When encoded with a 3D network of interconnected and pentadirectional waveguides, an otherwise passive polymer film transforms into an intelligent optical element-a waveguide encoded lattice (WEL)-that combines a panoramic field of view, infinite depth of field and powerful capacity to perform multiple imaging operations such as divergence-free transmission, focusing, and inversion. The lattices are moreover operable with coherent and incoherent light at all visible wavelengths, both individually (e.g., narrow band sources such as lasers, light-emitting diodes) and collectively (e.g., incandescent sources). This combination of properties is unprecedented in singlecomponent films and the WEL structures represent a new class of flexible, slim films that could confer advanced optical functionalities when integrated with light-based technologies (e.g., solar panels, smart phone cameras, and smart screens) and are amenable to the design and fabrication of new miniaturized optical and optoelectronic devices.

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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.

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.

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.