Table Of ContentSpringer Theses
Recognizing Outstanding Ph.D. Research
Christian Otto
Dynamics
of Quantum
Dot Lasers
Effects of Optical Feedback
and External Optical Injection
Springer Theses
Recognizing Outstanding Ph.D. Research
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Christian Otto
Dynamics of Quantum Dot
Lasers
Effects of Optical Feedback and External
Optical Injection
Doctoral Thesis accepted by
Technical University of Berlin, Germany
123
Author Supervisors
Dr. Christian Otto Prof.Eckehard Schöll
Instituteof Theoretical Physics Dr. KathyLüdge
Berlin InstituteofTechnology Instituteof Theoretical Physics
Berlin Berlin InstituteofTechnology
Germany Berlin
Germany
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-319-03785-1 ISBN 978-3-319-03786-8 (eBook)
DOI 10.1007/978-3-319-03786-8
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To Antje
Supervisors’ Foreword
Semiconductorlasersareveryimportanttooptoelectronics,whichhasapplications
inmanyaspectsofourdailylivesandwhosedevelopmentrepresentstheforefrontof
quantum electronics and quantum optics research. Semiconductor lasers are of
broad scientific interest because,for the past30–40 years, they have been used as
experimentalplatformsforinvestigatingnewandinterestingphenomenainphysics
and mathematics, on the one hand directly related to semiconductors, and on the
otherhandaseasy-to-handletest-bedsfornonlineardynamicalphenomenaoccur-
ringinamuchwidercontext.Thisthesisdealswiththedynamicsofstate-of-the-art
nanophotonic semiconductor structures, in particular with quantum-dot lasers,
i.e., semiconductor lasers that contain pyramid-shaped nanostructures (quantum
dots) coupled to a surrounding two-dimensional layer of semiconductor material.
They are of great interest with respect to fundamental aspects of nonlinear
dynamical systems on the one hand, and technological applications in modern
telecommunicationontheotherhand.Threedifferentcomplexlaserstructuresare
considered in detail: (i) a quantum-dot based semiconductor laser under optical
injectionfromamasterlaser,(ii)aquantum-dotlaserwithopticalfeedbackfroman
externalresonator,and(iii)a5-sectionquantum-welllaserstructureconsistingofa
mode-coupledlaserwithsaturableabsorberandanexternalresonator.Inallofthese
applications multiple timescales determine the dynamics. In fact, the interplay
betweentheinherenttimedelaysandtheintrinsicmicroscopicscatteringtimescales
leads to new nonlinear effects. These effects are investigated in detail here, and
parameter regimes of stable operation are predicted based on the underlying
bifurcationstructure.Onecentralmethodistheasymptotictheorythatallowsfora
reduction of the complex differential equations by exploiting the smallness of
certainparameters,andgivesanalyticexpressionsforbifurcationlines.Theeffect
ofpassivemode-locking,describedinPartIIIofthethesis,isthesynchronizationof
the phases of longitudinal modes of a laser achieved through the addition of a
saturableabsorber.Itproducesultrashortpicosecondpulsesathighrepetitionrates,
making them useful in data-communication, optical clocking, and microscopy,
however,withthedrawbackofarelativelylargetimingjitter.Theeffectofoptical
self-feedbackonthetimingjitterofthepulsetrainsisdiscussedindetailinthethesis,
and a careful and in-depth numerical analysis permits to successfully predict
parameterregimeswherestabilizationofthepulsetrainscanbeobtained.Thethesis
vii
viii Supervisors’Foreword
hasconsiderableapplicationpotential,sincequantum-dotlasersareverypromising
candidates for telecommunication applications and high-speed data transmission
due to their high temperature stability, their low value of the threshold current
density, their strongly damped relaxation oscillations, narrow linewidth, and low
sensitivity to optical feedback. It is shown within this thesis that most of the
interesting dynamical properties of quantum-dot lasers result from their relatively
slow internal charge-carrier scattering processes, which is discussed in detail and
provenbymeansofanalyticinvestigations.Thethesisisoutstandinginitsdepthand
breadth,andleadstonewfundamentalinsightsintotheinterplayofmicroscopically
basednonlinearlaserdynamicsandopticalperturbationsbydelayedfeedbackand
injection.Themethodscompriseabroadspectrumfrommicroscopicmodelingvia
numerical solution of nonlinear laser differential equations and numerical path
continuation techniques to analytical approximations of reductive perturbation
theory and asymptotic analysis, and from deterministic nonlinear dynamics to
stochasticeffects.
Berlin, September 2013 Eckehard Schöll
Kathy Lüdge
Abstract
In this thesis, I study the complex dynamics of different semiconductor laser
structures under optical injection and under external optical feedback.
InPartIofthisthesis,Iconcentrateonnanostructuredquantumdot(QD)lasers.
Here, the impact of the internal nonlinear carrier dynamics—and thus the impact
of the band structure—on the dynamics of these QD lasers is intensively studied.
Therefore, a microscopically based rate equation model is used, in which the
carrier scatteringdynamicsbetween thediscrete energylevelsoftheQDsandthe
surroundingcarrierreservoirisdescribedbyCoulombscatteringrates.Theserates
depend nonlinearlyon thecarrierdensities inthe carrier reservoirandthuson the
pumpingconditions.Further,theystronglydependontheenergyspacingbetween
thebandedgeofthecarrierreservoirandthediscreteQDlevels,whichpermitsto
describe different band structures. The impact of the scattering rates on the
damping of the relaxation oscillations (ROs) of the solitary laser are discussed in
detail.Besidestheimpactofthebandstructure,Iinvestigatethedependenceofthe
complex dynamics of a QD laser under optical injection on the pump current and
on the phase-amplitude coupling (a-factor). By means of multiscale analysis,
analytical approximations are derived for the saddle-node and Hopf bifurcations
bordering the region of stable continuous wave emission as well as for a
codimension-2 zero-Hopf point acting as organizing center for more complex
dynamics, and the minimal injection strength, below which no Hopf instability
may occur. Moreover, for the QD laser subject to optical feedback, an analytic
expression for the first supercritical Hopf bifurcation marking the boundary for
stable continuous wave emission is obtained. The analytic expressions for the
bifurcation lines and bifurcation points reveal their dependence on the RO
damping, and thus on the band structure, as well as on the a-factor. Further, the
possibilitytoemploytheQDlasersubjecttofeedbackasanexcitableopticalunit
isdiscussed.Byaddingwhitenoisetothedynamicequationfortheelectricfieldin
the cavity, coherence resonance is observed in the excitable regime, and its
dependence on the pump current is studied.
In Part II of this thesis, the response of a passively mode-locked two-section
laser to external optical feedback is studied. This type of laser permits to realize
compact devices that are well suited for optical telecommunication applications
due to their ability to emit trains of short optical pulses with a high repetition
frequencyof40GHz,whichisanupcomingIEEEstandard.Onemajordrawback
ix
x Abstract
ofpassivelymode-lockedlasersistheirrelativelylargetimingjitterdegradingthe
qualityofthepulsestream andthusincreasingthe bit-errorrate. Resonantoptical
feedback provides an easy-to-handle way of reducing the timing jitter. I analyze
theresonancesoftheinter-pulseintervaltimeandtheexternaldelaytime,anditis
shown that the resonances can be ordered in a Farey-sequence similar to the
resonances in externally driven systems, which allows for easy prediction of the
laserdynamics.Further,Idiscussthatthetimingjittercanbereduceddrasticallyin
the main resonances, where the largest stabilizing effect of the feedback is
obtained, which is of relevance for applications.
