Volumetric Metaoptic: 3D Nanophotonic Devices

• Volumetric metaoptic is a class of meta-optical devices defined by three-dimensional, inverse-designed nanophotonic structures that utilize sub-wavelength features and full-volume optimization.
• It achieves multifunctional sorting of wavelength, polarization, and angle through gradient-based inverse design, multilayer architectures, and sophisticated scattering mechanisms.
• These systems enhance imaging volume and depth of focus in applications like microscopes and miniscopes, despite challenges in fabrication efficiency and resolution trade-offs.

Searching arXiv for recent and core papers on volumetric meta-optics and related depth-extended/meta-optical imaging. Searching arXiv for exact paper titles and closely related work. Volumetric metaoptic denotes, in recent arXiv literature, a class of meta-optical devices and systems in which optical functionality is realized by exploiting three-dimensional structure, axial wavefront coding, or both. In the strict nanophotonic sense, it refers to inverse-designed dielectric elements whose full volume is structured at sub-wavelength scale and participates through multiple scattering and interlayer coupling, enabling multifunctional mappings such as spectral, polarization, and angular sorting or compact wavefront sensing (Camayd-Muñoz et al., 2020, Ballew et al., 2023, Roques-Carmes et al., 2021). In a broader systems sense, related work uses meta-optics to engineer extended depth of focus, depth sensitivity, or axial robustness in microscopes, miniscopes, and camera modules, thereby enlarging the usable imaging volume without conventional bulk optics or active refocusing (Whitehead et al., 2021, Brandmüller et al., 2024, Zhou et al., 19 Sep 2025).

1. Terminology and scope

The literature uses volumetric metaoptic in at least two closely related ways. The narrower usage denotes a genuinely three-dimensional, subwavelength-structured dielectric element in which the full refractive-index distribution is optimized throughout a finite volume rather than confined to a single patterned surface. This usage is explicit in work on 3D dielectric elements for color and polarization image sensors, few-wavelength-thick inverse-designed multilayer optics, and highly scattering inverse-designed media for multidimensional sensing (Camayd-Muñoz et al., 2020, Roques-Carmes et al., 2021, Ballew et al., 2023).

A broader usage emphasizes what the optic does along the axial dimension rather than whether the nanophotonic structure itself is volumetric. In that broader sense, extended-depth-of-focus metalenses, depth-sensitive point-spread-function engineering, and axially tolerant photoacoustic excitation can be treated as adjacent forms of volumetric meta-optics because they deliberately shape the response of the optical system over a depth interval rather than at a single focal plane (Whitehead et al., 2021, Brandmüller et al., 2024, Zhou et al., 19 Sep 2025).

This distinction is technically important. A single-layer metasurface is usually modeled as an ultrathin phase, amplitude, or polarization mask. A volumetric metaoptic, by contrast, uses thickness as an optical degree of freedom: internal scattering paths, near-field coupling across layers, and depth-dependent propagation become part of the design space. One paper further sharpens the definition by introducing “linear volume metaoptics” as freeform, nonperiodic, volumetric nanophotonic structures governed by linear wave scattering, while arguing that the resulting image can still be nonlinear with respect to an opaque scene’s depth map (Zhang et al., 26 Aug 2025).

2. Device classes and physical implementations

Strictly volumetric implementations span freeform 3D voxellized structures and closely packed multilayer architectures. A representative pixel-scale sensor optic is a $(2\,\mu\mathrm{m})^3$ polymer/air cube discretized into $100 \times 100 \times 100$ voxels of size $(20\,\mathrm{nm})^3$, alongside a fabrication-constrained alternative comprising five $400\,\mathrm{nm}$ TiO$_2$/SiO$_2$ layers with the same $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$ footprint and $2\,\mu\mathrm{m}$ total thickness (Camayd-Muñoz et al., 2020). A second class is the inverse-designed multilayer scattering volume for wavefront sensing: a $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$ device above a $3\times 3$ sensor-pixel region, built from 20 layers of TiO$100 \times 100 \times 100$0 and SiO$100 \times 100 \times 100$1, each $100 \times 100 \times 100$2 thick, with $100 \times 100 \times 100$3 minimum feature size (Ballew et al., 2023). A third class is the few-wavelength-thick 3D-printed inverse-designed optic, experimentally realized as a two-layer IP-Dip polymer concentrator at $100 \times 100 \times 100$4, with a $100 \times 100 \times 100$5 by $100 \times 100 \times 100$6 footprint, $100 \times 100 \times 100$7, and fabrication-aware extruded ridge geometry (Roques-Carmes et al., 2021).

