# Zero electromagnetic coupling of closely spaced identical helical resonators

## TL;DR

This paper shows how closely spaced helical resonators can have near-zero electromagnetic coupling, enabling better performance in microwave devices.

## Contribution

The study demonstrates near-zero coupling in closely spaced helical resonators through specific geometric design.

## Key findings

- Near-zero electromagnetic coupling is achieved between closely spaced helical resonators.
- 3D-printed metal samples confirm the numerical simulations of low coupling.
- Periodic chains of helices show controllable dispersion and near-zero group velocity.

## Abstract

The interaction between closely spaced elements in an electromagnetic array typically leads to significant inter-element coupling, altering the resonance properties of each element. This coupling influences, often limiting the performance of metamaterials, filters, and phased arrays. In this study using both numerical simulations and experimental validation, we explore the electromagnetic coupling between identical helical microwave resonators and demonstrate how, under specific geometric conditions, near-zero coupling can be achieved even at highly sub-wavelength separations (\documentclass[12pt]{minimal}
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\begin{document}$$<\frac{\lambda }{10}$$\end{document}). Experimental samples are produced using 3D-printed molds subsequently filled with low-melting-point Field’s metal, enabling precise and repeatable resonator construction. The numerical analysis is further extended to infinite periodic chains of identical helices, revealing that similar geometric conditions enable control over propagating mode dispersion, including near-zero group velocity.