Mie Void Lattices in High-Index Dielectrics

• Mie void lattices are periodic arrays of air-filled or low-index cavities embedded in a high-index medium, enabling enhanced resonant field access.
• They are engineered to tune optical responses for applications including sensing, structural coloration, transmission filtering, nonlinear enhancement, and emitter control.
• Fabrication methods such as focused ion beam milling, electron-beam lithography, and femtosecond laser printing allow precise geometric control and integration with active materials.

Mie void lattices are periodic arrays of air-filled or low-index cavities patterned into or onto a high-index dielectric membrane or substrate. They are the inverse of conventional dielectric Mie resonators: instead of high-index particles in a low-index background, the resonant object is a void embedded in a high-index medium, so resonant fields can be concentrated in an accessible low-index cavity while still interacting with the surrounding dielectric (Panov, 12 Jul 2026). Across silicon, gallium phosphide, gallium arsenide, silicon-rich nitride, Bi$_2$Te$_3$, and WSe$_2$ platforms, this inverse geometry has been used for resonant light confinement in air, structural color, transmission filtering, sensing, nonlinear optics, and emitter control, while also making clear that isolated void resonances, bridge modes, hybrid slab modes, and collective lattice effects must be distinguished carefully (Hentschel et al., 2022).

1. Inverse-dielectric definition and scope

The defining element of a Mie void lattice is a low-index cavity inside a high-index host. In the standard dielectric-resonator picture, resonant electric and magnetic modes are mainly confined inside a high-index particle. In a Mie void geometry, the refractive-index contrast is reversed: the cavity is air-filled or otherwise low-index, while the surrounding medium provides the confining boundary. This changes both field localization and the way the resonator interacts with matter placed in or near the cavity (Goldberg et al., 29 Mar 2026).

Several closely related terms are used in the literature. “Mie void metasurfaces,” “periodic Mie void arrays,” and “Mie void lattices” describe essentially the same class of structures when the architecture is a periodic array of subwavelength cavities in a high-index material. The dominant host materials reported include silicon, GaP, GaAs, silicon-rich nitride, Bi$_2$Te$_3$, and WSe$_2$, while the void itself may be spherical, cylindrical, frustum-shaped, hemispherical, or a laser-printed three-dimensional nanocavity (Goldberg et al., 12 Apr 2026).

The central practical distinction from conventional dielectric particles is that the resonant volume is open and accessible. The literature repeatedly emphasizes that this open-cavity geometry is useful for infiltrated materials, emitters, fluorophores, quantum dots, monolayers, and analytes, because the field maximum is relocated into air rather than buried inside the dielectric host (Fu et al., 27 Jan 2026). At the same time, this same inversion can limit host-mediated nonlinear enhancement, since the nonlinear medium is usually the high-index dielectric rather than the air-filled cavity.

2. Electromagnetic description and modal structure

The canonical theoretical description starts from a spherical inclusion problem. For a void of radius $R$ with refractive index $n_i$ inside a surrounding medium of refractive index $n_e$, the resonant-state frequencies are determined by the zeros of the Mie denominators. For nonmagnetic media, the paper on dielectric Mie voids writes the eigenfrequency conditions as

$$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$

$_3$0

with $_3$1, $_3$2, and $_3$3 (Hentschel et al., 2022). In this formulation, nothing forbids the inverted case $_3$4; the resulting modes are leaky quasi-normal resonances localized mainly inside the void.

The spherical-void theory developed for polaritonic Mie cavities further separates well-confined $_3$5 resonances from strongly delocalized low-$_3$6 $_3$7 modes, and gives a bare-cavity quality factor

$_3$8

In the high-contrast limit, the reported asymptotic scaling is $_3$9, so increasing host permittivity improves confinement, but only slowly (Ryabkov et al., 6 Oct 2025).

Experimental and numerical papers typically use a mode taxonomy closer to metasurface practice than to spherical-harmonic notation. Reported resonances include electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole responses, as well as electric-dipole-type void modes, magnetic-dipole-like void modes, and higher-order modes whose field maxima remain inside the air cavity (Gong et al., 23 Mar 2026). In finite films, however, these local modes are often not spectrally isolated. Transmission-mode silicon-rich nitride Mie-void metasurfaces explicitly show that replacing a semi-infinite host by a finite film introduces slab-guided and Fabry–Pérot-like contributions that hybridize with the underlying Mie-void response; thickness-dependent dispersion maps then reveal avoided crossings between interacting branches (Goldberg et al., 12 Apr 2026).

