Closed-Form Expressions for the Radiation Properties of Nanoloops in the Terahertz, Infrared and Optical Regimes

Since the pioneering work of Heinrich Hertz, perfect-electric conductor (PEC) loop antennas for RF applications have been studied extensively. Meanwhile, nanoloops are promising in the optical regime for their applications in a wide range of emerging technologies. Unfortunately, analytical expressions for the radiation properties of conducting loops have not been extended to the optical regime. This paper presents closed-form expressions for the electric fields, total radiated power, directivity, and gain for thin-wire nanoloops operating in the terahertz, infrared and optical regimes. This is accomplished by extending the formulation for PEC loops to include the effects of dispersion and loss. The expressions derived for a gold nanoloop are implemented and the results agree well with full-wave computational simulations, but with a speed increase of more than 300×. This allows the scientist or engineer to quickly prototype designs and gain a deeper understanding of the underlying physics. Moreover, through rapid numerical experimentation, these closed-form expressions made possible the discovery that broadband super-directivity occurs naturally for nanoloops of a specific size and material composition. This is an unexpected and potentially transformative result that does not occur for PEC loops. Additionally, the Appendices give useful guidelines on how to efficiently compute the required integrals.