In the fields of physics, mathematics, and engineering, partial differential equations (PDEs) are essential for modeling various phenomena, from heat diffusion to particle motion and wave propagation. While some PDEs can be solved analytically, many require numerical methods, which can be time-consuming and computationally intensive. To address these challenges, scientists have been exploring alternative computing paradigms, including photonic computing.
Photonic computing leverages light–matter interactions to perform high-speed calculations. A recent study from Newcastle University, published in Advanced Photonics Nexus , introduces a novel approach using electromagnetic (EM) waves to solve PDEs, specifically the Helmholtz wave equation. The researchers developed a network of interconnected waveguides filled with dielectric inserts, which mimics the behavior of traditional circuit elements.
This innovative structure, known as a metatronic network, effectively behaves like a grid of T-circuits. By adjusting the dimensions and permittivity of the dielectric inserts, the researchers demonstrated control over the parameters of the PDEs. This allows the network to solve various boundary value problems, such as EM wave scattering and light focusing.
Dr. Victor Pacheco-Peña, corresponding author for the report, highlights the potential of these devices as computational accelerators: "We envision that these devices may be used to produce fast approximate solutions for various partial differential equations," he remarked, adding that this research represents a significant step forward in the field of analogue computing, as a promising way to rapidly and efficiently solve complex equations.
For details, see the original Gold Open Access article by R.G. MacDonald, A. Yakovlev, and V. Pacheco-Peña, " Solving partial differential equations with waveguide-based metatronic networks ," Adv. Photon. Nexus 3(5), 056007 (2024), doi 10.1117/1.APN.3.5.056007 .