A further extension is the resonant-medium problem. For a spherical void loaded with a Lorentz dielectric,

$_2$0

the reported single-mode polaritonic equation is

$_2$1

with effective coupling $_2$2 and explicit weak- and strong-coupling thresholds (Ryabkov et al., 6 Oct 2025). This places Mie voids within the broader cavity-polariton literature, but with the cavity field concentrated in the void.

3. Geometries, materials, and fabrication routes

Early experimental work established the platform using focused-ion-beam-milled holes in bulk silicon wafers. The realized structures were conical or truncated-conical cylindrical holes at the silicon–air interface rather than closed buried spheres. Spectroscopically characterized arrays used representative dimensions of diameter $_2$3 nm, depth $_2$4 nm, and period $_2$5 nm; broader diameter and depth sweeps extended from roughly $_2$6 to $_2$7 nm in diameter and from $_2$8 to $_2$9 nm in depth (Hentschel et al., 2022). This work established that diameter and depth are both robust tuning knobs and that visible-to-UV resonances can be accessed in bulk silicon by carving the resonator into the host material rather than fabricating a raised particle.

A second fabrication direction is grayscale electron-beam lithography in silicon. In this approach, a $_2$0-period lattice of cylindrical or near-cylindrical holes is written into PMMA with spatially varying dose, then transferred into silicon by reactive ion etching. The reported simulation space sweeps radius over $_2$1–$_2$2 and depth over $_2$3–$_2$4, while experiment uses representative arrays with radius $_2$5 and pitch $_2$6. The process uses about $_2$7 nm total PMMA thickness, PMMA and Si etch rates of $_2$8 and $_2$9, and a selectivity of approximately $_3$0 (Goldberg et al., 29 Mar 2026). The principal result is that local void depth, rather than diameter, is the dominant spectral tuning parameter in this platform.

Transmission-mode visible devices required a different host. In silicon-rich nitride, the reported geometry is a periodic array of cylindrical voids with period $_3$1, nominal radius $_3$2 nm, depth varied from $_3$3 to $_3$4 nm, and film thickness about $_3$5 nm on SiO$_3$6/glass (Goldberg et al., 12 Apr 2026). Because the voids reside in a finite film rather than a semi-infinite host, this platform became the clearest demonstration that Mie-void physics in transmission is not simply the reflection geometry viewed from the opposite side.

Direct laser fabrication provides a third route. “Mie-lithography” produces air-filled nanocavities in high-index substrates by femtosecond-laser optical breakdown followed by resonance-assisted self-guided deepening. Reported printed cavities span from seed voids approximately $_3$7 nm wide and $_3$8 nm deep to deeper resonators around $_3$9 nm depth, with geometry controlled through pulse number, pulse energy, and polarization. The platform was demonstrated at $_2$0 pixels/s and $_2$1 DPI, with DUV–NIR spectral functionality over $_2$2–$_2$3 nm (Gong et al., 23 Mar 2026).

Scalable wafer-level fabrication has also been demonstrated for biosensing arrays. Silicon Mie void arrays for digital nanoparticle counting use a square lattice with period $_2$4 nm, cylindrical void diameter $_2$5 nm, depth $_2$6 nm, and edge-to-edge spacing $_2$7 nm, fabricated by deep-UV lithography on 4-inch wafers (Riabov et al., 1 Apr 2026).

4. Resonant regimes, hybridization, and the meaning of “lattice”

A recurring issue in the literature is that periodicity does not automatically imply collective lattice physics. Several sensing and emission papers fabricate regular arrays but interpret the optics mainly in terms of localized single-void resonances repeated across many sites. The nanoplastic-sensing platform in GaAs, for example, uses periodic arrays of circular and elliptical voids, yet explicitly treats the optical behavior as dominated by each individual void’s localized resonance and notes that pitch is chosen mainly to spatially separate sites and permit microscopy and automated image analysis (Ludescher et al., 29 May 2026). Attoliter refractive-index sensing in GaAs reaches the same conclusion: single-void sensitivity is similar to array sensitivity because the voids in the measured arrays interact only very weakly with one another (Arslan et al., 2024).

