A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrodinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

Optical rogue waves

Metastasis, the dissemination and growth of neoplastic cells in an organ distinct from that in which they originated, is the most common cause of death in cancer patients. This is particularly true for pancreatic cancers, where most patients are diagnosed with metastatic disease and few show a sustained response to chemotherapy or radiation therapy. Whether the dismal prognosis of patients with pancreatic cancer compared to patients with other types of cancer is a result of late diagnosis or early dissemination of disease to distant organs is not known. Here we rely on data generated by sequencing the genomes of seven pancreatic cancer metastases to evaluate the clonal relationships among primary and metastatic cancers. We find that clonal populations that give rise to distant metastases are represented within the primary carcinoma, but these clones are genetically evolved from the original parental, non-metastatic clone. Thus, genetic heterogeneity of metastases reflects that within the primary carcinoma. A quantitative analysis of the timing of the genetic evolution of pancreatic cancer was performed, indicating at least a decade between the occurrence of the initiating mutation and the birth of the parental, non-metastatic founder cell. At least five more years are required for the acquisition of metastatic ability and patients die an average of two years thereafter. These data provide novel insights into the genetic features underlying pancreatic cancer progression and define a broad time window of opportunity for early detection to prevent deaths from metastatic disease.

SF-010-4 Distant metastasis occurs late during the genetic evolution of pancreatic cancer

Ultrafast lasers, which generate optical pulses in the picosecond and femtosecond range, have progressed over the past decade from complicated and specialized laboratory systems to compact, reliable instruments. Semiconductor lasers for optical pumping and fast optical saturable absorbers, based on either semiconductor devices or the optical nonlinear Kerr effect, have dramatically improved these lasers and opened up new frontiers for applications with extremely short temporal resolution (much smaller than 10 fs), extremely high peak optical intensities (greater than 10 TW/cm2) and extremely fast pulse repetition rates (greater than 100 GHz).

Recent developments in compact ultrafast lasers

A smart phone or tablet includes laser diodes configured to be pulsed and generate near-infrared light between 700-2500 nanometers. Lenses direct the light to a sample. A detection system includes a photodiode array with pixels coupled to CMOS transistors, and is configured to receive light reflected from the sample, to be synchronized to the light from the laser diodes, and to perform a time-of-flight measurement of a time difference between light from the laser diodes and light reflected from the sample. The detection system is configured to convert light received while the laser diodes are off into a first signal, and light received while at least one laser diodes is on, which includes light reflected from the sample, into a second signal. The smart phone or tablet is configured to difference the first signal and the second signal and to generate a two-dimensional or three-dimensional image using the time-of-flight measurement.

Near-infrared time-of-flight cameras and imaging

Erbium-doped fiber amplifiers (EDFAs) have already made a large impact on fiber transmission systems, and they are also beginning to penetrate nonlinear optical applications. We show that EDFAs tailored with particular properties can have novel nonlinear applications in ultrafast, short pulse transmission, switching and lasers. In long distance fiber-optic transmission, low-doped, distributed EDFAs may counteract deleterious effects such as soliton self-frequency shift (SSFS) and Gordon-Haus jitter due to amplified spontaneous emission. Interaction between orthogonally polarized solitons in a rapidly amplifying birefringent EDFA can lead to large frequency shifts that can be used for switching or logic gates. Finally, highly doped, polarization-maintaining EDFAs have been used to generate sub-picosecond pulses from passively modelocked, stable, self-starting lasers. We focus on the required properties for the EDFAs and their features that enable these unique applications. >

Propagation, switching and lasers in special EDFA's

Near-infrared time-of-flight remote sensing

All-optical switching technologies could lead to increased flexibility of communication networks by overcoming electronic bottlenecks and opto-electronic conversions. The combination of soliton transmission, ultrafast header processing and all-optical demultiplexing permits a routing service on a frame-by-frame basis, which might provide cost savings to high-speed networks by reducing the reliance on expensive SONET add/drop multiplexers. Also, the single channel speeds approaching 100Gb/s could be used to upgrade each channel in a wavelength-division-multiplexed network. A soliton ring network architecture is described that exploits the speeds of all-optical technologies, and the key enabling sub-systems are the access nodes or “on-” and “off-ramps” operating at 100Gb/s. Packet-drop function for a time-division multiplexing network using 100 Gbit/s, eight-bit words is experimentally demonstrated by integrating all-optical header processing and payload demultiplexing with electro-optic packet routing. The header processor consists of two levels of all-optical logic gates based on low birefringent nonlinear optical loop minors (NOLMs), and the payload demultiplexer is a two-wavelength NOLM. Synchronized lasers with timing jitter under 1 ps drive both devices. The contrast ratios for both header processor and demultiplexer are 10:1 and that of the packet router is 17 dB. The switching energies for header processing and payload reading are 10 pJ/pulse and 1 pJ/pulse, respectively. In addition, to test the system performance we experimentally measure the eye diagram of an all-optical header processor using a cross-correlator to achieve picosecond resolution. By varying 100 Gbit/s header packets, we measure an eye diagram with a Q value of 7.1 at 12 pJ packet pulse energy. From the Q value, we also statistically calculate the potential bit-error rate performance of 7х10-13 with a confidence level of 95%. The major challenges for ultrafast, all-optical networks include power requirements, timing jitter, and avoidance of pulse distortion.

All-Optical Access Node Technologies

Selon un aspect, l'invention concerne un amplificateur optique permettant d'amplifier une pluralite de signaux de longueur d'onde optiques, au moins partiellement par amplification Raman. Ledit amplificateur comprend une entree destinee a recevoir une pluralite de signaux de longueur d'onde et une sortie destinee a communiquer une version amplifiee d'au moins certains signaux de longueur d'onde. L'amplificateur comprend egalement un ensemble de pompage destine a produire au moins un signal de pompage et un milieu de gain destine a recevoir la pluralite de signaux de longueur d'onde et le ou les signaux de pompage, et a faciliter l'amplification des signaux de longueur d'onde precites. Cet amplificateur est associe a un facteur de bruit dont la forme varie en fonction d'une longueur d'onde. Au moins l'un des signaux de pompage fonctionne de sorte que sa puissance varie afin de reguler selectivement la forme du facteur de bruit.

Mohammed N. Islam

Papers

Near-infrared time-of-flight cameras and imaging

Propagation, switching and lasers in special EDFA's

Near-infrared time-of-flight remote sensing

All-Optical Access Node Technologies

Systeme et procede permettant de reguler un facteur de bruit