@phdthesis{Heiligenthal2012,
  author    = {Heiligenthal, Sven},
  title     = {Strong and Weak Chaos in Networks of Semiconductor Lasers with Time-Delayed Couplings},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-77958},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {This thesis deals with the chaotic dynamics of nonlinear networks consisting of semiconductor lasers which have time-delayed self-feedbacks or mutual couplings. These semiconductor lasers are simulated numerically by the Lang-Kobayashi equations. The central issue is how the chaoticity of the lasers, measured by the maximal Lyapunov exponent, changes when the delay time is changed. It is analysed how this change of chaoticity with increasing delay time depends on the reflectivity of the mirror for the self-feedback or the strength of the mutal coupling, respectively. The consequences of the different types of chaos for the effect of chaos synchronization of mutually coupled semiconductor lasers are deduced and discussed. At the beginning of this thesis, the master stability formalism for the stability analysis of nonlinear networks with delay is explained. After the description of the Lang-Kobayashi equations and their linearizations as a model for the numerical simulation of semiconductor lasers with time-delayed couplings, the artificial sub-Lyapunov exponent \$\lambda_{0}\$ is introduced. It is explained how the sign of the sub-Lyapunov exponent can be determined by experiments. The notions of "strong chaos" and "weak chaos" are introduced and distinguished by their different scaling properties of the maximal Lyapunov exponent with the delay time. The sign of the sub-Lyapunov exponent \$\lambda_{0}\$ is shown to determine the occurence of strong or weak chaos. The transition sequence "weak to strong chaos and back to weak chaos" upon monotonically increasing the coupling strength \$\sigma\$ of a single laser's self-feedback is shown for numerical calculations of the Lang-Kobayashi equations. At the transition between strong and weak chaos, the sub-Lyapunov exponent vanishes, \$\lambda_{0}=0\$, resulting in a special scaling behaviour of the maximal Lyapunov exponent with the delay time. Transitions between strong and weak chaos by changing \$\sigma\$ can also be found for the R{\"o}ssler and Lorenz dynamics. The connection between the sub-Lyapunov exponent and the time-dependent eigenvalues of the Jacobian for the internal laser dynamics is analysed. Counterintuitively, the difference between strong and weak chaos is not directly visible from the trajectory although the difference of the trajectories induces the transitions between the two types of chaos. In addition, it is shown that a linear measure like the auto-correlation function cannot unambiguously reveal the difference between strong and weak chaos either. Although the auto-correlations after one delay time are significantly higher for weak chaos than for strong chaos, it is not possible to detect a qualitative difference. If two time-scale separated self-feedbacks are present, the shorter feedback has to be taken into account for the definition of a new sub-Lyapunov exponent \$\lambda_{0,s}\$, which in this case determines the occurence of strong or weak chaos. If the two self-feedbacks have comparable delay times, the sub-Lyapunov exponent \$\lambda_{0}\$ remains the criterion for strong or weak chaos. It is shown that the sub-Lyapunov exponent scales with the square root of the effective pump current \$\sqrt{p-1}\$, both in its magnitude and in the position of the critical coupling strengths. For networks with several distinct sub-Lyapunov exponents, it is shown that the maximal sub-Lyapunov exponent of the network determines whether the network's maximal Lyapunov exponent scales strongly or weakly with increasing delay time. As a consequence, complete synchronization of a network is excluded for arbitrary networks which contain at least one strongly chaotic laser. Furthermore, it is demonstrated that the sub-Lyapunov exponent of a driven laser depends on the number of the incoherently superimposed inputs from unsynchronized input lasers. For networks of delay-coupled lasers operating in weak chaos, the condition \$|\gamma_{2}|<\mathrm{e}^{-\lambda_{\mathrm{m}}\,\tau}\$ for stable chaos synchronization is deduced using the master stability formalism. Hence, synchronization of any network depends only on the properties of a single laser with self-feedback and the eigenvalue gap of the coupling matrix. The characteristics of the master stability function for the Lang-Kobayashi dynamics is described, and consequently, the master stability function is refined to allow for precise practical prediction of synchronization. The prediction of synchronization with the master stability function is demonstrated for bidirectional and unidirectional networks. Furthermore, the master stability function is extended for two distinct delay times. Finally, symmetries and resonances for certain values of the ratio of the delay times are shown for the master stability function of the Lang-Kobyashi equations.},
  subject      = {Halbleiterlaser},
  language  = {en}
}
@phdthesis{Albert2012,
  author    = {Albert, Ferdinand},
  title     = {Vertikale und laterale Emissionseigenschaften von Halbleiter-Quantenpunkt-Mikroresonatoren im Regime der schwachen und starken Licht-Materie-Wechselwirkung},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-93016},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Die vorliegende Arbeit besch{\"a}ftigt sich mit der Licht-Materie-Wechselwirkung in Quantenpunkt-Mikroresonatoren und deren vertikalen und lateralen Emissionseigenschaften. Quantenpunkte sind nanoskopische Strukturen, in denen die Beweglichkeit der Ladungstr{\"a}ger unterhalb der de-Broglie-Wellenl{\"a}nge eingeschr{\"a}nkt ist, wodurch die elektronische Zustandsdichte diskrete Werte annimmt. Sie werden daher auch als k{\"u}nstliche Atome bezeichnet. Um die Emissionseigenschaften der Quantenpunkte zu modifizieren, werden sie im Rahmen dieser Arbeit als aktive Schicht in Mikros{\"a}ulenresonatoren eingebracht. Diese bestehen aus einer GaAs lambda-Kavit{\"a}t, die zwischen zwei Braggspiegeln aus alternierenden GaAs und AlAs Schichten eingefasst ist. Diese Resonatoren bieten sowohl eine vertikale Emission {\"u}ber Fabry-Perot Moden, als auch eine laterale Emission {\"u}ber Fl� ustergaleriemoden. Die Licht-Materie-Wechselwirkung zwischen den Resonatormoden und lokalisierten Ladungstr{\"a}gern in den Quantenpunkten, genannt Exzitonen, kann in zwei Regime unterteilt werden. Im Regime der starken Kopplung wird der spontane Emissionsprozess in einem Quantenpunkt reversibel und das emittierte Photon kann wieder durch den Quantenpunkt absorbiert werden. Die theoretische Beschreibung der Kopplung eines Exzitons an die Resonatormode erfolgt {\"u}ber das Jaynes-Cummings Modell und kann im Tavis-Cummings Modell auf mehrere Emitter erweitert werden. Ist die D{\"a}mpfung des Systems zu gross, so befindet man sich im Regime der schwachen Kopplung, in dem die Emissionsrate des Quantenpunkts durch den Purcell-Effekt erh{\"o}ht werden kann. In diesem Regime k{\"o}nnen Mikrolaser mit hohen Einkopplungsraten der spontanen Emission in die Resonatormode und niedrigen Schwellpumpstr{\"o}men realisiert werden. Zur Charakterisierung der Proben werden vor allem die Methoden der Mikro-Elektrolumineszenz und der Photonenkorrelationsmessungen eingesetzt.},
  subject      = {Drei-F{\"u}nf-Halbleiter},
  language  = {de}
}