Opto-chemo-mechanical transduction in photoresponsive gels elicits switchable self-trapped beams with remote interactions.

Next-generation photonics envisions circuitry-free, rapidly reconfigurable systems powered by solitonic beams of self-trapped light and their particlelike interactions. Progress, however, has been limited by the need for reversibly responsive materials that host such nonlinear optical waves. We find that repeatedly switchable self-trapped visible laser beams, which exhibit strong pairwise interactions, can be generated in a photoresponsive hydrogel. Through comprehensive experiments and simulations, we show that the unique nonlinear conditions arise when photoisomerization of spiropyran substituents in pH-responsive poly(acrylamide-co-acrylic acid) hydrogel transduces optical energy into mechanical deformation of the 3D cross-linked hydrogel matrix. A Gaussian beam self-traps when localized isomerization-induced contraction of the hydrogel and expulsion of water generates a transient waveguide, which entraps the optical field and suppresses divergence. The waveguide is erased and reformed within seconds when the optical field is sequentially removed and reintroduced, allowing the self-trapped beam to be rapidly and repeatedly switched on and off at remarkably low powers in the milliwatt regime. Furthermore, this opto-chemo-mechanical transduction of energy mediated by the 3D cross-linked hydrogel network facilitates pairwise interactions between self-trapped beams both in the short range where there is significant overlap of their optical fields, and even in the long range--over separation distances of up to 10 times the beam width--where such overlap is negligible.

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.

Interplay of Luminophores and Photoinitiators during Synthesis of Bulk and Patterned Luminescent Photopolymer Blends.

Four-dimensional printing with embedded photoluminescence is emerging as an exciting area in additive manufacturing. Slim polymer films patterned with three-dimensional lattices of multimode cylindrical waveguides (waveguide-encoded lattices, WELs) with enhanced fields of view can be fabricated by localizing light as self-trapped beams within a photopolymerizable formulation. Luminescent WELs have potential applications as solar cell coatings and smart planar optical components. However, as luminophore-photoinitiator interactions are expected to change the photopolymerization kinetics, the design of robust luminescent photopolymer sols is nontrivial. Here, we use model photopolymer systems based on methacrylate-siloxane and epoxide homopolymers and their blends to investigate the influence of the luminophore Lumogen Violet (LV) on the photolysis kinetics of the Omnirad 784 photoinitiator through UV-vis absorbance spectroscopy. Initial rate analysis with different bulk polymers reveals differences in the pseudo-first-order rate constants in the absence and presence of LV, with a notable increase (∼40%) in the photolysis rate for the 1:1 blend. Fluorescence quenching studies, coupled with density functional theory calculations, establish that these differences arise due to electron transfer from the photoexcited LV to the ground-state photoinitiator molecules. We also demonstrate an in situ UV-vis absorbance technique that enables real-time monitoring of both waveguide formation and photoinitiator consumption during the fabrication of WELs. The in situ photolysis kinetics confirm that LV-photoinitiator interactions also influence the photopolymerization process during WEL formation. Our findings show that luminophores play a noninnocent role in photopolymerization and highlight the necessity for both careful consideration of the photopolymer formulation and a real-time monitoring approach to enable the fabrication of high-quality micropatterned luminescent polymeric films.

An optochemically organized nonlinear waveguide lattice with primitive cubic symmetry.

We describe the first example of a primitive cubic lattice assembled spontaneously from three mutually orthogonal and intersecting arrays of cylindrical, multimode waveguides. The lattice is generated in a single, room-temperature step with separate (mutually incoherent) incandescent light bulbs. To demonstrate its potential as a nonlinear photonic lattice, we generated a self-trapped lattice beam of incoherent white light. These two findings open entirely new experimental opportunities to study the behavior of spatially and temporally incoherent, polychromatic lattice solitons in 3-D Bravais lattices.

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.

A black beam borne by an incandescent field self-traps in a photopolymerizing medium.