Depth-functional but planar implementations occupy a different point in the design space. A visible cubic EDOF metasurface uses SiN nanoposts on quartz with $100 \times 100 \times 100$8 thickness, $100 \times 100 \times 100$9 lattice periodicity, $(20\,\mathrm{nm})^3$0 diameter, nominal focal length $(20\,\mathrm{nm})^3$1, and maximum $(20\,\mathrm{nm})^3$2 (Whitehead et al., 2021). In optical-resolution photoacoustic microscopy, resist-only PMMA metalenses at $(20\,\mathrm{nm})^3$3 replace the excitation lens, including a grating metalens with $(20\,\mathrm{nm})^3$4, $(20\,\mathrm{nm})^3$5, and diffraction angle $(20\,\mathrm{nm})^3$6 (Brandmüller et al., 2024). In miniscopes, a single-layer transmissive dielectric metasurface based on $(20\,\mathrm{nm})^3$7 silicon nitride on fused silica replaces the conventional objective module and implements hyperbolic, square-phase, EDOF, and double-helix designs within the UCLA Miniscope V4 architecture (Zhou et al., 19 Sep 2025).

A further systems-level category is not volumetric in the strict material sense but is relevant to volumetric functionality across multiple optical planes. A transformer-based framework models planar silicon metaoptics composed of cylindrical air holes at $(20\,\mathrm{nm})^3$8 wavelength and couples their learned electromagnetic response to OpticStudio physical optics propagation, thereby addressing multiscale design for optical chains containing multiple metaoptics (Ng et al., 26 Mar 2025).

3. Inverse-design formalisms and system models

The dominant design paradigm is gradient-based inverse design under full-wave Maxwell constraints. In the sensor-integrated 3D dielectric element, the figure of merit is the field intensity at a target point,

$(20\,\mathrm{nm})^3$9

and the adjoint sensitivity is

$400\,\mathrm{nm}$0

The same work introduces binary projection and differentiable dilation to enforce two-material designs and minimum feature size (Camayd-Muñoz et al., 2020).

In the multilayer 3D-printed concentrator, density-based topology optimization with the Method of Moving Asymptotes is combined with fabrication-aware filter-and-project regularization. The device is jointly optimized for five non-paraxial incident angles, all targeting the same focal line, and the paper explicitly motivates volumetric inverse design by noting that the intended functionality has no straightforward ray-optics prescription and conflicts with a reciprocal $400\,\mathrm{nm}$1 ABCD-matrix argument in the Supplementary Information (Roques-Carmes et al., 2021).

The wavefront-sensing volumetric metaoptic uses multi-objective adjoint-based topology optimization in Lumerical FDTD. Each training objective maps an incident plane wave defined by wavelength, angle, and polarization to power through a desired pixel; the structure is optimized in a continuous density phase and then thresholded for level-set optimization, with gradients averaged in the $400\,\mathrm{nm}$2-direction within each layer (Ballew et al., 2023).

A distinct forward model appears in the inference-oriented treatment of linear volume metaoptics. For an opaque 3D scene represented by a spectral surface intensity $400\,\mathrm{nm}$3 and depth map $400\,\mathrm{nm}$4,

$400\,\mathrm{nm}$5

and the detector measurement becomes

$400\,\mathrm{nm}$6

The paper’s central claim is that the optics remains linear in the electromagnetic sense while the measurement becomes nonlinear with respect to the latent depth map because depth enters the response function itself (Zhang et al., 26 Aug 2025).

At system scale, a different computational problem arises: accurate but tractable modeling of metasurfaces embedded in larger optical trains. The transformer-based framework addresses this by learning a local map from incident field plus meta-atom neighborhood to output electric field, stitching local predictions across the aperture, and alternating that step with OpticStudio physical optics propagation between optical planes (Ng et al., 26 Mar 2025).

4. Functional regimes

Across the literature, volumetric metaoptics are used for multifunctional sorting, coded sensing, angle-multiplexed concentration, and depth-extended or depth-sensitive imaging. The strict volumetric examples are characterized by many-to-few optical mappings: incoming wavelength, angle, or polarization are encoded into target pixels, sub-pixel quadrants, or designated focal regions. The depth-functional examples instead engineer axial invariance or axial coding into the point-spread function. Together they show that volumetricity can be expressed either as physical 3D nanophotonic structure or as designed axial response (Camayd-Muñoz et al., 2020, Ballew et al., 2023, Roques-Carmes et al., 2021, Whitehead et al., 2021, Brandmüller et al., 2024, Zhou et al., 19 Sep 2025).