Other platforms occupy a more genuinely hybrid regime. In transmission-mode silicon-rich nitride, the dominant spectral transformation occurs when the semi-infinite host is replaced by a finite film; the substrate then acts mainly as a secondary perturbation. The reported avoided crossing in the thickness-dependent transmission map is explicit evidence that the resonances are coupled states of void-localized, slab-guided, and Fabry–Pérot-like modes rather than pure local void modes (Goldberg et al., 12 Apr 2026).

The nonlinear GaP work sharpens this distinction by identifying two regimes within a void lattice itself. When voids are sufficiently separated, the optical response is dominated by isolated Mie void resonances; in GaP metasurfaces, these are observable when the separation between voids exceeds approximately $_2$8 nm. Below this threshold, the dominant mode develops in the high-index bridges between neighboring voids rather than inside the cavities. In the frustum lattice, the bridge mode prevails up to $_2$9, corresponding to a void separation of about $R$0 nm, while the strongest global Kerr-enhancement peak appears around $R$1, where the distance between voids is only about $R$2 nm (Panov, 12 Jul 2026). This is an explicit lattice-coupling threshold: beyond it one can still speak of individual-cavity Mie void resonances, below it the relevant optical object is the intervening high-index region.

A related caution comes from guided-mode-resonant photonic lattices. A study of periodic rod lattices showed that perfect reflection is caused by guided-mode resonance mediated by lateral Bloch modes excited by evanescent diffraction orders in the subwavelength regime, not by isolated-particle Mie resonance. The same work introduced “Mie modal memory” for cases where a collective lattice mode approaches the isolated-particle Mie field profile, causing the resonance locus to bend toward the Mie wavelength without changing its collective origin (Ko et al., 2020). This suggests that, in Mie void lattices as well, a Mie-like near field is not by itself sufficient evidence that a measured spectral feature is an isolated void resonance rather than a collective lattice or slab mode.

5. Nonlinear optics, exciton coupling, and quantum emission

The nonlinear-optical performance of Mie void lattices depends critically on where the field overlaps the nonlinear medium. In GaP membrane metasurfaces at $R$3 nm, 3D FDTD simulations retrieve the effective Kerr response from the transmitted phase shift using

$R$4

For spherical void lattices in a $R$5-thick GaP slab, the effective Kerr enhancement peaks near the magnetic-dipole void resonance at $R$6 nm with $R$7. For a more realistic frustum geometry with $R$8, $R$9, $n_i$0, and $n_i$1, the reported enhancement is only a bit above two (Panov, 12 Jul 2026). The same study concludes that genuinely isolated Mie void resonances typically produce less than tenfold Kerr enhancement, whereas the bridge mode between closely spaced voids can exceed two orders of magnitude relative to bulk because the energy density is then concentrated directly in nonlinear GaP.

Hybrid systems exploit the opposite virtue: access to the field in the void. In Bi$n_i$2Te$n_i$3 patterned with cylindrical Mie voids and covered by monolayer WS$n_i$4, the electric-dipole-like void resonance is aligned to the WS$n_i$5 A-exciton near $n_i$6 nm. The optimal simulated geometry at the exciton wavelength is approximately $n_i$7 nm and $n_i$8 nm, corresponding to $n_i$9. Experimentally, the structure yields $n_e$0 photoluminescence enhancement and $n_e$1 second-harmonic generation enhancement, while far-field SHG imaging maps the geometry-dependent nonlinear hotspots across the array (Lu et al., 18 Dec 2025). The arrays in this work were intentionally designed with negligible inter-void coupling, so the reported behavior is still unit-cell physics measured in an array format.

