Modulation instability and pattern formation in spatially incoherent light beams

Tailoring Two-Dimensional Matter Using Strong Light-Matter Interactions

The shaping of matter into desired nanometric structures with on-demand functionalities can enhance the miniaturization of devices in nanotechnology. Herein, strong light-matter interaction was used as an optical lithographic tool to tailor two-dimensional (2D) matter into nanoscale architectures. We transformed 2D black phosphorus (BP) into ultrafine, well-defined, beyond-diffraction-limit nanostructures of ten times smaller size and a hundred times smaller spacing than the incident, femtosecond-pulsed light wavelength. Consequently, nanoribbons and nanocubes/cuboids scaling tens of nanometers were formed by the structured ablation along the extremely confined periodic light fields originating from modulation instability, the tailoring process of which was visualized in real time via light-coupled in situ transmission electron microscopy. The current findings on the controllable nanoscale shaping of BP will enable exotic physical phenomena and further advance the optical lithographic techniques for 2D materials.

Filamented Light (FLight) Biofabrication of Highly Aligned Tissue-Engineered Constructs

Cell-laden hydrogels used in tissue engineering generally lack sufficient 3D topographical guidance for cells to mature into aligned tissues. A new strategy called filamented light (FLight) biofabrication rapidly creates hydrogels composed of unidirectional microfilament networks, with diameters on the length scale of single cells. Due to optical modulation instability, a light beam is divided optically into FLight beams. Local polymerization of a photoactive resin is triggered, leading to local increase in refractive index, which itself creates self-focusing waveguides and further polymerization of photoresin into long hydrogel microfilaments. Diameter and spacing of the microfilaments can be tuned from 2 to 30 µm by changing the coherence length of the light beam. Microfilaments show outstanding cell instructive properties with fibroblasts, tenocytes, endothelial cells, and myoblasts, influencing cell alignment, nuclear deformation, and extracellular matrix deposition. FLight is compatible with multiple types of photoresins and allows for biofabrication of centimeter-scale hydrogel constructs with excellent cell viability within seconds (<10 s per construct). Multidirectional microfilaments are achievable within a single hydrogel construct by changing the direction of FLight projection, and complex multimaterial/multicellular tissue-engineered constructs are possible by sequentially exchanging the cell-laden photoresin. FLight offers a transformational approach to developing anisotropic tissues using photo-crosslinkable biomaterials.

Selection and cloning of periodic optical patterns with a cold Rydberg atomic gas

We show that periodic optical patterns formed in a cold Rydberg atomic gas via electromagnetically induced transparency (EIT) can be selected by using a weakly modulated control laser field. We also show that the (hexagonal, stripe, square, etc.) patterns prepared in one probe laser field can be cloned onto another one with high fidelity via a double EIT.

Near-infrared image recovery based on modulation instability in CdZnTe:V

We propose a near-infrared image recovery method based on modulation instability in the photorefractive semiconductor CdZnTe:V. The formation mechanism of modulation instability in CdZnTe:V is discussed, and the theoretical gain model is derived. Theoretical results of optical image recovery at 1 µm and 1.5 µm wavelengths demonstrate that the maximum cross-correlation gain is 2.6 with a signal to noise intensity ratio of 0.1. These results suggest that our method could be one of potential aids for near-infrared imaging.

Nonlinear Localization of Dissipative Modulation Instability

Modulation instability (MI) in the presence of noise typically leads to an irreversible and complete disintegration of a plane wave background. Here we report on experiments performed in a coherently driven nonlinear optical resonator that demonstrate nonlinear localization of dissipative MI: formation of persisting domains of MI-driven spatiotemporal chaos surrounded by a stable quasi-plane-wave background. The persisting localization ensues from a combination of bistability and complex spatiotemporal nonlinear dynamics that together permit a locally induced domain of MI to be pinned by a shallow modulation on the plane wave background. We further show that the localized domains of spatiotemporal chaos can be individually addressed-turned on and off at will-and we explore their transport behavior as the strength of the pinning is controlled. Our results reveal new fundamental dynamics at the interface of front dynamics and MI, and offer a route for tailored patterns of noiselike bursts of light.

