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

Ultrafast processing of packets is demonstrated and the performance analyzed for the off-ramp portion of an all-optical access node. The off-ramp consists of synchronized fiber lasers driving an all-optical header processor that includes nonlinear optical loop mirrors (NOLM), electrooptic router, and demultiplexer in the form of a two-wavelength NOLM. We achieve switching contrasts of 10:1 for the header processor and demultiplexer with switching energies of 10 pJ and 1 pJ, respectively. Also, a proposed measurement technique to obtain eye diagrams is used to analyze the all-optical header processor using the synchronized lasers. Using this technique, we obtain an eye diagram with a Q value of 7.1/spl plusmn/0.36, which corresponds to a worst case BER value of 8.8/spl times/10/sup -12/ for a 95% confidence level. Finally, simulation models are used to verify and compare the experimental results, and we find good agreement. We also use the model to study the various causes for the degradation of the Q value through our system.

Demonstration and performance analysis for the off-ramp portion of an all-optical access node

In one aspect of the invention, an apparatus operable to facilitate optical signal processing includes a micro-electro-optic system (MEMS) device having a moveable mirror layer operable to receive a first copy of an input signal from a beam splitter and to reflect the first copy of the input signal for combination with a second copy of the input signal at an output to form an output signal. The moveable mirror layer being displaceable in a substantially piston-like motion to introduce a phase shift between the first and second signal copies at the output. The amplitude of the output signal varying depending on the displacement of the moveable mirror layer.

Apparatus and method for high speed optical signal processing

Summary form only given We generate >420 nm of supercontinuum (SC) by propagating pulses with energies <100 pJ through less than 2 m of dispersion-shifted fiber (DSF) in which the nonlinearity is enhanced by a factor of 45X over conventional DSF By using high nonlinearity (Hi-NL) fiber, we reduce required pulse energies by 56% while simultaneously increasing the bandwidth by 86 nm compared with SC generated in conventional DSF of the same length and dispersion We study the SC evolution as a function of pulse energy, fiber length and nonlinearity to find optimal conditions for maximum broadening without spectral distortion Fiber-based SC has been demonstrated as a promising candidate for TDM/WDM sources and is generated typically in several kilometers of dispersion-tailored fiber By generating the SC in a fiber shorter by three orders of magnitude, we obtain very stable pulses from the continuum and are able to accurately model the SC generation process The short fiber length, however, requires high average power sources at OC-192 repetition rates We reduce the average power required from a 10 Gb/s or OC-192 source to <550 mW by using 2 m of Hi-NL fiber

Low energy, enhanced supercontinuum generation in high nonlinearity dispersion-shifted fibers

A line scan interferometer, which comprises a visible supercontinuum source coupled to Fourier domain Michelson interferometer, is used to obtain 3D images of ~300 μm high solder balls on a semiconductor die with 125 nm axial and 15 μm lateral resolution. The ability to measure curved surfaces enables the determination of solder ball shape defects in addition to ball height. We show that the maximum measurable angular tilt from the sample surface normal for a given source power depends on the surface roughness of the sample. As an example, we demonstrate height measurement over +/-20 degrees from the normal on the solder balls and over +/-60 degrees on a rough steel ball bearing sample.

High resolution line scan interferometer for solder ball inspection using a visible supercontinuum source.

A tunable optical device includes a thin film device. The thin film device includes a plurality of cavities each including an electro-optic material. The electro-optic material includes an optical characteristic capable of being manipulated by application of an electric field. In this embodiment, at least some of the plurality of cavities are coherently coupled to others of the plurality of cavities. In this embodiment, the plurality of cavities include a sufficient number of cavities to result in an approximately square frequency response for the device.

Mohammed N. Islam

Papers

Demonstration and performance analysis for the off-ramp portion of an all-optical access node

Apparatus and method for high speed optical signal processing

Low energy, enhanced supercontinuum generation in high nonlinearity dispersion-shifted fibers

High resolution line scan interferometer for solder ball inspection using a visible supercontinuum source.

Square filter function tunable optical devices