A laser is based on the electromagnetic modes of its resonator, which provides the feedback required for oscillation. Enormous progress has been made toward controlling the interactions of longitudinal modes in lasers with a single transverse mode. For example, the field of ultrafast science has been built on lasers that lock many longitudinal modes together to form ultrashort light pulses. However, coherent superposition of longitudinal and transverse modes in a laser has received little attention. We show that modal and chromatic dispersions in fiber lasers can be counteracted by strong spatial and spectral filtering. This allows locking of multiple transverse and longitudinal modes to create ultrashort pulses with a variety of spatiotemporal profiles. Multimode fiber lasers thus open new directions in studies of nonlinear wave propagation and capabilities for applications.

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Deep-learning models have become pervasive tools in science and engineering. However, their energy requirements now increasingly limit their scalability1. Deep-learning accelerators2–9 aim to perform deep learning energy-efficiently, usually targeting the inference phase and often by exploiting physical substrates beyond conventional electronics. Approaches so far10–22 have been unable to apply the backpropagation algorithm to train unconventional novel hardware in situ. The advantages of backpropagation have made it the de facto training method for large-scale neural networks, so this deficiency constitutes a major impediment. Here we introduce a hybrid in situ–in silico algorithm, called physics-aware training, that applies backpropagation to train controllable physical systems. Just as deep learning realizes computations with deep neural networks made from layers of mathematical functions, our approach allows us to train deep physical neural networks made from layers of controllable physical systems, even when the physical layers lack any mathematical isomorphism to conventional artificial neural network layers. To demonstrate the universality of our approach, we train diverse physical neural networks based on optics, mechanics and electronics to experimentally perform audio and image classification tasks. Physics-aware training combines the scalability of backpropagation with the automatic mitigation of imperfections and noise achievable with in situ algorithms. Physical neural networks have the potential to perform machine learning faster and more energy-efficiently than conventional electronic processors and, more broadly, can endow physical systems with automatically designed physical functionalities, for example, for robotics23–26, materials27–29 and smart sensors30–32.

Multimode fibres (MMFs) are attracting interest for complex spatiotemporal dynamics, and for ultrafast fibre sources, imaging and telecommunications. This new interest is based on three key properties: their high spatiotemporal complexity (information capacity), the important role of disorder, and complex intermodal interactions. To date, phenomena in MMFs have been studied only in limiting cases where one or more of these properties can be neglected. Here we study MMFs in a regime in which all these elements are integral. We observe a spatial beam-cleaning process preceding spatiotemporal modulation instability. We show that the origin of these processes is a universal unstable attractor in graded-index MMFs. Both the self-organization of the attractor, as well as its instability, are caused by intermodal interactions characterized by cooperating disorder, nonlinearity and dissipation. The demonstration of a disorder-enhanced nonlinear process in MMF has important implications for telecommunications, and the multifaceted complexity of the dynamics showcases MM waveguides as ideal laboratories for many topics and applications in complexity science.Comment: http://www.nature.com/nphoton/journal/v10/n12/full/nphoton.2016.227.htm