Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Laser instabilities: a modern perspective

We use the finite-difference time-domain (FDTD) solution of the full-wave vectorial Maxwell-Bloch equations for a two-level quantum system developed earlier , to investigate the nonlinear gain spatio-temporal dynamics of active optical waveguides and semiconductor microcavities. The numerical model has been successfully validated against density matrix theory of gain saturation in homogeneously broadened two-level quantum systems for optical waveguides containing resonant gain nonlinearities. The semiclassical equations have been extended employing the Langevin formalism to account for the quantum noise and the spontaneous emission. We have numerically demonstrated the time evolution of the coherent oscillations build up at the output laser facet identifying the lasing threshold and the fast relaxation oscillations until the settlement of a steady-state emission. Our simulation predictions of the lasing wavelength in a number of vertical-cavity surface-emitting laser geometries, when the spontaneous emission is the only source of radiation, agree very well with standard results and, thus, allow us to infer and subsequently optimize important emission characteristics, such as the spontaneous emission rate, the laser line shape, and the relaxation oscillation frequencies and decay rates.

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FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities

Low-frequency fluctuations (LFFs) represent a dynamical instability that occurs in semiconductor lasers when they are operated near the lasing threshold and subject to moderate optical feedback. LFFs consist of sudden power dropouts followed by gradual, stepwise recoveries. We analyze experimental time series of intensity dropouts and quantify the complexity of the underlying dynamics employing two tools from information theory, namely, Shannon's entropy and the Mart\'{\i}n, Plastino, and Rosso statistical complexity measure. These measures are computed using a method based on ordinal patterns, by which the relative length and ordering of consecutive interdropout intervals (i.e., the time intervals between consecutive intensity dropouts) are analyzed, disregarding the precise timing of the dropouts and the absolute durations of the interdropout intervals. We show that this methodology is suitable for quantifying subtle characteristics of the LFFs, and in particular the transition to fully developed chaos that takes place when the laser's pump current is increased. Our method shows that the statistical complexity of the laser does not increase continuously with the pump current, but levels off before reaching the coherence collapse regime. This behavior coincides with that of the first- and second-order correlations of the interdropout intervals, suggesting that these correlations, and not the chaotic behavior, are what determine the level of complexity of the laser's dynamics. These results hold for two different dynamical regimes, namely, sustained LFFs and coexistence between LFFs and steady-state emission.

Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback

We measure experimentally the effects of injection current modulation on the statistical distribution of time intervals between power-dropout events occuring in an external-cavity semiconductor laser operating in the low-frequency fluctuation regime. These statistical distributions are sensitive indicators of the presence of pump current modulation. Under most circumstances, we find that weak low-frequency (in the vicinity of 19 MHz) modulation of the current causes the dropouts to occur preferentially at intervals that are integral multiples of the modulation period. The dropout events can be entrained by the periodic perturbations when the modulation amplitude is large (peak-to-peak amplitude /spl ges/8% of the dc injection current). We conjecture that modulation induces a dropout when the modulation frequency is equal to the difference in frequency between a mode of the extended cavity laser and its adjacent antimode. We also find that the statistical distribution of the dropout events is unaffected by the periodic perturbations when the modulation frequency is equal to the free spectral range of the external cavity. Numerical simulations of the extended-cavity laser display qualitatively similar behavior. The relationship of these phenomena to stochastic resonance is discussed and a possible use of the modulated laser dynamics for chaos communication is described.

https://www.phy.duke.edu/~qelectron/pubs/IEEEjqe36175.pdf

Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current

Semiconductor lasers with optical feedback can display sudden power-dropout events at irregular time intervals. We show numerically that, in some parameter regimes, spontaneous emission noise qualitatively influences the nature and statistics of the dropouts. Experimental measurements of the mean time between dropout events and its dependence on feedback strength agree well with analytic predictions made by Henry and Kazarinov [IEEE J. Quantum Electron. QE-22, 294 (1986)] based on the assumption that spontaneous emission noise induces these dropout events.

Angela Hohl

Papers

Determinism and stochasticity of power-dropout events in semiconductor lasers with optical feedback.