Naturally resonant emitters: Approaching fundamental antenna limits

Abstract

Antenna miniaturization remains a critical technological challenge across frequency scales—from microwave RF links in phones/wearables to VLF (3-30kHz)/ELF (3Hz-3kHz) for underwater-to-air communications and ionospheric probing. At deeply subwavelength scales (ka ≪ 1), conventional antennas require complex and lossy matching circuits due to absent intrinsic material resonances, motivating resonant electrically small emitters (ESEs) like mechanical resonators and quantum emitters. Here, we extend the theory of electrically small antennas to this broader ESE class, deriving the fundamental efficiency limit for a unit volume emitter at given frequency and bandwidth. Our figure of merit (FOM)—quantifying proximity to this limit—enables direct comparison across ESE types, frequencies, bandwidths, and scales. We demonstrate its utility using public data from ELF (decommissioned) and VLF Navy facilities alongside two mechanical ESEs reported in the literature. The measurements reveal that mechanical antennas operate near the theoretical FOM limit, questioning claims of possible further orders-of-magnitude gains. A naturally resonant emitter is still subject to the Chu–Harrington limit (CHL) under its standard assumptions. Indeed, we derive novel CHL-dictated constraints on atomic ESE properties: lower bound on excited-state lifetime and an upper bound on transition dipole moment. Classical CHL circumvention strategies—like non-Foster matching and nonlinear parametric antennas—have been researched for decades. Quantum degrees of freedom, such as superradiance via collective coherence represent the new frontier.