Optical polarization rogue waves and their identifications

Optical rogue waves are a class of pulses with extremely large amplitudes, whose probability of occurrence unexpectedly deviates from Gaussian-law statistics. To date, the mechanisms of rogue wave generation are still debated: investigations are under way, exploring the statistics of various pulse dimensions across different physical domains. Although polarization is one of the fundamental parameters of optical rogue waves, its statistics have received little attention until recently. Here, we review recent process of the polarization-dependent properties of optical rogue waves in ultrafast optics. Based on a two-dimensional statistical model, we introduce the concept of optical polarization rogue waves. Specifically, we consider the frequency of generation of waves with freak or rogue state of polarization, with a probability of occurrence deviating from a normal distribution. We demonstrate three nonlinear optical laser systems: a partially mode-locked laser, a dissipative soliton laser, and supercontinuum generation within a highly nonlinear fiber. Further, we identify optical polarization rogue waves in nonlinear laser systems, and discuss their generation mechanisms. Related results reveal that optical polarization rogue waves are embedded in optical systems with a deteriorated degree of coherence, which originates from vector four-wave-mixing processes. Polarization-dependent investigations will provide additional insight for our understanding of optical rogue waves.

Discrete image recovery via stochastic resonance in optically induced photonic lattices

We demonstrate numerically the discrete image recovery via stochastic resonance in optically induced photonic lattices. The underlying signals are regularly reinforced at the expense of scattering noise with the interplay of the periodic potentials and the self-focusing nonlinearity. We founded that the energy redistribution tends to be periodic and the signal reinforcement is promoted with the help of periodic potentials. The lattice intensity levels, applied voltages, and correlation lengths are important parameters to influence the recovery effects. The dynamic nonlinear evolution including intensity and power spectrum is modeled according to the two-dimensional quasi-particle motion model. Our results suggest a potential technology to detect the noisy images.

Nonlinear reconstruction of weak optical diffused images under turbid water

Forward scattering noise may degrade the imaging resolution and diffuse the image in turbid water. The reconstruction of diffused images hidden by forward scattering noise is crucial for underwater imaging. To overcome the limitation of forward scattering for optical imaging in turbid water, a nonlinear image reconstruction technology is proposed in the experiment. We experimentally demonstrated the reconstruction of the diffused images under turbid water via signal seeded incoherent modulation instability (MI) in a nonlinear photorefractive crystal. The reconstructed image with high quality and the minimum resolution of 28.51 lp/mm are observed in the experiment. This is the first time, to the best of our knowledge, that a spatial MI effect is used to process underwater weak optical diffused images in the experiment.

A soft photopolymer cuboid that computes with binary strings of white light

Next-generation stimuli–responsive materials must be configured with local computational ability so that instead of a discrete on-off responsiveness, they sense, process and interact reciprocally with environmental stimuli. Because of their varied architectures and tunable responsiveness to a range of physical and chemical stimuli, polymers hold particular promise in the generation of such “materials that compute”. Here, we present a photopolymer cuboid that autonomously performs pattern recognition and transfer, volumetric encoding and binary arithmetic with incandescent beams. The material’s nonlinear response to incident beams generates one, two or three mutually orthogonal ensembles of white-light filaments, which respectively self-organize into disordered, 1-D and 2-D periodic geometries. Data input as binary (dark-bright) strings generate a unique distribution of filament geometries, which corresponds to the result of a specific operation. The working principles of this material that computes with light is transferrable to other nonlinear systems and incoherent sources including light emitting diodes.

Some next-generation computing may be based in physical systems that respond directly and reciprocally to environmental stimuli. Here, the authors describe a photoresponsive material that autonomously performs computations with incident beams of incoherent white light.

Spin-current-mediated rapid magnon localisation and coalescence after ultrafast optical pumping of ferrimagnetic alloys

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of a universal rapid magnetic order recovery in ferrimagnets with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify magnon localisation and coalescence processes, whereby localised magnetic textures nucleate and subsequently interact and grow in accordance with a power law formalism. A hydrodynamic representation of the numerical simulations indicates that the appearance of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of 107 A cm-2. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. The magnon processes discussed here provide new insights for the stabilization of desired meta-stable states.

