Semiconductor Laser Linewidth Theory Revisited

More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission ($K$-factor) and the effective $\alpha$-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.Comment: semiconductor laser, spectral linewidth, coupled-wave equations, traveling wave model, noise, Langevin equations, Henry factor, Petermann factor, chirp reduction factor, population inversion facto

Semiconductor laser linewidth theory revisited

More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (K-factor) and the effective Alpha-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser

Planning and Optimization of Internal Transport Systems

The digital transformation is increasingly affecting the field of intralogistics. In order to develop corresponding concepts in logistics planning in a short time, software tools should profitably transfer the theoretical knowledge into practice and support the user in the best possible way. This article gives insight in particular into the typical tasks involved in the planning and optimization of internal transport processes and how LOGSOL as a consultany company addresses these with the help of the RoutMan planning tool.:1. Introduction 2. Planning of internal transport processes 3. LOGSOL's approach to planning and optimizing internal transport processes 4. Conclusio

IDENTIFICATION OF EMG FREQUENCY PATTERNS IN RUNNING BY WAVELET ANALYSIS AND SUPPORT VECTOR MACHINES

The purpose of this study was to identify EMG pattern of running at different speed and incline based on a trial-to-trial analysis. Eight subjects performed treadmill running at five different conditions (4, 5 and 6 m/s, 5m/s at 5° incline, 5m/s at 2° decline). EMG data of eight leg muscles were recorded and transformed by a wavelet analysis (van Tscharner, 2000). Ten subsequent steps of each subject and condition were classified by support vector machines. Between 93 and 100% of all EMG patterns were assigned correctly to the individual. According to the different running conditions recognition rates ranged between 78 and 88%. Hence, support vector machines can be considered as powerful nonlinear tool for the classification of dynamic EMG patterns

Zur Lage im Einzelhandel: Helfen staatliche Reglementierungen weiter?

Die zunehmende Intensität des Preiswettbewerbs, die steigende Zahl der Geschäftsaufgaben und Marktaustritte vor allem kleinerer Unternehmen des Einzelhandels sowie die gegenwärtige Krise der KarstadtQuelle-Gruppe sind Anlass vielfältiger Diskussionen um die Zukunft des Einzelhandels, auch um die Zweckmäßigkeit oder gar Notwendigkeit staatlicher Reglementierungen. Für Holger Wenzel, Hauptverband des Deutschen Einzelhandels, dürfen staatliche Reglementierungen im Einzelhandel nicht "zu Lasten des derzeitigen Distributionswettbewerbs ausfallen". Und auch Dr. Uwe Christian Täger, ifo Institut, sieht die Gefahr, dass staatliche Reglementierungen in der Regel "mehr oder minder negative Nebeneffekte für die genuinen Wettbewerbsprozesse in der Warendistribution (produzieren)". Prof. Dr. Edda Müller, Verbraucherzentrale, unterstreicht, dass vor allem Maßnahmen zur Stärkung des Verbrauchervertrauens nötig sind, während für Prof. Dr. Joachim Zentes, Universität des Saarlands, "zunächst keine zusätzlichen staatlichen Reglementierungen, sondern verstärkt konzertierte Aktionen auf unterschiedlicher Ebene (gefragt sind)".Einzelhandel, Preiswettbewerb, Marktanteil, Unternehmen, Facheinzelhandel, Konsumklima, Regulierung, Wettbewerb, Deutschland

Dynamics in high-power diode lasers

High-power broad-area diode lasers (BALs) exhibit chaotic spatio-temporal dynamics above threshold. Under high power operation, where they emit tens of watts output, large amounts of heat are generated, with significant impact on the laser operation. We incorporate heating effects into a dynamical electro-optical (EO) model for the optical field and carrier dynamics along the quantum-well active zone of the laser. Thereby we effectively couple the EO and heat-transport (HT) solvers. Thermal lensing is included by a thermally-induced contribution to the index profile. The heat sources obtained with the dynamic EO-solver exhibit strong variations on short time scales, which however have only a marginal impact on the temperature distribution. We consider two limits: First, the static HT-problem, with time-averaged heat sources, which is solved iteratively together with the EO solver. Second, under short pulse operation the thermally induced index distribution can be obtained by neglecting heat flow. Although the temperature increase is small, a waveguide is introduced here within a few-ns-long pulse resulting in significant near field narrowing. We further show that a beam propagating in a waveguide structure utilized for BA lasers does not undergo filamentation due to spatial holeburning. Moreover, our results indicate that in BALs a clear optical mode structure is visible which is neither destroyed by the dynamics nor by longitudinal effects

Improving the stability of distributed-feedback tapered master-oscillator power-amplifiers

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

Mode transitions in distributed-feedback tapered master-oscillator power-amplifier

Theoretical 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

Amplifications of picosecond laser pulses in tapered semiconductor amplifiers: Numerical simulations versus experiments

We apply a travelling wave model to the simulation of the amplification of laser pulses generated by Q-switched or mode-locked distributed-Bragg reflector lasers. The power amplifier monolithically integrates a ridge-waveguide section acting as pre-amplifier and a flared gain-region amplifier. The diffraction limited and spectral-narrow band pulses injected in to the pre-amplifier have durations between 10 ps and 100 ps and a peak power of typical 1 W. After the amplifier, the pulses reach a peak power of several tens of Watts preserving the spatial, spectral and temporal properties of the input pulse. We report results obtained by a numerical solution of the travelling-wave equations and compare them with experimental investigations. The peak powers obtained experimentally are in good agreement with the theoretical predictions. The performance of the power amplifier is evaluated by considering the dependence of the pulse energy as a function of different device and material parameters