We report that a self-trapped black optical beam that is spatially and temporally incoherent forms spontaneously in a nascent photopolymerization system. The black beam inscribes a permanent cylindrical channel, which prevents the propagation of visible light even under passive conditions (in the absence of polymerization). The finding opens a powerful new mechanism to manipulate light signals from incoherent sources such as LEDs through selective suppression of light propagation. This contrasts with approaches employed by photonic crystals and optical waveguides, which concentrate and guide light intensity within spatially localized regions. The self-trapped black beam forms when a broad incandescent beam bearing a negligible depression was launched into a photopolymerizable medium. Because of refractive index changes caused by polymerization, the depression narrows, deepens, and continually rejects the visible spectrum of light until it stabilizes as a black beam that propagates over long distances (≫ effective Rayleigh range) without significant divergence. As refractive index changes due to polymerization are irreversible, the cylindrical region occupied by the self-trapped black beam is inscribed as a black channel waveguide in the medium.

Spontaneous and sequential transitions of a Gaussian beam into diffraction rings, single ring and circular array of filaments in a photopolymer.

A Gaussian beam propagating in a photopolymer undergoes self-phase modulation to form diffraction rings and then transforms into a single ring, which in turn ruptures into a necklace of stable self-trapped multimode filaments. The transitions of the beam between the three distinct nonlinear forms only occur at intensities where the beam-induced refractive index profile in the medium slowly evolves from a Gaussian to a flattened Gaussian.

3-D Spiraling Self-Trapped Light Beams in Photochemical Systems.

A pair of visible laser beams self-trap and spiral about each other as they propagate through polymer gels undergoing two different photochemical reactions. When launched into gels that undergo photopolymerization of methacrylate substituents or photo-oxidation of iodide anion, two non-coplanar (skewed) Gaussian beams collide and spiral about each other as they advance through the evolving medium. In the absence of chemical reactions, the linearly polarized beams broaden naturally and propagate along their original, straight-pathed trajectories. By contrast, refractive index gradients generated by the photochemical reactions elicit self-trapping and introduce an attractive interaction between the self-trapped beams. The self-trapped beams spiral about each other when this mutual attraction perfectly counterbalances their original tendency to diverge away from each other. These findings show that the photochemically mediated interactions of incident optical fields within the gel medium impart a helical trajectory and angular velocity to the self-trapped beam pair.

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.

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.

Spontaneous Formation of Fractal Aggregates of Au Nanoparticles in Epoxy-Siloxane Films and Their Application as Substrates for NIR Surface Enhanced Raman Spectroscopy.

We present a facile, inexpensive route to free-standing, thermo-mechanically robust and flexible epoxy-siloxane substrates embedded with fractal aggregates of Au nanoparticles, and demonstrate their efficiency as substrates for surface enhanced Raman spectroscopy (SERS) at NIR wavelengths. The metallodielectric films are prepared by generating Au nanoparticles through the in-situ reduction of gold (III) chloride trihydrate in epoxypropoxypropyl terminated polydimethyl siloxane (EDMS). The metal nanoparticles spontaneously aggregate into fractal structures in the colloid, which could then be drop-cast onto a substrate. Subsequent UV-initiated cationic polymerization of epoxide moieties in EDMS transforms the fluid colloid into a thin, free-standing film, which contains a dense distribution of fractal aggregates of Au nanoparticles. We used electron and optical microscopy as well as UV⁻Vis⁻NIR spectrometry to monitor the evolution of nanoparticles and to optically and structurally characterize the resulting films. Raman spectroscopy of the chromophore Eosin Y adsorbed onto the metallodielectric films showed that they are excellent SERS substrates at NIR excitation with an enhancement factor of ~9.3 × 10³.

Reversibly Trapping Visible Laser Light through the Catalytic Photo-oxidation of I(-) by Ru(bpy)3(2+).

A Gaussian, visible laser beam traveling in a hydrogel doped with NaI and Ru(bpy)3Cl2 spontaneously transforms into a localized, self-trapped beam, which propagates without diverging through the medium. The catalytic, laser-light-induced oxidation of I(-) by [Ru(bpy)3](2+) generates I3(-) species, which create a refractive index increase along the beam path. The result is a cylindrical waveguide, which traps the optical field as bound modes and suppresses natural diffraction. When the beam is switched off, diffusion of I3(-) erases the waveguide within minutes and the system reverts to its original composition, enabling regeneration of the self-trapped beam. Our findings demonstrate reversible self-trapping for the first time in a precisely controllable, molecular-level photoreaction and could open routes to circuitry-free photonics devices powered by the interactions of switchable self-trapped beams.

Spontaneous pattern formation due to modulation instability of incoherent white light in a photopolymerizable medium.

