Induced homomorphism: Kirchhoff’s law in photonics
Induced homomorphism: Kirchhoff’s law in photonics
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DOI：
10.1515/nanoph-2020-0655
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发表时间：
2021-03
期刊：
影响因子：
7.5
通讯作者：
Shuai Sun;M. Miscuglio;Xiaoxuan Ma;Zhizhen Ma;Chen Shen;Engin Kayraklioglu;Jeff Anderson;T. El Ghazawi;V. Sorger
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文献类型：
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作者：
Shuai Sun;M. Miscuglio;Xiaoxuan Ma;Zhizhen Ma;Chen Shen;Engin Kayraklioglu;Jeff Anderson;T. El Ghazawi;V. Sorger
在求解、建模或推理复杂问题时，通常使用并行物理系统的知识来表示它是很方便的。这是集总电路抽象的例子，它可以用于表示机械和声学系统，热和热扩散问题以及一般的偏微分方程。集成光子平台通过映射到依赖于其信号的波动性质的硬件特定操作，而不依赖于逻辑门和电子等数字状态，从而具有固有的执行信号处理和模拟计算的前景。在这里，我们认为在没有直接的并行性的情况下，可以诱导同态。我们介绍了一个能够模拟光子学中的基尔霍夫定律的光子平台，并将其用作有限差分网格的节点，用于利用电信波长的单色光求解偏微分方程。我们的方法在实验上证明了一组任意的边界条件，生成一个拉普拉斯偏微分方程的一次离散解，相对于商业求解器，精度在95%以上。我们的光子引擎可以为下一代混合高性能计算提供实现芯片级，快速（10s / ps）和可集成可重新编程加速器的途径。摘要利用光子集成平台模拟了光子学中的基尔霍夫定律，实现了高通量、低能级的光非迭代近似求解偏微分方程。
Abstract When solving, modeling or reasoning about complex problems, it is usually convenient to use the knowledge of a parallel physical system for representing it. This is the case of lumped-circuit abstraction, which can be used for representing mechanical and acoustic systems, thermal and heat-diffusion problems and in general partial differential equations. Integrated photonic platforms hold the prospective to perform signal processing and analog computing inherently, by mapping into hardware specific operations which relies on the wave-nature of their signals, without trusting on logic gates and digital states like electronics. Here, we argue that in absence of a straightforward parallelism a homomorphism can be induced. We introduce a photonic platform capable of mimicking Kirchhoff’s law in photonics and used as node of a finite difference mesh for solving partial differential equation using monochromatic light in the telecommunication wavelength. Our approach experimentally demonstrates an arbitrary set of boundary conditions, generating a one-shot discrete solution of a Laplace partial differential equation, with an accuracy above 95% with respect to commercial solvers. Our photonic engine can provide a route to achieve chip-scale, fast (10 s of ps), and integrable reprogrammable accelerators for the next generation hybrid high-performance computing. Summary A photonic integrated platform which can mimic Kirchhoff’s law in photonics is used for approximately solve partial differential equations noniteratively using light, with high throughput and low-energy levels.