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.

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We propose and experimentally demonstrate the flexibility and versatility of photonic differentiators using a silicon-based Mach-Zehnder Interferometer (MZI) structure. Two differentiation schemes are investigated. In the first scheme, we demonstrate high-order photonic field differentiators using on-chip cascaded MZIs, including first-, second-, and third-order differentiators. For single Gaussian optical pulse injection, the average deviations of all differentiators are less than 6.5%. In the second scheme, we demonstrate multifunctional differentiators, including intensity differentiator and field differentiator, using an on-chip single MZI structure. These different differentiator forms rely on the relative shift between the probe wavelength and the MZI resonant notch. Our schemes show the advantages of compact footprint, flexible functions and versatile differentiation forms. For example, high order field differentiators can be used to generate complex temporal waveforms, such as high order Hermite-Gaussian waveforms. And intensity differentiators are useful for ultra-wideband pulse generation.