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.

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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

http://www.omnisciinc.com/files/12_201210-Alexander-Invited%20Paper.pdf

Modulation instability initiated high power all-fiber supercontinuum lasers and their applications

Using multiple-quantum-well (MQW) saturable absorbers, a NaCl color center was passively mode locked to produce 275-fs transform-limited, pedestal-free pulses with a peak power as high as 3.7 kW. The pulses are tunable from lambda =1.59 to 1.7 mu m by choosing MQWs with different bandgaps. The output pulses from the laser were shortened to 25 fs using the technique of soliton compression in a fiber. The steady-state operation of the laser requires the combination of a fast saturable absorber and gain saturation. >

Color center lasers passively mode locked by quantum wells

An ultrafast, all-optical, three-terminal NOR gate based on soliton dragging in fibers is demonstrated with a gain of 4.5 and a switching energy of 30 pJ. Cascadability is proved with a tandem of two NOR gates that are configured as inverters. Time shifts from soliton dragging between two orthogonally polarized pulses in a fiber can be used for logic operations in a clocked system. Larger-than-predicted time shifts are observed because of self- and cross-Raman amplification effects.

All-optical cascadable NOR gate with gain.

We have reduced the switching energy for an all-optical soliton dragging nor gate to 5.8 pJ by using a two-fiber configuration and optimizing the fiber and laser parameters. The cascadable nor gate has a fanout of six, restores both the logic level and timing, and can operate at bit rates of up to 0.2 THz. In addition, we show that soliton dragging can be represented as a generalized exclusive-or module with high functionality. Two such modules can be interconnected as nor and and gates or broadcast and routing switches.

Low-energy ultrafast fiber soliton logic gates.

By using a loop configuration formed by a polarization beam splitter, we experimentally demonstrate that the existing wavelength-division multiplexing (WDM) sources in C-band can be wavelength converted to the S-band with low polarization sensitivity and low crosstalk. Using a fiber parametric amplifier as a band converter, we achieve experimentally 4.7-dB conversion efficiency over 30-nm conversion bandwidth in 315 m of fiber. Compared to the conventional straight fiber wavelength conversion scheme, a more than 2-dB improvement in polarization sensitivity is measured. In addition to the polarization insensitivity, channel crosstalk is measured to be <-27 dB in 315 m of high nonlinearity fiber. In a detailed experimental study, the pattern of crosstalk in longer fiber lengths and the coupling between the polarization sensitivity and crosstalk are measured. For example, with a 430-m fiber length, we measure the degradation in polarization sensitivity to be /spl sim/4 dB for 12-dB increased signal power. The experimental results are also confirmed by theoretical calculations. Moreover, in a 32 channels systems simulation, the signal-to-noise ratio (SNR) of the converted signals after 800-km propagation is calculated to be only 0.8-dB degraded compared to using laser diodes with the same initial SNR values. Furthermore, we calculate the effect of pump noise and show that the relative intensity noise of the pump is transferred to the converted signals with an additional 8-dB/Hz degradation.

Mohammed N. Islam

Papers

Modulation instability initiated high power all-fiber supercontinuum lasers and their applications

Color center lasers passively mode locked by quantum wells

All-optical cascadable NOR gate with gain.

Low-energy ultrafast fiber soliton logic gates.

Fiber parametric amplifiers for wavelength band conversion