Reconstruction of an underwater scattered image via incoherent modulation instability

A technology of reconstructing a scattered image from turbid underwater is proposed, which is via stochastic resonance based on incoherent modulation instability in a noninstantaneous nonlinear medium. When intensity-dependent nonlinearity exceeds the threshold imposed by attenuation and scattering, instability preferentially reinforces the underlying signal modes at the expense of neighbor highly incoherent noise modes. Due to the directional energy transfer, noise-hidden signal images are effectively reconstructed with a cross-correlation gain high of 3.56. Results in turbid suspension demonstrated the wide applications of image detection in various dynamic scattering environments.

Programmable time-domain digital-coding metasurface for non-linear harmonic manipulation and new wireless communication systems

Optical non-linear phenomena are typically observed in natural materials interacting with light at high intensities, and they benefit a diverse range of applications from communication to sensing. However, controlling harmonic conversion with high efficiency and flexibility remains a major issue in modern optical and radio-frequency systems. Here, we introduce a dynamic time-domain digital-coding metasurface that enables efficient manipulation of spectral harmonic distribution. By dynamically modulating the local phase of the surface reflectivity, we achieve accurate control of different harmonics in a highly programmable and dynamic fashion, enabling unusual responses, such as velocity illusion. As a relevant application, we propose and realize a novel architecture for wireless communication systems based on the time-domain digital-coding metasurface, which largely simplifies the architecture of modern communication systems, at the same time yielding excellent performance for real-time signal transmission. The presented work, from new concept to new system, opens new pathways in the application of metamaterials to practical technology.

Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification

Convolutional neural networks (CNNs) excel in a wide variety of computer vision applications, but their high performance also comes at a high computational cost. Despite efforts to increase efficiency both algorithmically and with specialized hardware, it remains difficult to deploy CNNs in embedded systems due to tight power budgets. Here we explore a complementary strategy that incorporates a layer of optical computing prior to electronic computing, improving performance on image classification tasks while adding minimal electronic computational cost or processing time. We propose a design for an optical convolutional layer based on an optimized diffractive optical element and test our design in two simulations: a learned optical correlator and an optoelectronic two-layer CNN. We demonstrate in simulation and with an optical prototype that the classification accuracies of our optical systems rival those of the analogous electronic implementations, while providing substantial savings on computational cost.

Gain through losses in nonlinear optics

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied. In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing gain through losses. We discuss the concept of imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

Resonance in modulation instability from non-instantaneous nonlinearities

To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability from non-instantaneous nonlinearities in photorefractive crystals. With a temporally periodic modulation in the external bias voltage, corresponding to a modulation in the nonlinear strength, an enhancement in the visibility of MI at resonant frequency is reported through spontaneous optical pattern formations. Theoretical curves obtained from a nonlinear non-instantaneous Schrödinger equation give good agreement to experimental data.

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Light amplification by seeded Kerr instability

Amplification of femtosecond laser pulses typically requires a lasing medium or a nonlinear crystal. In either case, the chemical properties of the lasing medium or the momentum conservation in the nonlinear crystal constrain the frequency and the bandwidth of the amplified pulses. We demonstrate high gain amplification (greater than 1000) of widely tunable (0.5 to 2.2 micrometers) and short (less than 60 femtosecond) laser pulses, up to intensities of 1 terawatt per square centimeter, by seeding the modulation instability in an Y₃Al₅O₁₂ crystal pumped by femtosecond near-infrared pulses. Our method avoids constraints related to doping and phase matching and therefore can occur in a wider pool of glasses and crystals even at far-infrared frequencies and for single-cycle pulses. Such amplified pulses are ideal to study strong-field processes in solids and highly excited states in gases.

