2020/08/12 by Ankit Srivastava, Srivastava, Ankit · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · #Acoustic Wave Phenomena Research #Applied Physics (physics.app-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Optics (physics.optics) #Terahertz technology and applications
paper · pdf · doi:10.48550/arxiv.2008.05546
openalex publication_date 2020/08/12 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this review, we take an extensive look at the role that the principles of\ncausality and passivity have played in various areas of physics and\nengineering, including in the modern field of metamaterials. The aim is not to\nprovide a comprehensive list of references as that number would be in the\nthousands, but to review the major results and contributions which have\nanimated these areas and to provide a unified framework from which to\nunderstand the developments in different fields. Towards these goals, we chart\nthe early history of the field through its dual beginnings in the analysis of\nthe Sellmeier equation and in Hilbert transforms, giving rise to the far\nreaching dispersion relations in the early works of Kramers, Kronig, and\nTitchmarsh. However, these early relations constitute a limited result as they\nonly apply to a restricted class of transfer functions. To understand how this\nrestriction can be lifted, we take a quick detour into the distributional\nanalysis of Schwartz. This approach expands the reach of the dispersion\nanalysis to distributional transfer functions and also to those functions which\nexhibit polynomial growth properties. To generalize the results even further to\ntensorial transfer functions, we consider the concept of passivity - originally\nstudied in the theory of electrical networks. We clarify why passivity implies\ncausality. Subsequently, as special cases, we present examples of dispersion\nrelations from several areas of physics including electromagnetism, acoustics,\nseismology, reflectance measurements, and scattering theory. We discuss sum\nrules, derivative analyticity relations, and nearly local approximations.\nFinally we review the clever applications of ideas from causality and passivity\nto the recent field of metamaterials. These ideas have provided limits to what\ncan be achieved in metamaterial property design and metamaterial device\nperformance.\n