Spontaneous pattern formation due to modulation instability was observed in a broad uniform beam of incoherent white light propagating in an optically isotropic, photopolymerizable organosiloxane. Pattern formation originates from intensity-dependent refractive index changes due to polymerization, which cause competition between the natural diffraction (broadening) and self-induced refraction of the beam. Under these nonlinear conditions, weak intensity modulations in the beam, noise, that would be negligible under linear conditions are amplified. The amplified patterns become unstable over time and spontaneously divide into individual self-trapped filaments of white light of essentially identical diameter (76 +/- 3 microm), which propagate through the medium without diffracting. In the case of noise with a weak 1-D periodic modulation, for example, the uniform beam transformed into a 1-D periodic array of self-trapped lamellae, which in turn formed a 2-D array of self-trapped cylindrical filaments. Although the rate of pattern formation varied inversely with optical power (measured from 8.4 to 59.8 mW), the uniform beam always split into discrete filaments, demonstrating that they are the most stable form of light propagation under the nonlinear conditions created by polymerization. Each filament of light retained the spectral composition and incoherence of white light, which showed that the entire polychromatic, incoherent and unpolarized wavepacket collectively participated in pattern formation. These findings are consistent with recent theoretical models of nonlinear white light propagation and with experimental observations of pattern formation in coherent and partially coherent light. Because refractive index changes due to polymerization are permanent, pattern formation imparts microstructure to the organosiloxane. Optical micrographs revealed that, after pattern formation, the initially homogeneous medium consisted entirely of a closely packed array of narrow channel waveguides induced by self-trapped filaments.

The dynamics of self-trapped beams of incoherent white light in a free-radical photopolymerizable medium.

Detailed experimental studies of the dynamics of self-trapped beams of white light (400-800 nm) in a photosensitive organosiloxane medium are presented. Self-trapped white light beams with similar spatial profiles formed in the organosiloxane at intensities ranging across an order of magnitude (2.7-22.0 W.cm-2). Beam-profiling measurements showed that these spatially and temporally incoherent wave packets propagate without diffracting (broadening) by initiating free-radical polymerization of methacrylate groups and corresponding refractive index changes in the organosiloxane medium. Analyses of their temporal evolution showed that the intensity-dependent behavior of self-trapped white light is similar to that of self-trapped laser light despite the extreme differences in their phase structure and chromaticity; the self-trapped incoherent beams even show the complementary oscillations of width and intensity that is characteristic of self-trapped coherent light. Furthermore, the dynamics of the self-trapped white light beams was found to be strongly correlated to the kinetics of free-radical polymerization and corresponding rates of refractive index changes in the organosiloxane. These studies provide accessible photochemical routes to self-trapped incoherent wave packets, which are extremely difficult to generate in conventional nonlinear optical media that owe their responses to higher-order dielectric susceptibility tensors. This could enable the experimental verification of theoretical models developed for the nonlinear propagation of white light and stimulate research into more complex self-trapping phenomena such as the interactions of self-trapped incoherent beams and spontaneous pattern formation due to modulation instability in a uniform incoherent optical field. These findings also carry potential for the development of self-induced waveguide, optical solder and interconnect technology for incoherent light emitted by incandescent sources or LEDs.

Self-trapping of spatially and temporally incoherent white light in a photochemical medium.

We report that a beam of spatially and temporally incoherent white light self-traps by initiating free-radical polymerization in an organosiloxane medium. Refractive index changes due to polymerization lead to the formation of a narrow channel waveguide that traps and guides the entire multimode, broadband beam without diffraction. The response time of the system, which is determined by the inherently slow rate of free-radical polymerization, exceeds by several orders of magnitude the femtosecond-scale random phase fluctuations that characterize white light. Self-trapping of incoherent light is possible in the photochemical medium because it responds to the time-averaged intensity profile of the white light beam.

Visible laser self-focusing in hybrid glass planar waveguides.

We report that self-focusing occurs with simultaneous self-inscription of a cylindrical waveguide when 514.5-nm light from a cw argon-ion laser propagates in a solgel-derived silica methacrylate hybrid glass planar waveguide. Spatially localized free-radical polymerization of methacrylate substituents is initiated in the path of the guided wave. This causes intensity-dependent refractive-index changes that lead to self-lensing and focusing. A channel waveguide evolves in the matrix, which supports fundamental and higher-order optical modes and suppresses diffraction of the beam.