Observation of gain spiking of optical frequency comb in a microcavity

Optical frequency combs are crucial for both fundamental science and applications that demand a wide frequency range and ultra-high resolution. Recent advances in optical frequency combs based on the nonlinear Kerr effect in microcavities have opened up new opportunities with such compact platforms. Although optical frequency combs have previously been well studied in the steady state, some fundamental perspectives such as nonlinear phase modulation during comb generations are yet explored. Here we demonstrate transient nonlinear dynamics during the formation of optical frequency combs inside a Kerr microcavity. We show that gain spiking forms due to nonlinear phase modulation causing comb lines' self-detuning from nearby cavity resonances, which provides one key mechanism to stabilize optical frequency combs. Moreover, we have observed nonlinear beating by injecting an external probe to examine nonlinear cross-phase modulation between comb lines. These nonlinear dynamics reveal the hidden features of self-stabilization and cross modulation during transient comb generations, which may enable new applications in mode-locking comb and tunable comb generation in microcavities.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Strong amplitude and phase modulation of optical spatial coherence with surface plasmon polaritons

The degree of optical spatial coherence-a fundamental property of light that describes the mutual correlations between fluctuating electromagnetic fields-has been proven challenging to control at the micrometer scale. We use surface plasmon polaritons-evanescent waves excited on both surfaces of a thin metal film-as a means to mix the random fluctuations of the incident electromagnetic fields at the slit locations of a Young's double-slit interferometer. Strong tunability of the complex degree of spatial coherence of light is achieved by finely varying the separation distance between the two slits. Continuous modulation of the degree of spatial coherence with amplitudes ranging from 0 to 80% allows us to transform totally incoherent incident light into highly coherent light and vice versa. These findings pave the way for alternative methods to engineer flat optical elements with multifunctional capabilities beyond conventional refractive- and diffractive-based photonic metasurfaces.

Stochastic resonance based on modulation instability in spatiotemporal chaos

A novel dynamic of stochastic resonance in spatiotemporal chaos is presented, which is based on modulation instability of perturbed partially coherent wave. The noise immunity of chaos can be reinforced through this effect and used to restore the coherent signal information buried in chaotic perturbation. A theoretical model with fluctuations term is derived from the complex Ginzburg-Landau equation via Wigner transform. It shows that through weakening the nonlinear threshold and triggering energy redistribution, the coherent component dominates the instability damped by incoherent component. The spatiotemporal output showing the properties of stochastic resonance may provide a potential application of signal encryption and restoration.

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.

Low amplitude noise on an otherwise constant-intensity wave can grow exponentially and induce nonlinear dynamical behaviour. Here, the authors present time-domain measurements of a phenomenon arising from such modulation instability: the emergence of highly localised breathers in an optical fibre.

Nonlinear restoration of pulse and high noisy images via stochastic resonance

We propose a novel scheme for restoring pulse and high noisy images using stochastic resonance, which is based on the modulation instability and provides a cross-correlation gain higher than 8. As opposed to previously reported designs, this unique approach employs a continuous noise and pulse signal for the generation of modulation instability. The visibility and quality of output images can be improved by appropriately adjusting the system parameters. This provides a simple and feasible method for detecting low-level or hidden pulse images in various imaging applications.

Nonlinear spin-wave excitations at low magnetic bias fields

Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. Here we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni₈₀Fe₂₀ thin films. Our data show that the common model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behaviour in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes.

Nonlinear magnetization dynamics underlie the operation of important spintronic devices. Here, the authors study NiFe thin films via X-ray magnetic circular dichroism, to develop a model for nonlinear spin-wave excitation by ferromagnetic resonance under small applied magnetic fields.

Rogue waves lead to the instability in GaN semiconductors

A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors.

Constant-intensity waves and their modulation instability in non-Hermitian potentials

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

Reconstruction of pulse noisy images via stochastic resonance

We investigate a practical technology for reconstructing nanosecond pulse noisy images via stochastic resonance, which is based on the modulation instability. A theoretical model of this method for optical pulse signal is built to effectively recover the pulse image. The nanosecond noise-hidden images grow at the expense of noise during the stochastic resonance process in a photorefractive medium. The properties of output images are mainly determined by the input signal-to-noise intensity ratio, the applied voltage across the medium, and the correlation length of noise background. A high cross-correlation gain is obtained by optimizing these parameters. This provides a potential method for detecting low-level or hidden pulse images in various imaging applications.

