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- ItemNon-Poissonian statistics in an optical analog of quantum billiard with perfectly square boundaries(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Babushkin, IharWe study deviation from the Poissonian statistics of the frequency spacing distribution, appearing due to coupling of polarizational and transverse degrees of freedom in a perfectly square vertical cavity surface emitting laser. The deviation can be controlled by strength of the intracavity anisotropy and its alignment to the device boundaries.
- ItemScar-like structures and their localization in a perfectly square optical billiard(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Babushkin, IharWe show that scar-like structures (SLS) in a wide aperture vertical cavity surface emitting laser (VCSEL) can be formed even in a perfectly square geometry due to interaction of polarization and spatial degrees of freedom of light. We show also that dissipation in the system induces an order among the cavity modes, so that SLS become preferred at lasing threshold. More generally, modes which are more localized both in coordinate and momentum space have in average lower losses.
- ItemDirectional reversals and multimode dynamics in semiconductor ring lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Pérez-Serrano, Antonio; Javaloyes, Julien; Balle, SalvadorWe investigate the dynamics of longitudinal modes in quantum-well semiconductor ring lasers by means of a spatio-temporal travelling wave model. We report the existence of a novel multimode instability in such a system that provokes a periodic deterministic directional reversal involving jumps between consecutive longitudinal modes. The switching sequence follows the modal frequencies from blue to red, and every modal jump is accompanied by a reversal of the direction of emission. We characterize and analyze such instability via the bifurcation analysis of the full travelling wave model as well as by performing the linear stability analysis of the monochromatic solutions.
- ItemNonlinear dynamical properties of frequency swept fiber-based semiconductor lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Slepneva, Svetlana; Pimenov, AlexanderWe investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behaviour of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronisation regimes.We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterise these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilisation of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterise the instability threshold both theoretically and experimentally, and demonstrate deterioration of the FDML regime near the threshold.
- ItemSpectral delay algebraic equation approach to broad area laser diodes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Pérez-Serrano, Antonio; Javaloyes, Julien; Balle, SalvadorIn this work, we discuss an efficient modeling approach for the simulation of Broad Area Laser Diodes. Our method is based on the analytical solution in the spectral domain of the paraxial wave equations for the forward and backward slowly varying traveling waves. We show how to extend to the lateral dimension and to the influence of diffractive terms the idea of mesh decimation by recasting traveling wave models into coupled delay algebraic equations, as discussed in [1]. We compare the results of the dynamics obtained with our improved model with the results of a standard traveling wave description in the cases of straight current stripes as well as in the important configuration of high power tapered anti-reflection coated devices. We obtain an excellent agreement and an improvement of the integration time between one and two orders of magnitudes which may alleviate the necessity of using complex parallel codes. We discussed how the method can be further improved to other, more refined descriptions of the active medium and to the inclusion of thermal effects.
- ItemA PDE-constrained optimization approach for topology optimization of strained photonic devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Adam, Lukáš; Hintermüller, Michael; Surowiec, Thomas M.Recent studies have demonstrated the potential of using tensile-strained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multi-material phase-field approach to determine the optimal material configuration within a so-called Germanium-on-Silicon microbridge is considered. Here, an optimal configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the cross-section of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a non-linear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and second-order optimality conditions. For the numerical experiments, an array of first and second-order solution algorithms in function-space are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed.
- ItemNumerical study of coherence of optical feedback in semiconductor laser dynamics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Radziunas, Mindaugas; Little, Douglas J.; Kane, Deborah M.The nonlinear dynamics of semiconductor laser with coherent, as compared to incoherent, delayed optical feedback systems have been discussed and contrasted in prior research literature. Here, we report simulations of how the dynamics change as the coherence of the optical feedback is systematically varied from being coherent to incoherent. An increasing rate of phase disturbance is used to vary the coherence. An edge emitting, 830nm, Fabry Perot semiconductor laser with a long external cavity is simulated. Following this study, consideration of prior and future experimental studies should include evaluation of where on the continuum of partial coherence the delayed optical feedback sits. Partial coherence is a parameter that will affect the dynamics.
- ItemMulti-channel wavelength conversion using four-wave mixing in semiconductor ring lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Pérez-Serrano, Antonio; Javaloyes, Julien; Balle, SalvadorWe theoretically study all-optical simultaneous wavelength conversion of multiple channels by four-wave mixing in semiconductor ring lasers. Locking the semiconductor ring laser to a holding beam allows to achieve large conversion efficiencies with good signal-tonoise ratio in several channels at multi-Gb/s bit rates. Cross-talk between signals, arising from the peculiar four-wave mixing cascade of modes in semiconductor ring lasers and their cross-gain saturation, is studied in detail. We show that it can be controlled by adjusting the intensity of the holding beam, the bias current of the laser and the number, intensity and wavelength of signals that one wants to convert.
- ItemSpontaneous motion of cavity solitons induced by a delayed feedback(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Tlidi, Mustapha; Averlant, Etienne; Vladimirov, Andrei G.; Panajotov, KrassimirWe consider a broad area Vertical-Cavity Surface Emitting Laser (VCSEL) operating below the lasing threshold and subject to optical injection and time-delayed feedback. We derive a generalized delayed Swift-Hohenberg equation for the VCSEL system which is valid close to the nascent optical bistability. We first characterize the stationary cavity solitons by constructing their snaking bifurcation diagram and by showing clustering behavior within the pinning region of parameters. Then we show that the delayed feedback induces a spontaneous motion of two-dimensional cavity solitons in an arbitrary direction in the transverse plane. We characterize moving cavity solitons by estimating their threshold and calculating their velocity. Numerical 2D solutions of the governing semiconductor laser equations are in close agreement with those obtained from the delayed generalized Swift- Hohenberg equation.
- ItemDelayed feedback control of the self-induced motion of localized structures of light(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Vladimirov, Andrei G.; Pimenov, Alexander; Gurevich, Svetlana V.; Panajotov, Krassimir; Averlant, Eugene; Tlidi, MustaphaWe investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system namely the Vertical-Cavity Surface-Emitting Laser (VCSEL). In the absence of the delay feedback we present experimental evidence of stationary localized structures in a 80 m aperture VCSEL. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time-delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the self-mobility properties of the localized structures. We show that these two parameters affect strongly the space time dynamics of two-dimensional localized structures. We derive an analytical formula for the threshold associated with drift instability of localized structures and a normal form equation describing the slow time evolution of the speed of the moving structure.