Matrix computation, as a fundamental building block of information processing in science and technology, contributes most of the computational overheads in modern signal processing and artificial intelligence algorithms. Photonic accelerators are designed to accelerate specific categories of computing in the optical domain, especially matrix multiplication, to address the growing demand for computing resources and capacity. Photonic matrix multiplication has much potential to expand the domain of telecommunication, and artificial intelligence benefiting from its superior performance. Recent research in photonic matrix multiplication has flourished and may provide opportunities to develop applications that are unachievable at present by conventional electronic processors. In this review, we first introduce the methods of photonic matrix multiplication, mainly including the plane light conversion method, Mach–Zehnder interferometer method and wavelength division multiplexing method. We also summarize the developmental milestones of photonic matrix multiplication and the related applications. Then, we review their detailed advances in applications to optical signal processing and artificial neural networks in recent years. Finally, we comment on the challenges and perspectives of photonic matrix multiplication and photonic acceleration.

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.

Optical logic operations lie at the heart of optical computing, and they enable many applications such as ultrahigh-speed information processing. However, the reported optical logic gates rely heavily on the precise control of input light signals, including their phase difference, polarization, and intensity and the size of the incident beams. Due to the complexity and difficulty in these precise controls, the two output optical logic states may suffer from an inherent instability and a low contrast ratio of intensity. Moreover, the miniaturization of optical logic gates becomes difficult if the extra bulky apparatus for these controls is considered. As such, it is desirable to get rid of these complicated controls and to achieve full logic functionality in a compact photonic system. Such a goal remains challenging. Here, we introduce a simple yet universal design strategy, capable of using plane waves as the incident signal, to perform optical logic operations via a diffractive neural network. Physically, the incident plane wave is first spatially encoded by a specific logic operation at the input layer and further decoded through the hidden layers, namely, a compound Huygens’ metasurface. That is, the judiciously designed metasurface scatters the encoded light into one of two small designated areas at the output layer, which provides the information of output logic states. Importantly, after training of the diffractive neural network, all seven basic types of optical logic operations can be realized by the same metasurface. As a conceptual illustration, three logic operations (NOT, OR, and AND) are experimentally demonstrated at microwave frequencies.