A related all-van-der-Waals platform couples WS$n_e$2 excitons to air cavities etched into WSe$n_e$3. Here the design rule is a constructive-interference condition,

$n_e$4

which co-tunes diameter and depth to maximize field at the void opening (Sarbajna et al., 19 Dec 2025). The best reported single-void performance is up to $n_e$5-fold experimental photoluminescence enhancement, while a $n_e$6 nm-pitch array used for Fourier-plane measurements shows a forward-to-off-axis enhancement of $n_e$7 dB. Again, the array is used mainly to access directional emission rather than to study Bloch coupling.

Silicon Mie voids have also been used to engineer spontaneous emission with a quantitative separation between pump enhancement and quantum-yield enhancement. The paper defines

$n_e$8

with

$n_e$9

and

$$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$0

Gradient and uniform arrays of silicon voids filled with FITC-doped PVA show broad-band photoluminescence tuning and lifetime shortening from $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$1 ns on bare silicon to $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$2–$$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$3 ns in structured arrays, confirming accelerated radiative decay enabled by the void configuration (Fu et al., 27 Jan 2026).

6. Structural color, sensing, and present limitations

Structural color has become one of the most developed application classes. In silicon, depth-programmable Mie void metasurfaces tune reflection across the whole visible spectrum while keeping period and radius nearly fixed; uniform arrays, bullseye and mosaic patterns, and a sunset-lit mountain range demonstrate that local cavity depth can encode spatially varying color over a regular lattice (Goldberg et al., 29 Mar 2026). In silicon-rich nitride, the same depth variable supports visible transmission-mode structural colors and transmitted-light image encoding in a single inverse-dielectric architecture (Goldberg et al., 12 Apr 2026). Laser-printed air-cavity resonators extend this spectral design principle from the deep ultraviolet to the near infrared, including a $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$4 dispersion-pixel array that reconstructs spectra over $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$5–$$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$6 nm with $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$7 nm resolution (Gong et al., 23 Mar 2026).

Sensing applications exploit the fact that the analyte can occupy the resonant volume itself. In GaAs single-void refractive-index sensing, Mie voids define sensing volumes down to $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$8 attoliters, with single-void sensitivities of $$\text{TM modes:}\qquad \frac{\psi_l'(n_i k_0 R)}{\psi_l(n_i k_0 R)} = \frac{n_i}{n_e} \frac{\xi_l'(n_e k_0 R)}{\xi_l(n_e k_0 R)},$$9 nm/RIU for a $_3$00 aL cavity and $_3$01 nm/RIU for a $_3$02 aL void. Using a glycerol-filled $_3$03 aL cavity, the reported minimum detectable refractive-index change is $_3$04 (Arslan et al., 2024). In GaAs nanoplastic sensing, arrays of circular and elliptical voids distinguish PS, PMMA, and PET by refractive-index-dependent color signatures and separate spheres from ellipsoids by geometry-selective trapping, with a reported mis-trapping probability of $_3$05 for ellipsoids in circular voids (Ludescher et al., 29 May 2026).

Digital biosensing extends this logic to nanoparticle counting. Silicon Mie void arrays with period $_3$06 nm, diameter $_3$07 nm, and depth $_3$08 nm create a dark resonant reflection background whose signal readout is defined by interference of the large non-resonant reflection from the silicon substrate and the resonant scattering of light by the voids. Single $_3$09 nm Au nanoparticles captured inside and outside the cavities then produce opposite-sign local contrast, and a U-Net-based classifier enables digital counting. In an IL-6 sandwich assay, the reported limit of detection is $_3$10 pg/ml from $_3$11 sample volumes (Riabov et al., 1 Apr 2026).

The main limitation emerging across the literature is that a Mie void lattice is not simply the negative image of a conventional dielectric-particle lattice with the same performance envelope. If the design goal is host-mediated Kerr enhancement, isolated void resonances are usually not competitive with resonances that confine energy in the high-index dielectric. If the goal is near-100% reflection or ultranarrow lattice resonances, local Mie-void language can be misleading unless slab, Bloch, or guided-mode effects are explicitly checked. The durable strengths of the platform are instead low-index field access, broad material compatibility, depth programmability, and direct integration with emitters, analytes, and infiltrated media. The term should also not be conflated with “void lattices” or “void superlattices” in irradiated metals, which refer to a distinct Turing-instability problem in solid-state defect physics rather than an optical Mie platform (Noble et al., 2019).