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

A Mid-InfraRed FIber Laser (MIRFIL) has been developed that generates super-continuum covering the spectral range
from 0.8 to 4.5 microns with a time-averaged power as high as 10.5W. The MIRFIL is an all-fiber integrated laser with
no moving parts and no mode-locked lasers that uses commercial off-the-shelf parts and leverages the mature
telecom/fiber optics platform. The MIRFIL power can be easily scaled by changing the repetition rate and modifying
the erbium-doped fiber amplifier. Some of the applications using the super-continuum laser will be described in defense,
homeland security and healthcare. For example, the MIRFIL is being applied to a catheter-based medical diagnostic
system to detect vulnerable plaque, which is responsible for most heart attacks resulting from hardening-of-the-arteries
or atherosclerosis. More generally, the MIRFIL can be a platform for selective ablation of lipids without damaging
normal protein or smooth muscle tissue.

Mid-IR super-continuum generation

In one aspect of the invention, an apparatus operable to facilitate add/drop multiplexing of optical signals includes an input operable to receive an input optical signal and an added optical signal, the input operable to generate a first and a second copy of the input signal and a first and a second copy of the added signal. The apparatus further includes a plurality of at least substantially reflective surfaces, each operable to receive either the first signal copies or the second signal copies and to reflect the copies for ultimate combination at an output to form an output signal for transmission. At least one of the at least substantially reflective surfaces comprises a moveable mirror operable to change its position relative to the input to create a phase shift between the first and second signal copies so that either the input optical signal or the added optical signal is communicated as the output signal depending on the position of the at least one moveable mirror.

Apparatus and method for optical add/drop multiplexing

The timing restrictions for soliton-dragging logic gates can be relaxed by asymmetrizing the interaction between the orthogonally polarized control and signal pulses. In particular, by prechirping the signal pulse in a normal group-velocity dispersion fiber, we find experimentally that the timing restriction can be loosened from less than 2 pulse widths to over 3.3 pulse widths. For this passive prechirper arrangement the timing restrictions are loosened at the expense of increased minimum switching energy. Soliton-dragging logic gates with a signal prechirper can provide timing restoration as well as logic-level restoration, so that two inverter gates can be cascaded to implement an ultrafast, all-optical pulse regenerator.

Prechirper to relax the timing restrictions for soliton-dragging logic gates.

We experimentally demonstrate switching in a 50 m-long soliton logic gate with a switching energy of 40 pJ using 490 fs pulses at 1.553 /spl mu/m from an erbium-doped fiber laser. A full characterization of this gate shows a peak contrast ratio of 4.2:1, a timing window of 1.1 pulse width and cascadable operation. To our knowledge, the gate length of 50 m is at least six times shorter than other designs with comparable switching energies. The low-latency of this gate is possible due to a low-birefringent polarization-maintaining fiber that possesses a high polarization extinction ratio of up to 20 dB with a low birefringence of 2.6/spl times/10/sup -6/. The low birefringence leads to a longer walk-off length between two orthogonally polarized pulses, where the walk-off length for 490 fs pulses is 56 m. We also study this gate numerically and find good agreement between the simulations and experiments.

Experimental demonstration of a low-latency fiber soliton logic gate

In one aspect of the invention, a method of amplifying optical signals includes identifying one of a plurality of pump signals driving an amplification system as a failing pump signal comprising a reduced power compared to a normal power of the failing pump signal. The method further includes adjusting the power of at least one other of the plurality of pump signals based at least in part on the failing pump signal to at least partially compensate for a degradation of performance of the amplification system that would otherwise be caused by the reduction in power of the failing pump signal.

Mohammed N. Islam

Papers

Mid-IR super-continuum generation

Apparatus and method for optical add/drop multiplexing

Prechirper to relax the timing restrictions for soliton-dragging logic gates.

Experimental demonstration of a low-latency fiber soliton logic gate

High reliability optical amplification