Induced homomorphism: Kirchhoff’s law in photonics

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 case lumped-circuit abstraction, which can be used mechanical and acoustic systems, thermal heat-diffusion problems in general partial differential equations. Integrated photonic platforms hold prospective perform signal processing analog computing inherently, by mapping into hardware specific operations relies on wave-nature their signals, without trusting logic gates digital states like electronics. Here, we argue that absence straightforward parallelism homomorphism induced. We introduce platform capable mimicking Kirchhoff’s law photonics as node finite difference mesh solving equation using monochromatic light telecommunication wavelength. Our approach experimentally demonstrates an arbitrary set boundary conditions, generating one-shot discrete solution Laplace equation, with accuracy above 95% respect commercial solvers. engine provide route achieve chip-scale, fast (10 s ps), integrable reprogrammable accelerators next generation hybrid high-performance computing. Summary A integrated mimic approximately solve equations noniteratively light, high throughput low-energy levels.