Theory of Impedance Loaded Loop Antennas and Nanorings From RF to Optical Wavelengths

The analytical theory of perfectly conducting thin-wire closed-loop antennas with multiple loads in the periphery was formally derived in the 1950s and 1960s. In this paper, it is extended to loop antennas and nanorings for use in communications, in the “Internet of things,” and as metamaterials. The new derivation relies on recent work from 2013 that incorporates the surface impedance of metal wires into the standard theory, thus pushing its applicability into the gigahertz, terahertz, and optical regimes. Surface impedance effects cause losses and phase shifts in the current within the loop, which in turn cause wavelength scaling and degradation of signal strength. These effects are modeled using a critical point transition model of permittivity and of the index of refraction. The new results therefore extend standard loop antenna theory so that it now includes characteristics of multiply loaded loops over a very broad spectrum from radio frequencies to the optical region. The new model is verified using modern simulation tools. The examples given here include resistive and capacitive loading.