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

An optical communication system includes a first end terminal comprising a first transponder operable to receive a first electrical signal and generate an optical signal based at least in part on the first electrical signal for communication to a multiple span communication link. The optical signal experiences at least partial dispersion compensation from an optical dispersion compensating element as it traverses the communication link. The system also includes a second end terminal comprising a second transponder operable to receive the optical signal and generate a second electrical signal based at least in part on the optical signal. At least one of the first and second end terminals further includes an electronic dispersion compensation module operable to provide electronic dispersion compensation to at least a portion of at least one of the first and second electrical signals. The electronic dispersion compensation module is operable to at least partially compensate for at least a portion of a residual dispersion for which the optical dispersion compensating element does not compensate.

System and method for dispersion compensation in an optical communication system

We report room‐temperature confinement and photoluminescence near 3 μm in a mercury cadmium telluride multiple quantum well. The absorption spectra show transitions from the first heavy and light hole confined levels to the first conduction electron confined level. Photoluminescence is present even at room temperature. The transition energies and temperature dependence of our data can be described by a square well model provided that a temperature‐independent value of approximately 400 meV is used for the HgTe‐CdTe valence‐band offset.

Room‐temperature confinement and photoluminescence near 3 μm from HgCdTe multiple quantum wells

An optical amplifier includes at least one Raman amplification stage. The Raman amplification stage includes one or more pump sources operable to generate a plurality of pump signals capable of being delivered to a gain medium carrying an optical signal. In one particular embodiment, at least one of the plurality of pump signals comprises a time modulated pump signal and wherein an amplified spontaneous emission penalty associated with the at least one time modulated pump signal comprises no more than fifteen (15) decibels.

Controlling ASE in optical amplification stages implementing time modulated pump signals

A multi-stage Raman amplifier (100) includes a first Raman amplifier stage (120) having a first sloped gain profile (30) operable to amplify a plurality of signal wavelengths (116), and a second Raman amplifier stage (121) having a second sloped gain profile (40) operable to amplify at least most of the plurality of signal wavelengths after those wavelengths have been amplified by the first stage. The second sloped gain profile is approximately complementary slope to the slope of the first sloped gain profile. The combined effect of the first and second Raman stages contributes to an approximately flat overall gain profile (50) over the plurality of signal wavelengths.

System and method for wide band raman amplification

We demonstrate a cascadable, Boolean complete, conservative-logic interaction gate that is based on elastic collisions between temporal solitons in optical fibers. The two identical-frequency and polarization inputs are initially separated by 4.5 pulse widths, and they interact in a 7.5 walk-off length of polarization-maintaining fiber. The group velocity of one of the inputs is altered by passing the pulse through a beam splitter with a wavelength-dependent reflection coefficient. Although details within the interaction region depend on the phase between the two inputs, after the pulses separate the result is phase independent. We find that each of two 17-pJ solitons is displaced after interaction by 3.5 pulse widths so as to increase the pulses' separation.

Mohammed N. Islam

Papers

System and method for dispersion compensation in an optical communication system

Room‐temperature confinement and photoluminescence near 3 μm from HgCdTe multiple quantum wells

Controlling ASE in optical amplification stages implementing time modulated pump signals

System and method for wide band raman amplification

Billiard-ball soliton interaction gates.