Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a new photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.
Implementation of nearly arbitrary spatially-varying polarization transformations: a non-diffractive and non-interferometric approach using spatial light modulators
Hardware-Efficient Universal Linear Transformations for Optical Modes in the Synthetic Time Dimension
Department of Electrical and Computer Engineering, University of Maryland（马里兰大学电气与计算机工程系）；Institute for Research in Electronics and Applied Physics, and Joint Quantum Institute, University of Maryland（马里兰大学电子与应用物理研究所及联合量子研究所）；James C. Wyant College of Optical Sciences, University of Arizona（亚利桑那大学詹姆斯·C·怀安特光学科学学院）
All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）
本文设计了一种全光学衍射表面，用于在输入（N_i）和输出（N_o）之间进行任意复值线性变换，其中N_i和N_o分别表示输入和输出视场（FOV）处的像素数。首先，我们考虑一个单一的衍射表面，并使用基于矩阵伪逆的方法来确定衍射特征/神经元的复值透射系数，以全光学地执行期望的/目标线性变换。除了这种无数据设计方法之外，我们还考虑了一种基于深度学习的设计方法，通过使用与目标变换相对应的输入/输出场的示例来优化衍射表面的透射系数。我们比较了使用无数据设计以及数据驱动（基于深度学习）衍射设计实现的全光学变换误差和衍射效率，以全光学执行（i）任意选择的复值变换，包括酉变换，非酉变换和不可逆变换，（ii）2D离散傅立叶变换，（iii）任意2D置换运算，以及（iv）高通滤波相干成像。我们的分析表明，如果空间设计的衍射特征/神经元的总数（N）为N_i x N_o或更大，则两种设计方法都成功地实现了目标变换的全光学实现，实现了可忽略的误差。然而，与无数据设计相比，发现基于深度学习的衍射设计对于给定的N可以实现更大的衍射效率，并且它们的全光学变换对于N < N_i x N_o更准确。这些结论通常适用于采用空间工程衍射表面的各种光学处理器。
