---
title: Multi-Foci Metalens
url: https://www.emergentmind.com/topics/multi-foci-metalens
type: topic
---

# Multi-Foci Metalens

A multi-foci metalens is a metasurface optical device engineered to focus incident electromagnetic waves onto multiple, spatially distinct, and simultaneously addressable focal spots. Unlike conventional monofocal lenses, these ultrathin diffractive elements leverage subwavelength-scale phase modulation to achieve arbitrary control of both the number, position, and weighting (i.e., intensity) of focal points in one or more planes. The multi-foci paradigm encompasses pointwise arrays, longitudinal focal stacks, user-defined curves, and polarization- or wavelength-multiplexed spot sets, and is central to advanced imaging, multi-channel communications, trapping arrays, and information-processing applications across the electromagnetic spectrum.

## 1. Underlying Phase Profile Construction

The core principle of multi-foci metalens design is the synthesis of a spatial phase distribution $\phi(x,y)$ on the device surface so that the propagating field at the desired focal plane(s) reconstructs the specified set of focal spots. For $N$ distinct target foci at positions $(x_i, y_i, z_i)$, the ideal phase at each aperture position $(x, y)$ can be expressed as
$$
\phi_{\text{req}}(x, y) = \mathrm{Arg} \left\{ \sum_{i=1}^N w_i \exp\left[ -j k_0 \left( \sqrt{(x - x_i)^2 + (y - y_i)^2 + z_i^2} - z_i \right) \right] \right\}
$$
where $w_i$ controls the relative amplitude at focus $i$, $k_0=2\pi/\lambda$ is the free-space wavenumber, and $\lambda$ is the operational wavelength [2503.09176][2011.04790][2410.22469]. This “superposed phase” prescription—sometimes referred to as the “direct argument method”—has been employed for both single-layer and multilayer metasurface realizations.

In application-specific variants:
- The direct argument is applied for spatial arrays in the focal plane, often with additional amplitude weights to normalize spot intensities [2503.09176][2011.04790].
- For longitudinal multi-foci, a composite of hyperbolic phase terms across focal lengths is used (e.g., tri-focal metalens) [2402.11559].
- In full-Stokes polarimetric systems, independent Jones-matrix profiles are optimized so that each of $M$ target polarization states is sent to its own designated focus, with the full phase vector designed via adjoint-based inverse optimization [2307.01707].

## 2. Physical Platforms and Meta-Atom Architectures

Multi-foci metalenses have been demonstrated using a diverse range of material stacks and meta-atom geometries, dictated by operational wavelength and application context.

- **Dielectric nanopillar arrays:** High-index (e.g., Ge, TiO$_2$, Si$_3$N$_4$) pillars with tailored height and lateral geometry are widely used for the visible through mid-IR [2307.01707][2402.11559][2503.09176][2407.19249]. Si$_3$N$_4$ platforms support near-diffraction-limited, longitudinally multiplexed foci via nanofins with propagation phase and geometric phase tuning [2402.11559].
- **Metallic nanoslits and nanorods:** Gold nanoslits structured along confocal conics realize geometric-phase multi-foci operation in the visible and near-IR [1606.09351].
- **Phase-change and reconfigurable materials:** VO$_2$ nanofilms functioning as thermally/electrically/optically triggered phase shifters enable real-time, digitally reconfigurable multi-foci operation at THz frequencies, exploiting their insulator-to-metal phase transitions for high-speed switching [2011.04790].
- **Atomic emitter arrays:** Theoretical proposals show lattices of cold atoms can be engineered, via spatially varying interatomic spacings across stacked 2D arrays, to yield phase profiles that realize arbitrary multi-foci lensing with robust, low-loss characteristics [2410.22469].
- **Hybrid meta-atoms:** Polymer resist pillars with conformal atomic-layer-deposited TiO$_2$ coatings achieve full $0$–$2\pi$ phase coverage, polarization insensitivity, and low-loss uniform focal arrays suitable for scalable nanoimprint fabrication [2503.09176].

## 3. Optimization Algorithms and Uniformity Control

Direct phase superposition,
$$
\phi_{\rm super}(x,y) = \mathrm{Arg} \left[ \sum_{j=1}^N \exp(i \phi_j(x, y)) \right],
$$
yields nonideal performance for large $N$ due to strong sidelobe formation, non-uniform spot intensities, and cross-talk [2503.09176].

To address this, inverse-design strategies based on gradient-descent optimization, angular-spectrum propagation, and adjoint-field methods are employed. The loss is constructed to minimize the squared field error at each focus, enforce uniformity among peak intensities, and suppress off-target light:
$$
\mathcal{L} = W_{\text{foc}} \frac{1}{N}\sum_{j=1}^{N} \left| |U(x_{j},y_{j},f)| - U_{\text{target}}(x_{j},y_{j}) \right|^2 + W_{\text{non}} \frac{1}{P} \sum_{(x,y)\notin\{x_j,y_j\}} \left| U(x,y,f) \right|^2
$$
where $U(x, y, f)$ is the propagated field at focus, and optimization is performed over the phase profile $\phi(x, y)$. This approach yields focal arrays with standard deviation $\sigma < 5\%$ in intensity and sidelobes $< 10\%$ of the main peak, outperforming phase superposition in both contrast and fidelity [2503.09176][2307.01707].