Control modulation instability in photorefractive crystals by the intensity ratio of background to signal fields

By experimental measurements and theoretical analyses, we demonstrate the control of modulation instability in photorefractive crystals though the intensity ratio of coherent background to signal fields. Appearance, suppression, and disappearance of modulated stripes are observed in a series of spontaneous optical pattern formations, as the intensity of input coherent beam increases. Theoretical curves based on the band transport model give good agreement to experimental data, both for different bias voltages and different intensity ratios.

Hidden image recovery using a biased photorefractive crystal in the Fourier plane of an optical imaging system

Self-diffraction can be induced using a biased photorefractive crystal in the Fourier plane of an imaging system where the light beam intensity is naturally high due to the concentration effect of an optical lens. The spatial frequency spectrum of the output image is proportional to the optical power density distribution in the Fourier plane. A photorefractive crystal with small size can be used and hence an reduced amount of biased voltage is needed to obtain significant diffraction effect in the image plane. When the input image is an overlay of a signal and a noise pattern, theoretic model reveals that the induced diffraction in the Fourier plane may be preferably applied on the noise pattern. In order to illustrate the effect experimentally, a signal from a weakly illuminated object is coupled with an overwhelming noise pattern and then the hidden signal is successfully recovered using a SBN61 crystal with an applied voltage of 800 V in the Fourier plane. Such technology can be employed in encrypted spatial communication systems for security purposes.

Incoherent resonant seeding of modulation instability in optical fiber

We report control of the spectral and noise properties of spontaneous modulation instability (MI) in optical fiber using an incoherent seed with power at the 10(-6) level relative to the pump. We sweep the seed wavelength across the MI gain band, and observe significant enhancement of MI bandwidth and improvement in the signal-to-noise ratio as the seed coincides with the MI gain peak. We also vary the seed bandwidth and find a reduced effect on the MI spectrum as the seed coherence decreases. Stochastic nonlinear Schrödinger equation simulations of spectral and noise properties are in excellent agreement with experiment.

Self-localized states in photonic topological insulators

We propose solitons in a photonic topological insulator: self-localized wave packets forming topological edge states residing in the bulk of a nonlinear photonic topological insulator. These self-forming entities exhibit, despite being in the bulk, the property of unidirectional transport, similar to the transport their linear counterparts display on the edge of a topological insulator. In the concrete case of a Floquet topological insulator, such a soliton forms when a wave packet induces, through nonlinearity, a defect region in a honeycomb lattice of helical optical waveguides, and at the same time the wave packet populates a continuously rotating outer (or inner) edge state of that region. The concept is universal and applicable to topological systems with nonlinear response or mean-field interactions.

Observation of photorefractive surface waves in self-defocusing LiNbO3:Fe crystal

Photorefractive (PR) surface waves (SWs) in self-defocusing LiNbO(3):Fe are studied theoretically and experimentally. We demonstrate that SWs can also be formed in a self-defocusing nonlinear medium and that the nonlocal nonlinearity (such as the diffusion component of PR nonlinearity in this Letter) is the essential cause. The forming process of PR SWs with a self-deflection course of light beams has been observed. The results indicate the possibility of concentrating light energy in self-defocusing media, taking advantage of SWs.

Optochemical organization in a spatially modulated incandescent field: a single-step route to black and bright polymer lattices

