Photonic waveguides are prime candidates for integrated and parallel photonic interconnects. Such interconnects correspond to large-scale vector matrix products, which are at the heart of neural network computation. However, parallel interconnect circuits realized in two dimensions, for example, by lithography, are strongly limited in size due to disadvantageous scaling. We use three-dimensional (3D) printed photonic waveguides to overcome this limitation. 3D optical couplers with fractal topology efficiently connect large numbers of input and output channels, and we show that the substrate’s area and height scale linearly. Going beyond simple couplers, we introduce functional circuits for discrete spatial filters identical to those used in deep convolutional neural networks.

Photonic realizations of neural network computing hardware are a promising approach to enable future scalability of neuromorphic computing. The number of special purpose neuromorphic hardware and neuromorphic photonics has accelerated on such a scale that one can now speak of a Cambrian explosion. Work along these lines includes (i) high performance hardware for artificial neurons, (ii) the efficient and scalable implementation of a neural network’s connections, and (iii) strategies to adjust network connections during the learning phase. In this review we provide an overview on vertical-cavity surface-emitting lasers (VCSELs) and how these high-performance electro-optical components either implement or are combined with additional photonic hardware to demonstrate points (i-iii). In the neurmorphic photonics context, VCSELs are of exceptional interest as they are compatible with CMOS fabrication, readily achieve 30% wall-plug efficiency, >30 GHz modulation bandwidth and multiply and accumulate operations at sub-fJ energy. They hence are highly energy efficient and ultra-fast. Crucially, they react nonlinearly to optical injection as well as to electrical modulation, making them highly suitable as all-optical as well as electro-optical photonic neurons. Their optical cavities are wavelength-limited, and standard semiconductor growth and lithography enables non-classical cavity configurations and geometries. This enables excitable VCSELs (i.e. spiking VCSELs) to finely control their temporal and spatial coherence, to unlock terahertz bandwidths through spin-flip effects, and even to leverage cavity quantum electrodynamics to further boost their efficiency. Finally, as VCSEL arrays they are compatible with standard 2D photonic integration, but their emission vertical to the substrate makes them ideally suited for scalable integrated networks leveraging 3D photonic waveguides. Here, we discuss the implementation of spatially as well as temporally multiplexed VCSEL neural networks and reservoirs, computation on the basis of excitable VCSELs as photonic spiking neurons, as well as concepts and advances in the fabrication of VCSELs and microlasers. Finally, we provide an outlook and a roadmap identifying future possibilities and some crucial milestones for the field.

We propose single-step additive fabrication of graded-index optical elements by introducing the light exposure as the additional dimension to three-dimensional (3D) laser writing, hence (3 + 1)D writing. We use a commercial printer and photoresist to realize the proposed single-step fabrication method that can be swiftly adopted for research and engineering. After presenting the characterization of the graded-index profiles via basic structures, we demonstrate two different optical devices: volume holograms that are superimposed using angular and peristrophic multiplexing, and optical waveguides with well-defined refractive index profiles. In the latter, we precisely control the propagating modes via tuning the (3 + 1)D-printed waveguide parameters and report step-index and graded-index core–cladding transitions.

Neural networks are one of the disruptive computing concepts of our time. However, they fundamentally differ from classical, algorithmic computing. These differences result in equally fundamental, severe and relevant challenges for neural network computing using current computing substrates. Neural networks urge for parallelism across the entire processor and for a co-location of memory and arithmetic, i.e. beyond von Neumann architectures. Parallelism in particular made photonics a highly promising platform, yet until now scalable and integratable concepts are scarce. Here, we demonstrate for the first time how a fully parallel and fully implemented photonic neural network can be realized by spatially multiplexing neurons across the complex optical near-field of a semiconductor multimode laser. Discrete spatial sampling defines ∼90 nodes on the surface of a large-area vertical cavity surface emitting laser that is optically injected with the artificial neural networks input information. Importantly, all neural network connections are realized in hardware, and our processor produces results without pre- or post-processing. Input and output weights are realized via the complex transmission matrix of a multimode fiber and a digital micro-mirror array, respectively. We train the readout weights to perform 2-bit header recognition, a 2-bit XOR logical function and 2-bit digital to analog conversion, and obtain < 0.9 × 10 − 3 and 2.9 × 10⁻² error rates for digit recognition and XOR, respectively. Finally, the digital to analog conversion can be realized with a standard deviation of only 5.4 × 10⁻². Crucially, our proof-of-concept system is scalable to much larger sizes and to bandwidths in excess of 20 GHz.

Photonic waveguides are promising candidates for implementing parallel, ultra-fast and ultra-low latency interconnects. Such interconnects are an important technological asset for example for next generation optical routing, on and intra-chip optical communication, and for parallel photonic neural networks. We have recently demonstrated dense optical integration of multi-mode optical interconnects based on 3D additive manufacturing using two-photon-polymerization. The basis of such interconnects are 3D optical splitters, and here we characterize their performance against their splitting ratio, geometry, and conditions of the direct laser writing. Optical losses and splitting uniformity of 1 to 4, 1 to 9 and 1 to 16 splitters are evaluated at 632 nm. We find that, both, the uniformity of splitting ratios as well as the overall losses depend on the separation between the output waveguides as well as on the hatching distance (surface quality) of the 3D printing process.

We study and analyze the fundamental aspects of noise propagation in recurrent as well as deep, multilayer networks. The motivation of our study is neural networks in analog hardware; yet, the methodology provides insight into networks in general. Considering noisy linear nodes, we investigate the signal-to-noise ratio at the network’s outputs, which determines the upper limit of computational precision. We consider additive and multiplicative noise, which can be purely local as well as correlated across populations of neurons. This covers the chief internal-perturbations of hardware networks, and noise amplitudes were obtained from a physically implemented neural network. Analytically derived descriptions agree exceptionally well with numerical data, enabling clear identification of the components critical for management and mitigation of noise. We find that analog neural networks are surprisingly robust, in particular, against noisy neurons. Their uncorrelated perturbations are almost fully suppressed, while correlated noise can accumulate. Our work identifies notoriously sensitive points while highlighting a surprising robustness of such computational systems.