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- ItemVariation of constants formula for hyperbolic systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Lichtner, MarkA smooth variation of constants formula for semilinear hyperbolic systems is established using a suitable Banach space $X$ of continuous functions together with its sun dual space $X^odot ast$. It is shown that mild solutions of this variation of constants formula generate a smooth semiflow in $X$. This proves that the stability of stationary states for the nonlinear flow is determined by the stability of the linearized semigroup.
- ItemParallel simulation of high power semiconducor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Lichtner, Mark; Spreemann, MartinHigh power tapered semiconductor lasers are characterized by a huge amount of structural and geometrical design parameters and are subject to time-space instabilities like pulsations, self-focussing, filamentation and thermal lensing which yield restrictions to output power, beam quality and wavelength stability. Numerical simulations are an important tool for finding optimal design parameters, understanding the complicated dynamical behavior and for predicting new laser designs. We present fast dynamic high performance parallel simulation results based on traveling wave equations which are suitable for model calibration and parameter scanning of the long time dynamics in reasonable time. Simulation results are compared to experimental data.
- ItemOn the stability of periodic orbits in delay equations with large delay(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Sieber, Jan; Wolfrum, Matthias; Lichtner, Mark; Yanchuk, SerhiyWe prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay
- ItemThe spectrum of delay differential equations with large delay(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Lichtner, Mark; Wolfrum, Matthias; Yanchuk, SerhiyWe show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continuous spectrum. We show that the spectral curves and strong spectral points provide a complete description of the spectrum for sufficiently large delay and can be comparatively easily calculated by approximating expressions.
- ItemStripe-array diode-laser in an off-axis external cavity : theory and experiment(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Jechow, Andreas; Lichtner, Mark; Menzel, Ralf; Radziunas, Mindaugas; Skoczowsky, Danilo; Vladimirov, AndreiStripe-array diode lasers naturally operate in an anti-phase supermode. This produces a sharp double lobe far field at angles α depending on the period of the array. In this paper a 40 emitter gain guided stripe-array laterally coupled by off-axis filtered feedback is investigated experimentally and numerically. We predict theoretically and confirm experimentally that at doubled feedback angle 2α a stable higher order supermode exists with twice the number of emitters per array period. The theoretical model is based on time domain traveling wave equations for optical fields coupled to the carrier density equation taking into account diffusion of carriers. Feedback from the external reflector is modeled using Fresnel integration.
- ItemPrinciple of linearized stability and smooth center manifold theorem for semilinear hyperbolic systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Lichtner, Mark[no abstract available]
- ItemMode transitions in distributed-feedback tapered master-oscillator power-amplifier(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Radziunas, Mindaugas; Tronciu, Vasile Z.; Bandelow, Uwe; Lichtner, Mark; Spreemann, Martin; Wenzel, HansTheoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.
- ItemImproving the stability of distributed-feedback tapered master-oscillator power-amplifiers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Tronciu, Vasile Z.; Lichtner, Mark; Radziunas, Mindaugas; Bandelow, U.; Wenzel, H.We report theoretical results on the wavelength stabilization in distributed-feedback master-oscillator power-amplifiers which are compact semiconductor laser devices capable of emitting a high brilliance beam at an optical power of several Watts. Based on a traveling wave equation model we calculate emitted optical power and spectral maps in dependence on the pump of the power amplifier. We show that a proper choice of the Bragg grating type and coupling coefficient allows to optimize the laser operation, such that for a wide range of injection currents the laser emits a high intensity continuous wave beam.
- ItemSpectral mapping theorem for linear hypervolic systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Lichtner, Mark[no abstract available]
- ItemImprovement of output beam quality in broad area lasers with off-axis feedback(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Lichtner, Mark; Tronciu, Vasile; Vladimirov, Andrej G.We report a method to improve the beam quality of broad area lasers by using a V-shaped external cavity formed by two off-axis feedback mirrors that allow to select a single transverse mode with the intensity modulated in the transverse direction. We find that in the case when one of the two feedback mirrors is absent a spontaneous formation of self-induced transverse population grating leading to a reduction of the lasing threshold is observed. Most favorable conditions for stabilization of single transverse supermode and creation of a high power and high brightness plane wave traveling in the extended cavity are obtained for equal re ectivities of the two external reflectors.