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Modern antenna theory forms the bulwark of our knowledge of how radiation and metallic structures interact in the radio frequency (RF) and microwave (MW) regions. The theory has not yet penetrated the terahertz, infrared, and optical regions to the same degree. In this paper, we provide a rigorous analysis of closed circular loop antennas from first principles. Using antenna theory, we tie together their long wavelength behavior with their behavior at short wavelengths through the visible region. We provide analytic forms for the input impedance, current, quality factor, radiation resistance, ohmic loss, and radiation efficiency. We provide an exact circuit model for the closed loop in the RF and MW regions, and extend it through the optical region. We also provide an implicit analytic form for the determination of all modal resonances, allowing prediction of the resonance saturation wavelength for loops. Through simulations, we find that this behavior extends to hexagonal and square loops. All results are applicable to loop circumferences as short as 350 nm. Finally, we provide a precise analytic model of the index of refraction, as a tool in these computations, which works equally well for metals and semi-conductors.

Theory of the circular closed loop antenna in the terahertz, infrared, and optical regions