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

We show that isochronous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of such synchronization solutions in a chain of three coupled semiconductor lasers with long interelement coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that zero-lag synchronized chaotic dynamical states can occur over long distances through relaying, without restriction by the amount of delay.

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Zero-lag long-range synchronization via dynamical relaying.

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

http://users.df.uba.ar/morelli/morelli/home_files/CurrBiol_20_1244-1253_2010.pdf

Intercellular Coupling Regulates the Period of the Segmentation Clock

Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the presomitic mesoderm (PSM), generating dynamic stripe patterns of oscillatory gene-expression across the field of PSM cells. How these spatial patterns, the clock’s collective period, and the underlying cellular-level interactions are related is not understood. A theory encompassing temporal and spatial domains of local and collective aspects of the system is essential to tackle these questions. Our delayed coupling theory achieves this by representing the PSM as an array of phase oscillators, combining four key elements: a frequency profile of oscillators slowing across the PSM; coupling between neighboring oscillators; delay in coupling; and a moving boundary describing embryonic axis elongation. This theory predicts that the segmentation clock’s collective period depends on delayed coupling. We derive an expression for pattern wavelength across the PSM and show how this can be used to fit dynamic wildtype gene-expression patterns, revealing the quantitative values of parameters controlling spatial and temporal organization of the oscillators in the system. Our theory can be used to analyze experimental perturbations, thereby identifying roles of genes involved in segmentation.

/pdf/delayed-coupling-theory-of-vertebrate-segmentation-h7h6sfspoh.pdf

Delayed coupling theory of vertebrate segmentation

Two delay-coupled semiconductor lasers are studied in the regime where the coupling delay is comparable to the time scales of the internal laser oscillations. Detuning the optical frequency between the two lasers, novel delay-induced scenarios leading from optical frequency locking to successive states of periodic intensity pulsations are observed. We demonstrate and analyze these dynamical phenomena experimentally using two distinct laser configurations. A theoretical treatment reveals the universal character of our findings for delay-coupled systems.

/pdf/synchronization-of-delay-coupled-oscillators-a-study-of-268p1yctgu.pdf

Synchronization of delay-coupled oscillators: a study of semiconductor lasers.

All-optical clock recovery from 40-Gb/s nonreturn-to-zero (NRZ) pseudorandom binary sequence data streams based on self-pulsating lasers is presented. A compact preprocessing circuit is utilized to convert an NRZ signal to a pseudoreturn-to-zero sequence before injecting into the optical clock. It comprises a semiconductor optical amplifier followed by a periodical wavelength-division-multiplexing demultiplexer filter. A stable sinusoidal clock signal with a root-mean-square jitter below 700 fs is detected at the output of the self-pulsating laser within data dynamic range of more than 8 dB. The performance of the all-optical clock recovery scheme is investigated by varying the bit rates between 39.81 and 43.02 Gb/s as well as for various wavelengths in the C-band.

Bit rate and wavelength transparent all-optical clock recovery scheme for NRZ-coded PRBS signals

Passive Feedback Lasers for operation at 1.3 µm are developed with 32 GHz bandwidth and 7 dB extinction ratio. Transmission over 20 km uncompensated fibre link is demonstrated at 28 Gb/s and 40 Gb/s.

1.3 µm Passive Feedback Laser for 28 Gb/s and 40 Gb/s transmission over uncompensated SSMF links

We analyze the impact of intensity fluctuations on the jitter of a 40 GHz self-pulsating laser. A jitter reduction from 1.7 ps to 600 fs due to intensity-noise suppression is demonstrated for locking to 40 Gb/s.

Self-pulsating DFB for 40 GHz clock-recovery: impact of intensity fluctuations on jitter

Self-pulsating DFB lasers are devices with a unique combination of features. An overview for these devices is given and their key features are outlined. Examples show their potential for applications in high speed communication networks.

http://ieeexplore.ieee.org/iel5/8868/28021/01251592.pdf

J. Kreissl

Papers

Synchronization of delay-coupled oscillators: a study of semiconductor lasers.

Bit rate and wavelength transparent all-optical clock recovery scheme for NRZ-coded PRBS signals

1.3 µm Passive Feedback Laser for 28 Gb/s and 40 Gb/s transmission over uncompensated SSMF links

Self-pulsating DFB for 40 GHz clock-recovery: impact of intensity fluctuations on jitter

Self-pulsating multi-section DFB lasers and their applications