Maxwell's equations and electromagnetics after 150+ years

Abstract

Maxwell's equations have been around for over 150 years since its inception. But due to their enduring legacy, their importance has not diminished over the years. In fact, electromagnetic theory finds applications in increasing number of areas and relationship to deeper mathematics. For instance, electromagnetics is important for quantum information, quantum optics, and increasingly being used in photonic and bio technologies. An amazing feature of Maxwell's equations is their validity from subatomic length scale to galactic length scale. Consequently, they are valid over a vast frequency range with diverse wavelengths. Furthermore, they are also valid in classical as well as in quantum electromagnetics. Because of the highly predictive value of Maxwell's equations, there has been a quest for their efficient and accurate solutions. Various methods to solve Maxwell's equations have been developed since the dawn of their discovery. With the advent of computers, the need for more accurate and robust solutions does not diminish. In this presentation will discuss the history of different solution methods in electromagnetic theory, ranging from approximate methods, to fast numerical methods, namely, the computational electromagnetics methods. We will also discuss future directions in this area.