Synthetic Achromatic Metalens

• Synthetic achromatic metalenses are flat-optics devices that combine multiple optical and computational mechanisms to neutralize wavelength-dependent focal shifts.
• They employ diverse strategies, including composite stacked metasurfaces, hybrid refractive–metasurface systems, and inverse design to overcome monolithic design limitations.
• Their distributed synthesis of chromatic correction improves focal precision and imaging efficiency, making them pivotal for advanced broadband optical systems.

A synthetic achromatic metalens is a metalens whose achromatic behavior is assembled from multiple coordinated optical or computational mechanisms rather than obtained solely from a monolithic single-layer phase law. In the literature, that synthesis may be physical—through vertically stacked metasurfaces, multilayer thin films, hybrid refractive–metasurface systems, or full-structure inverse design—or computational, where a chromatic or wavefront-coded metalens is paired with post-capture reconstruction so that the combined imaging system behaves achromatically (Avayu et al., 2016, Balli et al., 2019, Hu et al., 2022, Dong et al., 2023, Huang et al., 2020). The topic therefore spans multispectral achromats, broadband achromats, hybrid achromats, achromatic metafibers, and computational achromatic cameras, all linked by the same objective: suppressing wavelength-dependent focal shift and color blur in an ultrathin or compact flat-optics platform.

1. Definition and taxonomy

In this literature, “synthetic” denotes functional composition. Instead of requiring every meta-atom in one surface to simultaneously provide the correct spatial phase and the correct chromatic dispersion, synthetic approaches distribute the achromatization burden across layers, distinct optical elements, free-form geometric degrees of freedom, or computation (Avayu et al., 2016, Zhang et al., 2021). This contrasts with intrinsically achromatic single-layer metasurfaces, where broadband correction is expected to arise directly from the local dispersion law of each unit cell.

The main architecture classes are summarized below.

Architecture class	Representative works	Synthetic mechanism
Composite stacked metasurfaces	(Avayu et al., 2016)	Spectral multiplexing across vertically stacked layers
Hybrid refractive–metasurface or phase-plate systems	(Balli et al., 2019, Hu et al., 2022, Zhang et al., 2024)	Distribute optical power and chromatic correction across different elements
Inverse-designed single-layer or multilayer structures	(Chung et al., 2019, Zhang et al., 2021, Pan et al., 2023)	Optimize the full geometry to satisfy broadband focusing objectives
Layered thin-film spectral synthesis	(Hooper et al., 2022)	Use engineered multilayer transmission or reflection spectra rather than local phase alone
Computational or hybrid optical-digital systems	(Dong et al., 2023, Huang et al., 2020, Colburn et al., 2019)	Accept chromatic or coded raw capture and reconstruct an achromatic image afterward

These classes are not mutually exclusive. A multilayer printed device can also be inverse-designed, and a hybrid refractive–metasurface front end can also be embedded in a differentiable computational imaging system (Pan et al., 2023, Zhang et al., 2024). This suggests that synthetic achromatic metalenses are better understood as a design philosophy than as a single device topology.

2. Optical basis and fundamental constraints

The underlying difficulty is the diffractive nature of metalenses. In the Fresnel-zone formulation used for a conventional binary zone plate, the zone radii satisfy

$r_n^2 = n \lambda (f + m\lambda),$

which can be rewritten as

$$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$

For fixed zone radii, the focal length therefore varies with wavelength. A conventional zone plate designed to focus green light at $\lambda=550\,\text{nm}$ to $f=1\,\text{mm}$ produces a visible focal-plane spread of more than $400\,\mu\text{m}$ (Avayu et al., 2016).

More generally, the ideal achromatic phase condition can be written as

$$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$

so the design problem is not only phase matching at one frequency but also control of the local group delay

$$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$

In practice, broadband achromatization over a finite band requires at minimum the correct phase and first-order phase dispersion, while residual higher-order phase errors limit performance at band edges (Zhang et al., 2021).

