The theoretical and experimental aspects of the microwave, terahertz, and infrared properties of superconductors are discussed. Electrodynamics can provide information about the superconducting condensate as well as about the quasiparticles. The aim is to understand the frequency dependence of the complex conductivity, the change with temperature and time, and its dependence on material parameters. We confine ourselves to conventional metallic superconductors, in particular, Nb and related nitrides and review the seminal papers but also highlight latest developments and recent experimental achievements. The possibility to produce well-defined thin films of metallic superconductors that can be tuned in their properties allows the exploration of fundamental issues, such as the superconductor-insulator transition; furthermore it provides the basis for the development of novel and advanced applications, for instance, superconducting single-photon detectors. 1. Introduction 1.1. Historical Developments The history of superconductivity in the 1950s is one of the best examples of how the interplay of experiment and theory advances science towards a profound understanding. After having moved to Urbana in 1951 and even more intense after having received the Nobel Prize for the development of the transistor in 1956, John Bardeen was pressing to solve the longstanding problem of superconductivity. During these years he was very well aware of the experimental facts and recent developments but also triggered experimental investigations and pushed certain measurements. The presence of an energy gap in the density of states of a superconductor (and thus in the excitation spectrum) can be inferred from the temperature dependence of the specific heat that had been measured already in Heike Kamerlingh Onnes’ laboratory in Leiden [1]; however, it was Bardeen who seriously discussed this idea in more detail in 1955 [2, 3] based on considerations proposed by Welker [4] years earlier. He assumed “that in the superconducting state a finite energy gap is required to excite electrons from the surface of the Fermi sea.” Cooper developed this concept further when he introduced the electron pairs in the following year [5]. In the seminal BCS paper of 1957 [6], Bardeen, Cooper and Schrieffer finally derived the fundamental ratio and the temperature dependence of the energy gap. In their calculation of the matrix elements, they explicitly refer to the ongoing NMR relaxation-rate experiments by Hebel and Slichter [7, 8], ultrasound-attenuation measurements by Morse and Bohm [9], and
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