Causality and passivity: From electromagnetism and network theory to metamaterials

In this review, we take an extensive look at the role that principles of causality and passivity have played in various areas physics engineering, including modern field metamaterials. The aim is not to provide a comprehensive list references as number would be thousands, but review major results contributions which animated these unified framework could useful understanding developments different fields. Towards goals, chart early history through its dual beginnings analysis Sellmeier equation Hilbert transforms, giving rise far reaching dispersion relations works Sokhotskii, Plemelj, Kramers, Kronig, Titchmarsh. However, constitute limited result they only apply restricted class transfer functions. To understand how restriction can lifted, quick detour into distributional Schwartz, discuss context distribution theory. This approach expands reach functions also those exhibit polynomial growth properties. generalize even further tensorial functions, consider concept — originally studied theory electrical networks. We clarify why implies present generalized applicable are distributional, tensorial, possibly exhibiting growth. Subsequently, special cases, examples from several electromagnetism, acoustics, seismology, reflectance measurements, scattering sum rules follow infinite integral integrals may simplified either by truncating them under appropriate assumptions or replacing with derivative relations. These relations, termed analyticity form basis so called nearly-local approximations extensively employed many fields acoustics. Finally, clever applications ideas recent ways, provided limits what achieved metamaterial property design device performance.