Finite‐Difference Time‐Domain Solution of Maxwell's Equations

Abstract For over 100 years after the publication of Maxwell's equations in 1865, essentially all solution techniques for electromagnetic fields and waves were based on Fourier‐domain concepts, assuming a priori a time‐harmonic (sinusoidal steady‐state) field variation and possibly the existence of a particular Green's function or a set of spatial modes. In 1966, Kane Yee's seminal paper introduced a complete paradigm shift in how to solve Maxwell's equations, reporting a field evolution‐in‐time technique that subsequently evolved into the finite‐difference time‐domain (FDTD) method. In the decades since the publication of Yee's paper, there has been an explosion of interest in FDTD and related grid‐based time‐marched solutions of Maxwell's equations among scientists and engineers. During this period, FDTD modeling has evolved to an advanced stage enabling large‐scale simulations of full‐wave time‐domain electromagnetic wave interactions with volumetrically complex structures over large frequency ranges, spatial scales, and timescales. Currently, FDTD modeling spans the electromagnetic spectrum from ultralow frequencies to visible light. FDTD modeling is routinely conducted as an invaluable virtual laboratory bench in scientific inquiry and exploration in electrodynamics; as an integral part of the electromagnetic engineering design and optimization process; and as a powerful forward solver in imaging and sensing inverse problems. This article reviews the technical basis of the key features of FDTD solution techniques for Maxwell's equations and provides 18 modeling examples spanning the electromagnetic spectrum to illustrate the power, flexibility, and robust nature of FDTD computational electrodynamics simulations.