Regime	Representative implementation	Demonstrated behavior
Multifunctional sensor optics	3D dielectric cube or five-layer TiO$400\,\mathrm{nm}$7/SiO$400\,\mathrm{nm}$8 stack	RGB sorting, green-band polarization splitting, and focusing to four target regions
Multidimensional wavefront sensing	20-layer TiO$400\,\mathrm{nm}$9/SiO$_2$0 scattering medium above $_2$1 pixels	Simultaneous encoding of direction, wavelength, and polarization
Angle-multiplexed concentration	Two-layer 3D-printed IP-Dip device	Five non-paraxial input angles focused to the same focal line
Static varifocal-like imaging	Cubic EDOF metasurface	Axially elongated focus and finite-conjugate imaging across multiple object distances
Depth-extended microscopy	Grating metalens in OR-PAM; EDOF miniscope objective	Larger usable axial range without conventional refocusing
Depth encoding	Double-helix miniscope objective	Depth mapped to PSF rotation angle

The sensor-integrated volumetric optic above image pixels sorts blue $_2$2, green $_2$3, and red $_2$4 light into four $_2$5 target regions located $_2$6 below the device, with the green band split by two orthogonal linear polarizations (Camayd-Muñoz et al., 2020). The multidimensional wavefront sensor instead maps five plane-wave directions, two wavelengths, and two orthogonal linear polarizations into a $_2$7 sensor code, using brightness ratios rather than spot displacement as the encoding variable (Ballew et al., 2023). The inverse-designed concentrator focuses illumination from $_2$8 into the same focal line, establishing an experimentally validated angularly multiplexed function that is not captured by a single thin-lens phase profile (Roques-Carmes et al., 2021).

Depth-oriented meta-optical systems pursue a different functionality. The cubic EDOF metasurface adds a cubic perturbation to the focusing phase and uses deconvolution to support imaging over a focal range from $_2$9 to $_2$0 (Whitehead et al., 2021). In OR-PAM, a grating metalens both separates the desired first-order focus from parasitic zeroth-order transmission and produces a more axially elongated focal structure, improving tolerance to defocus (Brandmüller et al., 2024). In the miniscope setting, one metasurface objective is inverse-designed so that the point-spread function extends over a target depth range, while another generates a double-helix PSF whose lobe rotation is used for depth estimation (Zhou et al., 19 Sep 2025).

5. Reported performance and trade-offs

Performance metrics vary sharply with device class, fabrication constraint, and task. In the freeform visible sensor optic, the reported band-averaged sorting efficiencies are $_2$1 for red, $_2$2 for green, and $_2$3 for blue. Under stronger fabrication constraints, the five-layer TiO$_2$4/SiO$_2$5 version reports $_2$6 sorting efficiency, $_2$7 color contrast, and $_2$8 polarization contrast, and maintains functionality up to about $_2$9 incidence (Camayd-Muñoz et al., 2020).

The multidimensional wavefront-sensing volume metaoptic is less a focusing element than a coded encoder. Averaged over all training states, it sends $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$0 of the input power to the correct pixels, $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$1 to incorrect pixels, and $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$2 elsewhere. The same paper reports that across 20 alternative pixel distributions, the average overlap of the transmission behavior is greater than $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$3 for all functionalities, indicating that the smooth ratio-based encoding is not strongly tied to a single pixel assignment (Ballew et al., 2023).

The 3D-printed inverse-designed concentrator shows the characteristic strengths and weaknesses of present low-index volumetric implementations. For the five measured zero-shift angles, the focal-line FWHM values are $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$4, about $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$5 larger than designed and close to the diffraction-limited width computed from $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$6 with $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$7. Measured absolute efficiencies are about $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$8 smaller than predicted numerically, while relative efficiencies within the field of view differ by about $2\,\mu\mathrm{m} \times 2\,\mu\mathrm{m}$9, implicating scattering outside the detector field of view as a major loss channel (Roques-Carmes et al., 2021).

In static EDOF imaging, the cubic metasurface reports a focal range from $2\,\mu\mathrm{m}$0 to $2\,\mu\mathrm{m}$1, corresponding to $2\,\mu\mathrm{m}$2 to $2\,\mu\mathrm{m}$3 optical power and a reported $2\,\mu\mathrm{m}$4 elongation of depth of focus relative to a standard lens. The price is resolution loss: reconstructed USAF-chart resolution is reported as $2\,\mu\mathrm{m}$5 horizontally and $2\,\mu\mathrm{m}$6 vertically, versus a $2\,\mu\mathrm{m}$7 diffraction-limited estimate under the same condition (Whitehead et al., 2021).

