SOA). The coupled spatio-temporal dynamics of light-fieldsand carriers in a spatially inhomogeneous dot ensemble isdescribed on the basis of Maxwell-Bloch equations. In thisapproach the light fields within the QD-SOA are calculated usingwave equations that are coupled to Quantum Dot Bloch equationsdescribing the dynamics of the carriers in the active gain medium.In addition, we simulate the dynamics of the carriers in the em-bedding medium, including scattering of charge carriers betweenwetting layer and quantum dots. Our numerical results showthat the shape and duration of an ultra-short pulse propagatingthrough the amplifier is determined by a complex combinationof hole level burning and dynamic scattering processes.I. INTRODUCTIONA quantum dot amplifier is a system in which opticallyinjected and laser-internal light fields dynamically interact withcharge carriers confined to quantum dots. In turn, the dynamicsof the electron and the hole distributions is determined by theinteraction with light fields, carrier-carrier and carrier-phononscattering.We numerically investigate the propagation of an ultra-fastlight pulse in the active area of a quantum dot semiconductoroptical amplifier (QD-SOA). Our model is based on the theorypresented in [1]. In this model the occupation probability ofeach bound quantum dot (QD) state (refering to electronsand holes) and the corresponding interband polarization iscalculated using QD-Bloch equations. By summing the mi-croscopic interlevel polarization over every electron-hole pairthe macroscopic polarization of the medium is calculated. Thisquantity is used as a source term in a classical wave equation,describing the dynamics of the light fields within the QD-SOA. In our approach the equations have been extended toinclude a more detailed description of the interaction betweencarriers in the QDs and carriers in the embedding medium.The QD-SOA discussed in this work has an active area thatconsists of QDs embedded in a quantum well (QW). In orderto calculate dynamical scattering rates which depend on theoccupied and empty QD and QW states the chemical potentialfor electrons and holes is calculated in every integration timestep. This procedure allows the calculation of the (energyresolved) density of occupied QW states and the scatteringrates to each QD-electron and QD-hole state. The scatteringrates enter the calculation of the occupation probability of eachQD-state in the next time integration step. The pumping ofelectrons and holes into the system is accounted for by a pumpterm in the equations describing the QW charge density.In principle, our model can be adapted to describe any QD-SOA with a ’dots-in-a-well’ active area. The simulation resultspresented in this work refer to an edge-emitting QD-SOA withIn0.65Ga0.35As QDs embedded in a In0.2Ga0.8As QW, whichin turn is embedded in a GaAs matrix. The QDs have the shapeof a truncated pyramid with an average lateral width of 25.4nm and an average hight of 3.4 nm. The width of the wettinglayer QW is 4.5 nm. Figure 1 shows the band diagram ofthe QD structure. The transition energy between the electron6?1424 meV6?1260 meV6?1131 meV (QD ground state transition)GaAsInGaAs QDInGaAs QWFig. 1. Band diagram of the QD structure showing the radiative transitionbetween electron and hole QD ground state.ground state and the hole ground state corresponds to a photonwavelength of 1.095µm.II. NUMERICAL RESULTSThe simulation results presented here show how a light pulse(in resonance with the transition mentioned above) affects theQD carrier population, after being injected into the amplifier.Figure 2a shows the pulse envelope (of a Gaussian shapedNUSOD '051310-7803-9149-7/05/$20.00 ©2005 IEEEAuthorized licensed use limited to: University of Surrey. Downloaded on February 5, 2010 at 06:45 from IEEE Xplore.  Restrictions apply. Fig. 2. Occupation dynamics and hole burning of electron levels (b) andhole levels (c) due to the passage of an amplified light pulse (a).normalized pulse of duration 300 fs) after a propagation lengthof 5µm as well as the occupation of 5 electron levels Fig. 2band 5 hole levels Fig. 2c. The initial occupation of electron andhole levels has been set to 0.6, where a value of 1.0 refers to acomplete filling of the levels. The propagating pulse leads to asignificant depletion of the electron and hole states. After thepassage of the pulse a partial re-establishment of the inversionvia intra-dot scattering and scattering processes involving QWwetting layer states occurs. We note that due to the smallerlevel separation and confinement energy of the hole states thelevel hole burning of the hole ground state is less pronouncedand the re-population of hole states with carriers from the QWwetting layer is more effective compared to the re-populationof electron states.Fig. 3. Amplification and reshaping of a light pulse (initially Gaussian shapedand with a duration of 300fs) during the propagation through the QD-SOAafter a distance of 5µm (a), 105µm (b) and 255µm (c) from the input facet.Figure 3 shows the amplification and reshaping of the pulseduring its propagation through the inverted active area ofthe QD-SOA for a propagation distance of 5µm, 105µm and255µm from the input facet. The leading part of the pulseis amplified to a higher degree than the trailing part, since it’sees’ the full initial inversion whereas the trailing part of thepulse experiences a carrier population that has already beensignificantly reduced.III. CONCLUSIONWe have investigated the dynamic interaction of a femto-second light pulse with the charge carrier population in theactive area of a QD-SOA. Our simulation results visualize thedynamics of level hole burning and dot refilling via complexscattering processes leading to a dynamic amplification andreshaping of a propagating light pulse.Our spatially and temporally resolved model allows the sys-tematic analysis of the influence of material properties (QDenergy level, dipole matrix elements, confinement energies andQW wetting layer band structure) and device geometry onshape and spectra of an amplified pulse. This may contributeto the design of QD-SOAs with improved properties.ACKNOWLEDGMENTThe authors would like to thank Andrei Schliwa from theTechnical University Berlin for kindly supplying parameterson the investigated QD structure.REFERENCES[1] E. Gehrig, and O. Hess, “Mesoscopic spatiotemporal theroy of quantum-dot lasers,” Phys. Rev. A, vol. 65, no. 033804, Feb. 2002.[2] X. Q. Li,and Y. Arakawa, “Phonon bottleneck in quantum dots: Role oflifetime of the confined optical phonons,” Phys. Rev. B, vol. 59, no. 7,Feb. 1999.NUSOD '05132Authorized licensed use limited to: University of Surrey. Downloaded on February 5, 2010 at 06:45 from IEEE Xplore.  Restrictions apply. 

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Theory and simulation of ultrafast carrier dynamics and nonlinear pulse propagation in quantum dot semiconductor optical amplifiers

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