We report that incandescent beams patterned with amplitude depressions (dips) suffer instability in a photopolymerizable system and organize into lattices of black and bright self-trapped beams propagating respectively, through self-induced black and bright waveguides. Such optochemically organized lattices emerge when beams embedded with a hexagonal or square array of dips initiate free-radical polymerization and corresponding changes in refractive index (Δn) along their propagation paths. Under these nonlinear conditions, the dips evolve into a hexagonal or square lattice of black beams, while their bright interstitial regions become unstable and divide spontaneously into multiple filaments of light. These filaments have a characteristic diameter (d(f)) and organize into a variety of geometries, which are determined by the shape and dimensions of the bright interstices. At interstitial widths > 2d(f), filaments are randomly positioned in space, whereas at widths < 2d(f), the interstices are occupied by a single file of filaments encircling each dark channel. When the interstitial width ≈ d(f), the filaments organize into lattices with long-range hexagonal or square symmetry. By employing anisotropic interstices such as rectangles, filamentation can be selectively elicited along the long axis, leading to a lattice of filament doublets. This work demonstrates the versatility and significant potential of optochemical organization to generate complex, optically functional polymer lattices, which cannot be constructed through conventional lithography or self-assembly. Specifically, the study introduces a new generation of waveguide lattices, in which light propagation is co-operatively managed by black and bright waveguides; the former suppress local light propagation and, in this way, enhance light confinement and guidance in proximal bright waveguides.

Oscillons, solitons, and domain walls in arrays of nonlinear plasmonic nanoparticles

The study of metal nanoparticles plays a central role in the emerging novel technologies employing optics beyond the diffraction limit. Combining strong surface plasmon resonances, high intrinsic nonlinearities and deeply subwavelength scales, arrays of metal nanoparticles offer a unique playground to develop novel concepts for light manipulation at the nanoscale. Here we suggest a novel principle to control localized optical energy in chains of nonlinear subwavelength metal nanoparticles based on the fundamental nonlinear phenomenon of modulation instability. In particular, we demonstrate that modulation instability can lead to the formation of long-lived standing and moving nonlinear localized modes of several distinct types such as bright and dark solitons, oscillons, and domain walls. We analyze the properties of these nonlinear localized modes and reveal different scenarios of their dynamics including transformation of one type of mode to another. We believe this work paves a way towards the development of nonlinear nanophotonics circuitry.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Self-induced transparency in diblock copolymer dispersions

We report on the versatile effect of weak red laser light impinging on diblock copolymer [poly(isoprene-b-styrene)] dispersions in two selective solvents for each block. In the strongly scattering but transparent micellar solutions in hexane (a good solvent for polyisoprene), higher refractive index copolymer-rich fibers were formed. In the turbid dispersions of the same copolymer in ethyl acetate (a good solvent for polystyrene), the effect of self-induced transparency was observed. A two-step patterning mechanism caused the generation of a transparent microchannel, increasing light transmission. The analogy between the current effect and that observed in homopolymer polyisoprene solutions in different solvents is discussed toward an understanding of the unanticipated light-soft-matter interaction.

Spectral dynamics of spatially incoherent modulation instability

To date, all experiments in nonlinear statistical optics have relied on beams whose transverse spatial statistics were Gaussian. Here, we present a new technique to generalize these studies by using a spatial light modulator to create spatially incoherent beams with arbitrary spectral distributions. As a specific example of the new dynamics possible, we consider the spatial modulation instability of a partially coherent beam. We show that, for statistical beams of uniform intensity and equal correlation length, the underlying spectral shape determines the threshold and visibility of intensity modulations as well as the spectral profile of the growing sidebands. We demonstrate the behavior using statistical light, but the results will hold for any wave-kinetic system, such as plasma, ultracold gases, and turbulent acoustic waves.

Vortex induced rotation dynamics of optical patterns

We demonstrate that modulation instability leading to optical pattern formation can arise by using nonconventional counterpropagating beams carrying an orbital angular momentum (optical vortices). Such a vortex beam is injected into a nonlinear single feedback system. We evidence different complex patterns with peculiar phase singularities and rotating dynamics. We prove that the dynamics is induced by the vortex angular momentum and the rotation velocity depends nonlinearly on both the vortex topological charge and the intensity of the input beam.

Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays

We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasiperiodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and moving oscillating nonlinear localized modes--plasmon oscillons.

Instability-driven recovery of diffused images

We demonstrate the nonlinear recovery of diffused images in a self-focusing photorefractive medium. The method is based on the convolution property of nonlinearity, in which related modes reinforce each other as they propagate. The resulting mode coupling enables energy transfer from the scattered light to the underlying signal. The dynamics is well described by a model in which the signal seeds a modulation instability in the diffused background.