In photoacoustic microscopy, the grating metalens sacrifices focal compactness for axial tolerance. Its experimental spot FWHM is $2\,\mu\mathrm{m}$8, compared with $2\,\mu\mathrm{m}$9 for the original metalens and $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$0 for the glass lens; its optical efficiency is $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$1, dropping to $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$2 when absorption and scattering losses are considered, versus $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$3 transmission efficiency for the glass lens. Nonetheless, the paper states that for the grating metalens “even for distances of up to \SI{500}{\micro\meter} from the focal plane, the resolution and signal strength stays high,” whereas the conventional lens and the original metalens degrade more quickly away from focus (Brandmüller et al., 2024).

In the miniscope, the measured PSF-based depth of field is about $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$4 for the square metalens and about $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$5 for the EDOF metalens, while system-level USAF measurements show the EDOF metascope preserving resolving capability over $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$6. The double-helix design estimates a $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$7 depth difference between two $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$8 fluorescent beads against a $$3~\mu\text{m} \times 3~\mu\text{m} \times 4~\mu\text{m}$$9 ground truth (Zhou et al., 19 Sep 2025).

A separate but consequential trade-off concerns simulation fidelity. For single metaoptics from approximately $3\times 3$0 to $3\times 3$1, the transformer-based solver reports an average percent difference in irradiance of $3\times 3$2 relative to full-wave simulation, compared with $3\times 3$3 for an ideal model and about $3\times 3$4 for the local phase approximation, while remaining more than 3 orders of magnitude faster than traditional FDTD according to the abstract (Ng et al., 26 Mar 2025).

6. Open problems, misconceptions, and research trajectory

A recurrent misconception is to equate any depth-extended meta-optical system with true volumetric imaging. The literature is more specific. The photoacoustic microscopy study does not present full volumetric reconstructions; it demonstrates compact excitation optics and an extended-focus metalens that preserves lateral image quality over a larger axial range (Brandmüller et al., 2024). The metasurface miniscope shows EDOF and depth sensitivity, but not dense 3D reconstruction or computational refocusing from a captured 4D light field (Zhou et al., 19 Sep 2025). The cubic EDOF camera module provides varifocal-like functionality through deconvolution, not sectioned volumetric imaging (Whitehead et al., 2021).

A second misconception is that volumetric metaoptics must always be arbitrary freeform 3D nanostructures. Several influential demonstrations are instead few-layer or closely packed multilayer systems whose volumetric behavior arises because interlayer multiple scattering matters and the full thickness participates in the optical transformation (Roques-Carmes et al., 2021, Camayd-Muñoz et al., 2020). This suggests that volumetricity is a matter of electromagnetic coupling and design freedom, not only of geometric appearance.

A third misconception is that linear passive optics cannot support nonlinear inference. The inference-oriented formulation of linear volume metaoptics shows otherwise: for opaque scenes represented by a 2D depth map, the measurement is nonlinear in the latent depth variables even though the material response obeys linear Maxwell equations (Zhang et al., 26 Aug 2025). A plausible implication is that future volumetric metaoptics may be optimized not only for image formation but also for task-specific sensing of scene geometry.

The principal bottlenecks remain fabrication, efficiency, calibration, and multiscale modeling. Low-index polymers and 3D printing simplify volumetric fabrication but presently incur efficiency penalties and structural fragility; visible-band scaling remains difficult for truly freeform 3D devices (Roques-Carmes et al., 2021). Multifunctional sensor optics lose efficiency as fabrication constraints tighten (Camayd-Muñoz et al., 2020). Highly scattering sensing volumes require calibration and still route substantial power away from desired pixels (Ballew et al., 2023). Planar depth-functional systems often depend on narrowband operation, shift-invariant reconstruction assumptions, or calibration of engineered PSFs (Whitehead et al., 2021, Zhou et al., 19 Sep 2025). These constraints explain the current interest in fabrication-aware inverse design, surrogate full-system simulation, and hybrid optical-computational co-design (Ng et al., 26 Mar 2025).

Taken together, the field indicates a research trajectory from planar wavefront shaping toward axially expressive and fully volumetric optical transformations. One branch pursues richer three-dimensional scattering media for multifunctional sensing, pixel-level optics, and task-specific encoding. Another pursues compact planar meta-optics with engineered axial response for microscopy and machine vision. Their convergence would amount to a genuinely volumetric metaoptic: a compact, fabrication-realistic, three-dimensional nanophotonic system whose full volume is optimized jointly with downstream inference or reconstruction to control wavelength, angle, polarization, and depth in a single optical front end.