Terahertz all-optical analog differential operator based on diffractive neural networks

With the exponential growth in demand for high-speed data transmission, the 5G system infrastructure, despite its impressive peak data rate of 10 gigabits per second, is increasingly inadequate for emerging applications. This technological gap has propelled 6G technology based on THz communication into the research spotlight to provide new solutions for the Internet of Things (IoT) and autonomous systems due to its superior peak data rates, low latency, and ultra-low power consumption. However, the transition to THz frequencies introduces unprecedented technical hurdles that fundamentally differ from those encountered in conventional microwave systems. The current digital signal processing components (ADCs and DACs) are unable to simultaneously fulfill the requirements in terms of operating bandwidth, power consumption, and heat dissipation. Besides, a wide range of different materials and fabrication processes required for optoelectronic devices severely makes it difficult to achieve the integration of an entire THz communication system on a single chip. To overcome these difficulties, there has been an increasing scholarly focus on high-speed and efficient analog computing. In contrast to digital computing's discrete-value processing, analog computing executes mathematical operations natively through continuous physical quantities, eliminating the need for iterative analog-to-digital conversions throughout the computational pipeline. In recent decades, the superiority of optical devices in computing systems brings new developments for analog optical computing strategies, including Fourier filtering which can achieve spatial-frequency transform functions with precisely engineered 4f system, and Green’s function (GF) approaches that directly operate by modulating the angle-dependent scattering spectrum of the incident wave, making it possible to surpass the restriction of digital computing method. Nevertheless, conventional analog optical computing architectures face fundamental limitations in functional versatility. The widely adopted 4f optical system suffers from intricate fabrication processes. Meanwhile, the GF approaches exhibit inherent angular dispersion in their scattering spectra, which constrains its application. Recent advances have demonstrated the remarkable potential of all-optical DNN to accelerate the process of metasurface design by simply treating the phase modulation of individual unit cells as trainable neural weights. This solution enables a novel approach to the optical operator, which has been demonstrated in defect detection, target recognition, logic operation, quantum computing, optical communication, etc. Nevertheless, current implementations face a critical limitation: most optical DNNs operate with binary (1-bit) or severely quantized weight representations, making it challenging to envisage its applications in various technological platforms.

Here, we propose a THz all-optical analog differential operator for performing high-throughput, ultrafast differential operations on arbitrary 2D input signals. This diffractive network is trained to recognize 2D analog signals in the form of electric field distribution on the input layer and outputs the results in the same way on the imaging plane behind several hidden layers. We resort to the Fourier transform, which can be used to decompose the analog input signal into a sum of trigonometric signals: The all-optical DNN is trained to perform differential operations on several trigonometric signals, thus enabling the differential operation of input signals which contain these trigonometric components. For physical implementation, we leverage multilayer all-dielectric metasurfaces to achieve wavefront manipulation while the 3D-printing technologies ensure precision alignment of multilayer structures for scalable application. Our work features several unique advantages: Firstly, the designed all-optical analog differentiator achieves differential operations at the speed of light, which meets the requirements of an ultrafast THz communication system. In addition, our method obviates the reliance on energy-intensive ADCs and DACs, overcoming the limitation in speed and energy consumption of traditional THz communication systems based on traditional electronic architectures. Although previous works have implemented 2D differential operations at visible and infrared frequencies, the focus on THz frequencies is lacking. Our design achieves an approximation to the original differentiation, demonstrating robust performance with 78% SSIM and 28.5 dB PSNR for step functions and 68.1% SSIM/25.5 dB PSNR for character recognition.

Our method can be flexibly replicated at infrared and visible frequencies by employing nanoscale dielectric blocks or other metasurface elements as hidden layer nodes, offering promising applications in ultrafast optical communications and image processing. Notably, the design of multilayer DNNs at visible frequencies requires overcoming challenges in fabrication and alignment between physical network layers. The number of expansion terms selected in our work can fully capture the key features of certain complex two-dimensional signals, as experimentally validated in the manuscript. On the other hand, for more complex input signals, our method allows for further increasing the number of expansion terms, the size of hidden layers, and the number of layers to enhance the performance of such optical computing systems. Since the operation is based on Fourier series expansion terms rather than direct processing of the raw signal, the proposed method shows superior adaptability to input signals compared with traditional optical computing solutions under the same computational resources and hardware configuration, revealing great potential in THz communication applications including satellite communications, healthcare devices, and ultrafast signal processing.