Pattern formation using optical vortices in a photorefractive single feedback system

We analyze numerically the dynamics of optical patterns in a photorefractive single feedback system where a vortex beam is used as the input beam. Depending on the topological charge of the vortex and on the nonlinear photorefractive coupling strength, we observe different pattern geometries with a rotating dynamics.

Diffraction from an edge in a self-focusing medium

We experimentally demonstrate diffraction from a straight edge in a medium with self-focusing nonlinearity. Diffraction into the shadow region is suppressed with increasing nonlinearity, but mode coupling leads to excitations and traveling waves on the high-intensity side. Theoretically, we interpret these modulations as spatially dispersive shock waves with negative pressure.

Modulation instability of a coherent-incoherent mixture

We examine the nonlinear coupling and modulation instability of a coherent beam with one that is partially spatially incoherent. Using a mutual coherence approach, we derive the growth rate for perturbations and show that the presence of any amount of coherent component eliminates the nonlinear threshold for instability. The fraction of coherent light is shown to determine the gain and characteristic period of the resulting patterns. Theoretical considerations are confirmed by numerical simulation and by experimental observations in a self-focusing photorefractive crystal.

Nonlinear focusing and defocusing of partially coherent spatial beams

We consider the propagation of a partially coherent spatial beam in both self-focusing and self-defocusing nonlinear media. Using a Gaussian-Schell model, we derive an equation governing the width of highly incoherent beams as they propagate in both types of media and confirm its validity by using numerical simulations. Experiments performed in a biased photorefractive crystal match the predicted scaling.

Spectral dynamics of spatially incoherent bump-on-tail instability

We examine an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially incoherent spatial beams. Using a radiation transport approach, we develop plasmalike dispersion relations for perturbation modes and show that a positive gradient in the power spectrum can trigger instability. Theoretical considerations are confirmed by experiment and numerical simulation.

Excitation of chaotic spin waves through modulational instability

This Letter reports the first experimental demonstration of chaotic excitations through modulational instability for waves with a repulsive nonlinearity. The experiments were carried out for surface spin waves in a magnetic thin film strip in an active feedback ring configuration. At a low ring gain level, one observes the self-generation of one eigenmode. With an increase in the ring gain, one observes the production of additional modes and the onset and enrichment of chaotic behaviors.

Generation of broadband two-dimensional multicolored arrays in a sapphire plate

Broadband 2-D multicolored arrays with more than ten periodic columns and more than ten rows were generated in a sapphire plate using two crossed femtosecond laser beams overlapping in time and space. These multicolored 2-D arrays were sensitive to rotation of the sapphire plate in the plane normal to the incident beams. The broadband spectrum, pulse duration less than 40fs, and less than 1%RMS power stability of the array signals make them well suited for various applications, for example multicolor pump-probe experiments.

Spatiotemporal pulse-train solitons

We propose spatiotemporal solitons that consist of trains of short pulses. The pulses are collectively trapped in the transverse directions by a slow nonlinearity and each pulse is self-trapped in the longitudinal direction by a fast nonlinearity. We demonstrate numerically spatiotemporal bright pulse-train solitons (trains of light bullets) and temporally-dark spatiotemporal pulse-train solitons in an experimentally feasible scheme.

Optical pattern transitions from modulation to transverse instabilities in photorefractive crystals

We show by experimental measurements and theoretical analyses that there exists a pattern transition from optical modulation instability to transverse instability in nonlinear media. An input coherent beam propagating in the photorefractive crystals is observed to break up into stripe filaments at a first threshold voltage. By modeling the periodic strip filaments as cnoidal waves, we demonstrate that a second threshold voltage for forming dot filaments comes from the transverse instability, resulting in a good agreement with the experimental data.

Fiber cross-sectional imaging by manually controlled low coherence light sources

We couple a variable-coherence light beam into a multimode optical fiber and observe the fiber cross-sectional images. The variation in the fiber imaging is explored as we change the degree of optical coherence of the incident light. Low coherence light is shown to be capable of improving the quality of the fiber images. Various mode patterns of a multimode optical fiber are also shown numerically and experimentally to elucidate the fiber coupling characteristics.