标题： 使用衍射处理器的大规模并行和非线性函数的通用逼近 显示英文标题

标题： Massively parallel and universal approximation of nonlinear functions using diffractive processors

摘要： 非线性计算对于广泛的信息处理任务至关重要，但由于光学非线性的弱性和高能耗特性，使用光学系统实现非线性函数仍然是一项挑战。 无需依赖非线性光学材料来克服这一限制，可以为超快和并行的光学计算系统开辟前所未有的机会。 在此，我们展示了可以通过由被动相位仅表面组成的优化衍射处理器，使用线性光学进行大规模非线性计算。 在此框架中，非线性函数的输入变量被编码到光波前的相位中，例如通过空间光调制器（SLM），并通过具有空间变化点扩散函数的优化衍射结构进行转换，以产生输出强度，这些强度近似表示一大组独特的非线性函数，全部并行进行。 我们提供了证明，确立了这种架构作为任意一组带限非线性函数的通用函数逼近器，也涵盖了多变量和复数值函数。 我们还数值地展示了百万个不同非线性函数的并行计算，在衍射光学处理器输出处以波长尺度的空间密度准确执行。 此外，我们通过原位光学学习验证了这个框架，并使用一个由SLM和图像传感器组成的紧凑装置在单次拍摄中近似了35个独特的非线性函数。 这些结果确立了衍射光学处理器作为大规模并行通用非线性函数逼近的可扩展平台，为基于线性材料的模拟光学计算的新能力铺平了道路。 显示英文摘要

摘要： Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront, e.g., via a spatial light modulator (SLM), and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions, all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering multi-variate and complex-valued functions. We also numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.