Fano resonance in metallic grating via strongly coupled subwavelength resonators

TL;DR

This paper studies Fano resonance phenomena in metallic gratings with strongly coupled subwavelength slit resonators, revealing how interference between different resonant modes causes characteristic transmission anomalies.

Contribution

It provides a rigorous analysis of the resonant poles and their interference, demonstrating the origin of Fano resonance in coupled subwavelength resonator structures.

Findings

Two groups of resonances with different decay rates identified.

Fano interference causes narrow-band transmission anomalies.

Resonance behavior persists for small slit apertures.

Abstract

We investigate the Fano resonance in grating structures by using coupled resonators. The grating consists of a perfectly conducting slab with periodically arranged subwavelength slit holes, where inside each period, a pair of slits sit very close to each other. The slit holes act as resonators and are strongly coupled. It is shown rigorously that there exist two groups of resonances corresponding to poles of the scattering problem. One sequence of resonances have imaginary part on the order of $\varepsilon$, where $\varepsilon$ is the size of the slit aperture, while the other sequence have imaginary part on the order of $\varepsilon^2$. When coupled with the incident wave at resonant frequencies, the narrow-band resonant scattering induced by the latter will interfere with the broader background resonant radiation induced by the former. The interference of these two resonances generates the Fano type transmission anomaly, which persists in the whole radiation continuum of the grating structure as long as the slit aperture size is small compared to the incident wavelength.