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

We experimentally measure the scattered reflectance of particles deposited on smooth substrates with a mid-wave to long-wave supercontinuum source and a FTIR based sensor at 36 m We measure the scattering return from sparse particles of 1,3,5-Trinitroperhydro-1,3,5-triazine, caffeine, and acetaminophen deposited on smooth aluminum, silicon, and glass substrates We also measure mono-disperse 54, 108, and 194  μm diameter polystyrene spheres deposited on aluminum We demonstrate that spectra obtained using our supercontinuum FTIR sensor can be accurately simulated using a Bobbert–Vlieger model, and non-spherical particle spectra can be approximated by spherical results The Bobbert–Vlieger model can then be used to create a library that can account for the trace chemical and underlying substrate for standoff chemical identification

Long-wave infrared scattering spectra and modeling of trace particles on surfaces for standoff detection

Low-latency Soliton Logic Gate In EDFA's

We place an erbium-doped fiber amplifier (EDFA) in the interaction region between orthogonally polarized control and signal pulses to widen the timing window for a soliton-dragging logic gate (SDLG). In general, the two inputs to an SDLG must overlap within a pulse width to obtain a time shift at the device output However, by introducing gain during the interaction between the two pulses, we can asymmetrize the walk-off and, thereby, broaden the timing window [1].

Soliton-Dragging Logic Gate with an Erbium-Doped Fiber Amplifier

Summary form only given.We enhance the gain of fiber-optic parametric amplifier (PA) by >6 dB by quasi-phase matching (QPM) the pump and signal waves. In a PA with 96 m dispersion-shifted (DS) fiber and 16 W peak pump power, we realize QPM by inserting 6 m SMF-28 fiber at 50 m point. Due to the abrupt phase change by SMF-28, the maximum gain is increased from 3.7 dB to 9.8 dB. Simulation shows that QPM causes unidirectional flow of energy from pump to signal and >13 dB gain enhancement can be obtained with three-stage QPM PA. With QPM technique, it is possible to solve the problem of low PA gain without using near-/spl lambda//sub 0/ pumping or high nonlinearity fiber.

Quasi-phase-matched fiber-optic parametric amplifier and gain enhancement

An apparatus and method are described for combining optical amplification and dispersion compensation in a Raman amplifier (Fig. 4a). Dispersion-Managing Raman Amplifier (DMRA) (Fig. 4a) combines Raman amplification with dispersion compensation by selecting the length and dispersion of the gain fiber (100) to balance the dispersion of the link. The pumping level is adjusted to balance the losses from the gain fiber (100) and transmission link (130). For WDM transmission systems based on dispersion-shifted fiber (DSF), operation in the 'violet band' between 1430-1530 nm is based on Raman amplification. By using a DMRA (550), a dispersion (510) and nonlinearity managed system can be implemented. Furthermore, gain equalization can be added to the DMRA by cascading one or two Mach-Zehnder frequency filters. The invention also includes a method for symmetrically adding channels below and above the C-band, the gain tilt within the C-band can be minimized. To minimize the interaction between pumps for different bands (Fig. 16d), alternate band pumps can be spatially dispersed and/or cross-polarized (Fig. 16d).

Dispersion compensating and amplifying optical element, method for minimizing gain tilt and apparatus for minimizing non-linear interaction between band pumps

Mohammed N. Islam

Papers

Long-wave infrared scattering spectra and modeling of trace particles on surfaces for standoff detection

Low-latency Soliton Logic Gate In EDFA's

Soliton-Dragging Logic Gate with an Erbium-Doped Fiber Amplifier

Quasi-phase-matched fiber-optic parametric amplifier and gain enhancement

Dispersion compensating and amplifying optical element, method for minimizing gain tilt and apparatus for minimizing non-linear interaction between band pumps