This requirement is bounded by delay–bandwidth physics. A thin passive time-invariant metalens must satisfy a relation of the form

$\Delta T\,\Delta \omega \leq \kappa,$

where the required center-to-edge delay grows with focal length and numerical aperture (Presutti et al., 2020). This is why simultaneous large aperture, high NA, short focal length, small thickness, and broad bandwidth are difficult to realize in a single thin layer. Related analyses generalize the problem further: wavefront shaping need not be strictly phase-only, since spectrally varying transmission magnitudes can also be used to synthesize focusing, especially in multilayer thin-film architectures (Hooper et al., 2022).

3. Principal synthetic-achromat design strategies

The earliest explicit physical example of this philosophy is the composite functional metasurface. In a three-layer visible RGB lens, red, green, and blue are assigned to separate narrowband diffractive layers that are densely stacked vertically and focused to the same plane, so achromaticity emerges from spectral multiplexing rather than from a single broadband meta-atom law (Avayu et al., 2016). The same paper extended the concept to a self-aligned STED optic and to anomalous dispersive focusing, showing that stacked metasurfaces can synthesize several wavelength-selective functions in one ultrathin element.

Hybrid strategies redistribute the optical workload differently. The Hybrid Achromatic Metalens combines a phase plate with a nanopillar metalens into one thin 3D optical element, so the metasurface no longer has to provide the full achromatic phase excursion by itself (Balli et al., 2019). Visible hybrid designs place a metasurface on the flat side of a plano-convex refractive lens, using the refractive component for most of the optical power and the metasurface as a chromatic corrector with engineered negative dispersion (Hu et al., 2022). A later formulation recast this same idea inside differentiable ray tracing, optimizing the phase distribution of the metalens and the parameters of the refractive lens jointly (Zhang et al., 2024).

A third strategy is full-structure inverse design. Chung and Miller showed that standard unit-cell approaches are basis-limited at high NA and used adjoint optimization of the entire device to obtain broadband achromatic focusing across $450$–$700\,\mathrm{nm}$, including NA $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$0 in translation-invariant films and NA $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$1 in freeform structures (Chung et al., 2019). Library-free inverse design of random-shaped meta-atoms extended this logic by directly searching free-form dielectric geometries that satisfy phase and dispersion requirements while retaining four-fold symmetry for polarization independence (Zhang et al., 2021).

A fourth strategy is synthetic spectral design in multilayer media. Thin-film formulations treat achromatization as a generalized phase-matching problem over layered TiO$$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$2/MgF$$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$3 stacks, and 3D printed multilayer achromats realize that idea experimentally by topology-optimizing several closely spaced printed layers rather than a single metasurface sheet (Hooper et al., 2022, Pan et al., 2023).

Finally, computational synthetic achromats move the correction from the wavefront to the image plane. In these systems the optical front end is allowed to remain chromatic or intentionally wavefront-coded, while deconvolution or learned reconstruction produces an achromatic image after detection (Dong et al., 2023, Huang et al., 2020, Colburn et al., 2019). This suggests that the term encompasses both physically achromatic optics and system-level achromatic cameras.

4. Representative realizations across platforms and spectral regimes

Visible composite and reflective implementations established the basic categories. A three-layer RGB metalens with Au, Ag, and Al layers, separated by $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$4 silica spacers, focused $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$5, $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$6, and $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$7 to the same $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$8 focal plane, with focal-spot FWHM values of $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$9, $\lambda=550\,\text{nm}$0, and $\lambda=550\,\text{nm}$1, measured focusing transmission efficiency of $\lambda=550\,\text{nm}$2 to $\lambda=550\,\text{nm}$3, and interlayer spectral crosstalk below $\lambda=550\,\text{nm}$4 of the main beam at the design channels (Avayu et al., 2016). A different visible route used a reflective TiO$\lambda=550\,\text{nm}$5/SiO$\lambda=550\,\text{nm}$6/Al metasurface with guided-mode-resonance-assisted dispersion engineering to hold the focal length nearly constant from $\lambda=550\,\text{nm}$7 to $\lambda=550\,\text{nm}$8, with measured focal-length variation of $\lambda=550\,\text{nm}$9, while also demonstrating a metalens with reverse chromatic dispersion (Khorasaninejad et al., 2017).

