Mie-tronics supermodes and symmetry breaking in nonlocal metasurfaces

TL;DR

This work develops Mie-tronics as a unified framework that connects diffraction-based and scattering-based views of nonlocal metasurfaces. It shows that symmetry breaking in finite arrays can simultaneously enhance in-plane nonlocal coupling and the quality factor $Q$ of Mie-tronics supermodes, counter to infinite-lattice expectations. The authors reveal that bonding and anti-bonding Mie supermodes arise from multipole interactions beyond Bloch bands and that symmetry-breaking pathways redistribute radiation channels to boost confinement. They also demonstrate that symmetry breaking enables polarization conversion in diffractive nonlocal metasurfaces, linking unit-cell geometry to controllable out-of-plane and in-plane emission. Collectively, the results establish design principles for multi-functional metasurfaces that leverage nonlocality for advanced light manipulation, computation, and emission control, while bridging scattering and diffraction theories through a common Mie-mode basis.

Abstract

It is usually believed that symmetry breaking in photonic systems leads to weaker optical confinement, such as in the case of metasurfaces when bound states in the continuum are replaced by quasi-bound states with lower quality factors (Q factors). Here we show that symmetry breaking can instead enhance light trapping by strengthening in-plane nonlocal coupling pathways. We consider finite-size arrays of optical resonators supporting Mie resonances (a Mie-tronics platform) and employ diffraction and multiple-scattering analyses. We demonstrate that diffractive bands and Mie-tronics supermodes originate from the same underlying Mie resonances but differ fundamentally in their physical nature. Finite arrays exhibit Q-factor enhancement driven by redistributed radiation channels, and reversing the trends predicted by infinite-lattice theories. We reveal that controlled symmetry breaking opens new electromagnetic coupling channels, enabling polarization conversion in nonlocal metasurfaces. These novel findings establish a unified wave-physics platform linking both scattering and diffraction theories. Also, they outline the design principles for multi-functional metasurfaces that exploit nonlocality for advanced light manipulation, computation, and emission control.

Figures (7)

• Figure 1: Beyond spheres: unit cells in Mie-tronics. (a) Schematic of a magnetic dipole ($m_x$) interacting with an array of air holes in a silicon slab. Insets show two unit cells that are equivalent from a photonic-crystal perspective but distinct in Mie-tronics, with the geometrical parameters indicated. (b) Four functionally equivalent unit cells and their parameters. The spherical unit cell has a period of 425 nm, while the square and T-shaped unit cells have a period of 720 nm. All unit cells are composed of silicon ($n=3.5$) and surrounded by vacuum.
• Figure 2: Spectral dependence of the lowest-order Mie coefficients of the silicon sphere in Fig. \ref{['F1']}. Internal (left) and external (right) electric-dipole (ED) and magnetic-dipole (MD) coefficients reveal broad overlapping resonances. Values exceeding unity in the internal coefficients indicate enhanced energy storage within the particle, consistent with whispering-gallery–type behavior.
• Figure 3: Mie-tronics origin of supermodes in finite arrays and their connection to Bloch bands in photonic crystals. (a) Purcell-factor spectrum for the configuration in the inset, revealing two well-separated bands (anti-bonding and bonding) with pronounced supermodes labeled $A_{1,2}$ and $B_1$. (b),(c) Magnetic ($H_x$) and electric ($E_z$) field distributions for the anti-bonding mode $A_1$; the inset shows the corresponding far-field radiation pattern. (d) Bloch bands associated with the anti-bonding and bonding supermodes in (a). (e),(f) Same as (b),(c), but for the bonding mode $B_1$; the inset highlights dominant in-plane radiation leakage.
• Figure 4: Symmetry breaking enhances in-plane multiple scattering, preserves anti-bonding supermodes, and suppresses bonding counterparts in square and T-shaped arrays. (a) Purcell-factor spectrum for a magnetic dipole $m_x$ at the center of a $9\times9$ array of square unit cells. The presence of a quartz substrate ($n \simeq 1.45$) suppresses the bonding mode $B_1$, while the anti-bonding mode $A_1$ remains nearly unaffected. (b),(c) Magnetic near-field distribution and vortex-like far-field pattern of $A_1$. (d)–(f) Same as (a)–(c) but for the T-shaped array. The far-field pattern highlights enhanced in-plane multiple scattering along in-plane channels (ICs) versus suppressed out-of-plane channels (OCs).
• Figure 5: Symmetry breaking lowers the $Q$ of Bloch modes in infinite lattices but enhances the $Q$ of supermodes in finite metasurface arrays. (a) anti-bonding Bloch bands above the light line for the four unit-cell types. (b) $Q$ of Bloch modes at $\Gamma$: symmetry breaking reduces the divergent $Q$ of the square unit to a finite value in the T-shaped unit, while sphere and hole lattices show much higher $Q$. (c) $Q$ of supermodes in finite arrays: symmetry breaking boosts the $Q$ of T-shaped arrays beyond that of square arrays for sizes $5\times5$ to $33\times33$, with both outperforming sphere and hole arrays.