Dmitrii Rachinskii

Quantum-Dot Mode-Locked Lasers With Dual-Mode Optical Injection

Quantum-dot mode-locked lasers are injection-locked by coherent two-tone master sources. Spectral tuning, significantly improved time-bandwidth product, and low jitter are demonstrated without deterioration of the pulse properties.

Hybrid Mode Locking in Semiconductor Lasers: Simulations, Analysis, and Experiments

Hybrid mode locking in a two-section edge-emitting semiconductor laser is studied numerically and analytically using a set of three delay differential equations. In these equations, the external RF signal applied to the saturable-absorber section is modeled by the modulation of the carrier relaxation rate in this section. The estimation of the locking range where the pulse repetition frequency is synchronized with the frequency of the external modulation is performed numerically and the effect of the modulation shape and amplitude on this range is investigated. Asymptotic analysis of the dependence of the locking range width on the laser parameters is carried out in the limit of small-signal modulation. Our numerical simulations indicate that hybrid mode locking can be also achieved in the cases when the frequency of the external modulation is approximately twice and half of the pulse repetition frequency of the free-running passively mode-locked laser fP . Finally, we provide an experimental demonstration of hybrid mode locking in a 20-GHz quantum-dot laser with the modulation frequency of the reverse bias applied to the absorber section close to fP/2.

Differential Equations with Hysteresis via a Canonical Example

Analysis of closed-loop system is needed and these systems are described by differential equations with hysteresis, and hysteresis terms are to be taken into account in various areas of differential equations, thus leading to numerous distinct branches of study, depending on the subject area, type of hysteresis operators that are used, etc. Operators of hysteresis nonlinearities often admit a simple “picture definition,” however their properties are quite different from the properties of more classical operators. The investigation of differential equations with hysteresis nonlinearities requires new mathematical methods. In return, methods that have been originally suggested for the analysis of differential equations with hysteresis appear to be useful in the classical theory of differential-operator equations. This chapter demonstrates the theory of differential equations with hysteresis via a simple canonical example. Essentially, the semi-linear Duffing oscillator is considered with the Preisach non-linearity. The chapter presents various results on existence and uniqueness, on properties of periodic motions, on the convergence of numerical solutions, etc. Moreover, it shows how these fuse with, and complement each other. Apart from results in traditional areas, the chapter also presents a version of the shadowing lemma specifically designed for the analysis of systems with hysteresis.

Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser

Bifurcation mechanisms of the development and break up of different operation regimes in a passively mode-locked monolithic semiconductor laser are studied by solving numerically partial differential equations for amplitudes of two counterpropagating waves and carrier densities in gain and absorber sections. It is shown that mode-locking regimes with different repetition rates can be multistable for a wide range of laser parameters and that the harmonic mode-locking regime with two counterpropagating pulses in the cavity can exhibit a period-doubling bifurcation leading to different amplitudes and separations of the pulses. The effect of linewidth enhancement factors in gain and absorber sections on the laser dynamics is discussed.

Timing jitter of passively-mode-locked semiconductor lasers subject to optical feedback: A semi-analytic approach

We propose a semi-analytical method of calculating the timing fluctuations in mode-locked semiconductor lasers and apply it to study the effect of delayed coherent optical feedback on pulse timing jitter in these lasers. The proposed method greatly reduces computation times and therefore allows for the investigation of the dependence of timing fluctuations over greater parameter domains. We show that resonant feedback leads to a reduction in the timing jitter and that a frequency-pulling region forms about the main resonances, within which a timing jitter reduction is observed. The width of these frequency-pulling regions increases linearly with short feedback delay times. We derive an analytic expression for the timing jitter, which predicts a monotonous decrease in the timing jitter for resonant feedback of increasing delay lengths, when timing jitter effects are fully separated from amplitude jitter effects. For long feedback cavities the decrease in timing jitter scales approximately as

Mechanism of Synchronization in Frequency Dividers

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Q-switching instability in a mode-locked semiconductor laser

with the increase of the feedback delay time

Topological degree in analysis of canard-type trajectories in 3-D systems

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Stability of large cycles in a nonsmooth problem with Hopf bifurcation at infinity

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Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study

We investigate the mechanism leading to synchronization in injection-locked frequency dividers using methods of asymptotic analysis. We introduce a response function which allows for qualitative evaluation and intuitive interpretation of the locking phenomenon. We show that the linear asymptotic approximation predicts the locking intervals with high accuracy for a class of models and parameter sets reported in the literature. The accuracy of the approach is evaluated by comparing the theoretical prediction with numerical results. We use phase space analysis to study the case where the limit cycle is dominated by a strongly anharmonic oscillation.