High-efficiency and inverse-designed NIR achromats broadened the operational envelope. The Hybrid Achromatic Metalens operated from $f=1\,\text{mm}$0 to $f=1\,\text{mm}$1, delivered diffraction-limited performance for NA $f=1\,\text{mm}$2, $f=1\,\text{mm}$3, and $f=1\,\text{mm}$4, and showed average focusing efficiencies of $f=1\,\text{mm}$5, $f=1\,\text{mm}$6, and $f=1\,\text{mm}$7, with maximum efficiencies up to $f=1\,\text{mm}$8 (Balli et al., 2019). In a different NIR platform, free-form inverse-designed random-shaped meta-atoms achieved experimentally demonstrated achromatic focusing from $f=1\,\text{mm}$9 to $400\,\mu\text{m}$0, a $400\,\mu\text{m}$1 bandwidth, with focusing efficiency from $400\,\mu\text{m}$2 to $400\,\mu\text{m}$3, Strehl ratio above $400\,\mu\text{m}$4, and polarization-insensitive operation (Zhang et al., 2021).

Large-aperture visible hybrid systems moved synthetic achromats toward conventional camera scales. A centimeter-scale metasurface–refractive hybrid metalens working from $400\,\mu\text{m}$5 to $400\,\mu\text{m}$6 with $400\,\mu\text{m}$7 diameter, effective focal length $400\,\mu\text{m}$8, and $400\,\mu\text{m}$9 reduced focal shift from $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$0 in the bare refractive lens to $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$1, corresponding to $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$2 chromatic-aberration suppression, and showed focusing efficiency around $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$3 at $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$4 (Hu et al., 2022). A related differentiable-ray-tracing design for a $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$5, $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$6, $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$7–$$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$8 hybrid system reduced the focal-length range from $$\phi(r,\omega)= -\frac{\omega n}{c}\sqrt{r^2+F^2}+f(\omega),$$9–$$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$0 to $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$1–$$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$2, with simulated USAF-chart improvement from PSNR $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$3, SSIM $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$4 to PSNR $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$5, SSIM $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$6 (Zhang et al., 2024).

Other realizations show how broad the concept has become. A single-layer silicon metalens for $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$7–$$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$8 achieved an $$\tau_g(r)=\frac{\partial \phi(r,\omega)}{\partial \omega}.$$9 field of view and a measured relative focal-length shift as low as $\Delta T\,\Delta \omega \leq \kappa,$0, with a twofold increase in focusing efficiency relative to a conventional quadratic reference metalens (Cao et al., 22 Jul 2025). A 3D printed multilayer achromatic metalens with $\Delta T\,\Delta \omega \leq \kappa,$1 diameter operated over $\Delta T\,\Delta \omega \leq \kappa,$2–$\Delta T\,\Delta \omega \leq \kappa,$3 at NA $\Delta T\,\Delta \omega \leq \kappa,$4 and $\Delta T\,\Delta \omega \leq \kappa,$5, with measured efficiencies up to $\Delta T\,\Delta \omega \leq \kappa,$6 and white-light imaging (Pan et al., 2023). A 3D nanoprinted achromatic metafiber on an SMF-28 end face covered the full telecommunications band from $\Delta T\,\Delta \omega \leq \kappa,$7 to $\Delta T\,\Delta \omega \leq \kappa,$8, increased the time-bandwidth product to $\Delta T\,\Delta \omega \leq \kappa,$9, and provided a group-delay modulation range from $450$0 to $450$1 (Ren et al., 2022). At the opposite spectral extreme, a transmissive UVC metalens based on cross-shaped SiO$450$2 meta-atoms on sapphire operated from $450$3 to $450$4 with average focusing efficiency of $450$5, focal shift less than $450$6, and polarization-insensitive behavior (Fang et al., 28 Dec 2025).

5. Computational synthetic achromats and performance evaluation

A major branch of the field makes the imaging system achromatic even when the standalone metalens is not. In one example, a conventional chromatic single metalens on a $450$7 silicon-on-sapphire wafer, with $450$8 diameter, $450$9 focal length, and design wavelength $700\,\mathrm{nm}$0, was paired with a U-Net-based neural network that “refocuses red, green and blue channels” from the raw sensor capture (Dong et al., 2023). The reported gains were more than $700\,\mathrm{nm}$1 PSNR improvement and about $700\,\mathrm{nm}$2 increase in SSIM for test images from the training distribution, and over $700\,\mathrm{nm}$3 PSNR with approximately $700\,\mathrm{nm}$4 SSIM increase on an additional out-of-distribution validation set. In the explicit comparison of Table 1, the raw image improved from PSNR $700\,\mathrm{nm}$5, SSIM $700\,\mathrm{nm}$6 to PSNR $700\,\mathrm{nm}$7, SSIM $700\,\mathrm{nm}$8. The optical front end remained chromatic; achromatization occurred after capture.

