Fabry-Pérot Metacavities with Single-Layered Dielectric Metamirrors

TL;DR

The paper addresses the challenge of achieving highly controllable, high-Q optical resonances in compact cavities by introducing dielectric Fabry-Pérot metacavities built from simple, single-layer metamirrors. It develops an analytical framework by combining 2D cylinder scattering with 1D periodic arrays to obtain closed-form metamirror reflection amplitudes and phases, and then derives an explicit FP cavity response under negligible near-field coupling. Key contributions include closed-form expressions for the cylinder scattering coefficients $a_m^{p,s}$, metamirror reflectivity $R^{p,s}(\\

Abstract

The Fabry-Pérot resonator is a cornerstone of photonics and wave physics, providing a universal mechanism for spectral confinement and resonant enhancement of wave-matter interactions. In this work, we establish an analytically tractable class of Fabry-Pérot metacavities in which the reflecting elements are realized by single-layer periodic arrays of circular dielectric cylinders acting as metamirrors. Both the reflection efficiency and reflection phase of such metamirrors are obtained in closed form and shown to be widely and independently tunable, encompassing ideal electric and magnetic mirror limits with unit reflectivity. Building on these results, we derive explicit analytical expressions that fully describe the optical responses of Fabry-Pérot cavities composed of two such parallel metamirrors. Our combined analytical and numerical investigations reveal that these metamirrors provide exceptional flexibility for tailoring Fabry-Pérot resonances across a broad spectral range, enabling precise control over resonance positions and quality factors. In particular, the framework naturally predicts the emergence of Fabry-Pérot bound states in the continuum with formally infinite Q-factors. These results establish dielectric-metamirror-based Fabry-Pérot cavities as a versatile and fundamentally transparent platform for engineering high-Q optical resonances.

Figures (8)

• Figure 1: Schematic illustration of a plane wave (wavevector $\textbf{k}$ and incident angle $\phi$) interacting with a Fabry-Pérot metacavity consisting of two parallel periodic arrays of dielectric cylinders (metamirrors): the two arrays share the same period $d$ and cylinder refractive index $\mathbbm{n}$, are gaped by metacavity length $L$ along x direction and offset by $\Delta s$ along y direction. The radii of the cylinders for the two arrays are $\mathbbm{r}_1$ and $\mathbbm{r}_2$, respectively. The incident wave could be $s$-polarized (electric field along z direction) or $p$-polarized (electric field perpendicular to z direction).
• Figure 2: Reflectivity [Eq. (\ref{['reflection_efficiency1']})] and reflection phase [Eq. (\ref{['reflection_efficiency2']})] spectra (with respect to incident wavelength) for a single-layered array (period $d=280$ nm, refractive index $\mathbbm{n}=3.6$, and cylinder radius $\mathbbm{r}=100$ nm). The incident wave could be $p$-polarized [(a) and (c)] and $s$-polarized [(b) and (d)], and the results cover both scenarios of normal incidence [$\phi=0$ for (a) and (b)] and oblique incidence [$\phi=30^{\circ}$ for (c) and (d)].
• Figure 3: Transmission spectra with respect to $L$ for the whole metacavity consisting of two identical arrays ($d=280$ nm, $\mathbbm{n}=3.6$, and $\mathbbm{r}_1=\mathbbm{r}_2=100$ nm) without offset ($\Delta s=0$). The incident wave could be $p$-polarized [(a) and (c); $\lambda=618~$nm] and $s$-polarized [(b) and (d); $\lambda=690~$nm], and the two sets of results [numerical simulation through COMSOL and Eq. (\ref{['transmission-fb-identical']})] cover both scenarios of normal incidence [$\phi=0$ for (a) and (b)] and oblique incidence [$\phi=30^{\circ}$ for (c) and (d)].
• Figure 4: Transmission spectra with respect to $L$ for the whole metacavity consisting of two identical arrays ($d=280$ nm, $\mathbbm{n}=3.6$, and $\mathbbm{r}_1=\mathbbm{r}_2=100$ nm). The normally incident wave ($\phi=0$) could be $p$-polarized [(a) and (c); $\lambda=601~$nm] and $s$-polarized [(b) and (d); $\lambda=551~$nm], and the two sets of results [numerical simulation and Eq. (\ref{['transmission-fb-identical']})] cover both scenarios with offsets [$\Delta s=70$ nm and $80$ nm for (c) and (d), respectively] and without offset [$\Delta s=0$ for (a) and (b)]. For all cases, numerical near-field distributions for one unit-cell are included as insets (in terms of electric field amplitude; the corresponding positions are marked by green dots): $L=200$ nm for (a) and (c); $L=250$ nm for (b) and (d).
• Figure 5: Transmission spectra with respect to $L$ for the whole metacavity consisting of two different arrays ($d=280$ nm, $\mathbbm{n}=3.6$, $\mathbbm{r}_1=100$ nm and $\mathbbm{r}_2=75$ nm) without offset ($\Delta s=0$). The incident wave could be $p$-polarized [(a) and (c); $\lambda=620~$nm] and $s$-polarized [(b) and (d); $\lambda=620~$nm], and the two sets of results [numerical simulation and Eq. (\ref{['transmission-fb']})] cover both scenarios of normal incidence [$\phi=0$ for (a) and (b)] and oblique incidence [$\phi=30^{\circ}$ for (c) and (d)].