Naturally Resonant Emitters: Approaching Fundamental Antenna Limits

TL;DR

This paper extends the theory of electrically small antennas to a broader class of emitters, deriving fundamental efficiency limits and introducing a figure of merit for comparing different ESEs across scales.

Contribution

It provides a unified theoretical framework and a new figure of merit for electrically small emitters, demonstrating near-limit performance of mechanical antennas and deriving novel constraints from the Chu-Harrington limit.

Findings

Mechanical antennas operate near the theoretical efficiency limit.

The figure of merit enables direct comparison across ESE types and scales.

Mechanical antennas challenge claims of orders-of-magnitude improvements.

Abstract

Antenna miniaturization remains a critical technological challenge across frequency scales - from microwave RF links in phones and wearables to VLF for underwater-to-air communications and ionospheric probing. At deeply subwavelength scales 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 (ESAs) 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 and VLF Navy facilities alongside two mechanical ESEs reported in literature. The measurements reveal that mechanical antennas operate near 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.