A second computational route uses extended depth of focus rather than learned inversion. An EDOF metalens plus deconvolution system based on symmetric phase masks—especially logarithmic-aspherical and shifted-axicon masks—produced much broader wavelength tolerance than a standard metalens: the reported bandwidths at half maximum of the PSF-similarity coefficient were $700\,\mathrm{nm}$9 for both the log-asphere and shifted axicon, $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$00 for SQUBIC, $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$01 for the cubic mask, and only $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$02 for the ordinary metalens (Huang et al., 2020). The corresponding image model was written as

$$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$03

followed by Wiener-Hunt deconvolution. A related visible system based on two conjugate quartic metasurfaces generated a tunable quadratic lens term and a tunable cubic wavefront-coding term simultaneously, enabling focal tuning from $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$04 to $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$05, a $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$06-diopter change, $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$07 zoom, and average diffraction efficiency of $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$08 while maintaining a near spectrally invariant PSF across the visible regime (Colburn et al., 2019).

Because synthetic achromatic metalenses often trade efficiency against blur invariance, system metrics are central. One experimentally validated criterion is the average signal-to-noise ratio,

$$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$09

which combines low-frequency SNR and the area under the MTF up to the detector Nyquist frequency (Engelberg et al., 2020). For the tested $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$10 Huygens metalens, this metric yielded an optimal operating spectral range of approximately $$f(\lambda) = \frac{r_n^2 - (n\lambda)^2}{n\lambda}.$$11. This is important because a nominally “achromatic” metalens can still be inferior if the gain in blur correction is offset by throughput loss or noise amplification.

6. Limitations, misconceptions, and outlook

Synthetic achromatic metalenses do not remove the underlying physical trade space; they redistribute it. Multispectral stacked lenses are strongest at their design channels and retain residual aberration away from them because each plasmonic or resonant layer has finite linewidth (Avayu et al., 2016). Thin passive broadband designs remain subject to delay–bandwidth limits, so larger NA, shorter focal length, and broader bandwidth demand greater delay span, thickness, or material contrast (Presutti et al., 2020). Visible large-aperture devices still face the diameter–NA–waveband compromise identified in hybrid metalens work (Hu et al., 2022). Wide-field systems add another difficulty: lateral chromatic aberration, pupil wander, and stop-position optimization become decisive, as emphasized in a later wide-FOV design methodology inspired by the human visual system (Engelberg et al., 3 Feb 2025).

A common misconception is to treat all synthetic achromats as optically equivalent. Computational systems are achromatic at the camera-system level, not necessarily as standalone wavefront-correcting elements. Their performance depends on training priors, sensor characteristics, aperture, object distance, and scene statistics, and RGB reconstruction is not the same as continuous-spectrum achromatization (Dong et al., 2023). Another misconception is that hybrid or stacked architectures are merely expedients. In fact, several of the strongest reported bandwidth–NA combinations rely precisely on distributing optical power and chromatic correction across multiple mechanisms rather than concentrating them in one layer (Balli et al., 2019, Pan et al., 2023).

The current direction of the field suggests continued convergence among multilayer nanofabrication, inverse design, and computational co-design. Composite metasurfaces were already proposed as scalable to more layers and other material systems (Avayu et al., 2016). Differentiable hybrid optics provide a route to joint optimization of refractive elements, metasurfaces, and downstream algorithms (Zhang et al., 2024). Multilayer printed structures indicate that fabrication-compatible 3D architectures can relax single-layer phase–dispersion constraints (Pan et al., 2023). This suggests that the mature form of the synthetic achromatic metalens may be neither purely metasurface-only nor purely computational, but a deliberately heterogeneous flat-optics system in which achromatization is synthesized across materials, geometry, spectral channels, and post-detection processing.