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 identify shape defects on ∼300µm high solder balls by measuring the 3D profile over +/−20 degrees down the ball surface. A broadband line scan interferometer enables measurement of ball height with 125nm axial resolution.

Measurement of solder ball height and shape defects using a visible supercontinuum based line scan interferometer

A GaAs-based surface-normal optical modulator using the free-carrier effect is demonstrated for the first time to our knowledge. The device exhibits ~43% modulation depth compared to 24% for a previously demonstrated Si-based device with twice the interaction length. Simulations predict ~1.8 times the speeds for GaAs-based devices compared to Si. Operation in conjunction with a supercontinuum source is used to characterize the wavelength response of the modulator. Potential for colorless operation makes the modulator a candidate for wavelength-division multiplexed networks with broadband light sources.

GaAs-based surface-normal optical modulator compared to Si and its wavelength response characterization using a supercontinuum laser.

A medical device includes an insertable portion capable of being inserted into an orifice associated with a body of a patient. The insertable portion comprising an automated head unit capable of being manipulated in at least two axes of motion based at least in part on one or more control signals. The medical device further includes one or more controllers coupled to the automated head unit. In one particular embodiment, the one or more controllers generate the one or more control signals based at least in part on an input signal.

System and method for generating infrared light for use in medical procedures

We experimentally demonstrate the adding, dropping, and passing
through of 100-Gbit/s word packets in a looped-back all-optical
time-division-multiplexed (TDM) access node Packets are routed
with a 17-dB contrast ratio and demultiplexed with a 20-dB contrast
ratio This node uses short 100-Gbit/s words to demonstrate its
potential to process data packets from multiple sources and to perform
packet switching in a multinode ring network configuration The
ability to tolerate timing jitter as well as varying input signal
characteristics is essential to an all-optical access node in a
multinode network For 2-ps input pulses, the header processor has
a timing window of ∼5 ps, and the demultiplexer has a timing window
of ∼55 ps This allows for tolerance to bit-to-bit timing
jitters or to an increase in the pulse width of as much as 3
ps Packet-to-packet timing jitter is detected and compensated by
the technique used to synchronize the local source to each
packet The key enabling technologies of an all-optical TDM packet
add–drop multiplexer are discussed, including an erbium-doped fiber
laser, a nonlinear optical loop mirror logic gate, self-synchronization
to incoming packets with a fast-saturation/slow-recovery gain element
followed by an intensity discriminator, a two-wavelength nonlinear
optical loop mirror demultiplexer, and synchronization of new packets
to the network packet rate with a phase-locked loop The local
source is automatically synchronized to the incoming packet, because it
uses an extracted pulse from the packet, which has a contrast ratio of
>20 dB to the rest of the packet Finally, new packets are added
by use of a local laser and a synchronization method, which gives a
timing jitter of ∼1 ps Using a statistical method of measuring
Q value with picosecond resolution, we show that a
header processor with two cascaded logic gates has a Q
value of 71 with a 95% confidence level

All-optical 100-Gbit/s word packet time-division-multiplexed access node in a looped-back configuration: enabling technologies for sequential add-drop functionality.

We show that fiber logic gates based on soliton interactions can be shortened to less than a soliton period in length by incorporating erbium-doped fiber amplifiers (EDFA’s) into the switches. For example, we describe an all-optical, cascadable logic gate with a fan-out of 2.7 and energy contrast of 5.5 in a soliton-period-long, moderately birefringent EDFA. We compare two configurations: a distributed amplifier, in which the solitons interact while being amplified, and a discrete amplifier, in which the pulses are amplified before interacting. Although asymmetric walk-off and rapid amplification during interaction may play a role in the distributed amplifier, the primary benefit of introducing EDFA’s appears to be the resulting high pulse intensities.

Mohammed N. Islam

Papers

Measurement of solder ball height and shape defects using a visible supercontinuum based line scan interferometer

GaAs-based surface-normal optical modulator compared to Si and its wavelength response characterization using a supercontinuum laser.

System and method for generating infrared light for use in medical procedures

All-optical 100-Gbit/s word packet time-division-multiplexed access node in a looped-back configuration: enabling technologies for sequential add-drop functionality.

Low-latency soliton logic gates in erbium-doped fiber amplifiers