## 4. Reconfigurable, Electrically Tunable, and Polarization-Multiplexed Multi-Foci

Reconfigurability and multi-channel selection are achieved via several mechanisms:
- **Electrically tunable layering:** Cascading $N$ polarization-multiplexed bi-focal metalenses interleaved with voltage-controlled nematic liquid crystal (LC) waveplates yields $2^N$ independently selectable focal channels. The parabolic phase of each layer adds reciprocally, setting the effective focal length:
$$
1/f_e = \sum_{j=1}^{N} 1/f_j^{(u_j)}
$$
where $u_j\in\{|D\rangle,|A\rangle\}$ is the polarization state at layer $j$. Efficiency up to $10\%$ and FWHM down to $19\,\mu$m are achieved with eight-channel switches in a 6-mm-thick multilayer stack [2505.10953].
- **Polarization control:** Dual- or multi-foci can be partitioned across orthogonal linear or circular polarization channels, such that, for instance, each co- and cross-polarized transmission carries a different focal phase: $\phi_{\text{co}}(x,y;\lambda)\approx\phi_1(x, y; \lambda)$ and $\phi_{\text{cross}}(x,y;\lambda)\approx\phi_2(x, y; \lambda)$. This enables simultaneous and independent point formation for multiple orthogonal input states, with theoretical efficiency per channel up to $80.5\%$ [2407.19249], or four-foci full-Stokes polarimetric routing with $54.6\%$ total efficiency [2307.01707].
- **Phase-change materials:** VO$_2$-based reconfigurable metalenses permit arbitrary and real-time adjustment of the number, position, intensity, and width of focal spots, with sub-ns to sub-s switching speeds depending on bias modality [2011.04790].

## 5. Fabrication Technologies and Scalability

Large-area, wafer-scale, and scalable multi-foci metalens manufacturing can be realized by
- **Nanoimprint lithography (NIL):** Combined with atomic layer deposition (ALD) for conformal high-index coatings, NIL enables batch fabrication of polarization-insensitive, highly uniform focal arrays ($\sigma < 3.5\%$) across arbitrary geometries, with measured spot FWHM within 1.1$\times$ the diffraction limit and $70\%$ transmission [2503.09176].
- **Electron-beam lithography and reactive-ion etching:** Provide sub-20 nm fidelity in high-index dielectrics (e.g., Si$_3$N$_4$, Ge), critical for phase accuracy and spot Strehl ratio [2402.11559][2307.01707].
- **Focused ion beam (FIB) milling:** Used for fabricating metal nanoslit arrays in Au, achieving geometric-phase encoding for conic-shaped multifocal lenses [1606.09351].
- **Layered atomic arrays:** Theoretical designs recommend stacking three sub-wavelength 2D atomic lattices, with precise spatial control over lattice constant and interlayer spacing, to realize the target phase and maximize cooperative transmission [2410.22469].

Critical process parameters include aspect-ratio control, resist viscosity, anti-adhesion measures, and ALD uniformity for pillar-based meta-atoms, as well as subwavelength alignment and retardance uniformity for polarization-multiplexed and electrically tunable devices [2503.09176][2505.10953].

## 6. Performance Metrics and Application Domains

Multi-foci metalenses are characterized by focusing efficiency, spot uniformity, crosstalk, speed, chromatic performance, and fabrication scalability. Representative metrics include:
- **Efficiency:** Up to $80.5\%$ per channel in dual-focal, broadband, polarization-insensitive metalenses [2407.19249]; $\sim$30–40% for THz VO$_2$-based reflection metalenses [2011.04790]; $10\%$ in electrically tunable 8-channel stacks [2505.10953].
- **Uniformity:** Intensity variation $\sigma < 5\%$ across multiple foci [2503.09176][2307.01707].
- **Spot size and Strehl ratio:** FWHM within 10–15% of the diffraction limit; Strehl ratios $\gtrsim$0.8 for all foci in Si$_3$N$_4$ tri-focal devices [2402.11559].
- **Crosstalk:** Inter-focus isolation $\geq10$ dB for foci separated by more than twice the FWHM [2011.04790].
- **Switching speed:** Picosecond to sub-second range for phase-change devices; milliseconds for liquid-crystal switching [2011.04790][2505.10953].
- **Scalability:** Large-area wafer-imprinted arrays for trapping, imaging, and optical tweezers; compact, monolithic integration in infinity-corrected, multi-magnification microscopes [2402.11559][2503.09176].

Core application areas include multifunctional optical trapping arrays, AR/VR depth scanning, LiDAR and 3D sensing, parallel nanolithography, multi-channel terahertz or wireless communication, full-vector polarimetric imaging, and compact, microscopy-grade objective lenses with tunable or multi-plane imaging capability.

## 7. Extensions, Limitations, and Outlook

- **Extension to arbitrary focal patterns:** Inverse-Fourier and propagation-phase techniques permit the design of continuous focus curves or 2D patterns (e.g., lines, rings, alphanumeric shapes) subject to the constraints of sampling pitch, NA, and propagation-induced amplitude variation [1906.10681].
- **Longitudinal multi-foci:** Multiple focal planes with engineered relative magnifications and longitudinal spacing can be realized by harmonic-phase superpositions or polarization-multiplexing [2402.11559].
- **Achromatic and broadband design:** Dispersion-engineered meta-atom libraries and global optimization (e.g., particle swarm) enable achromatic, polarization-independent multi-foci metalenses with sub-4% focal length deviation across broad visible bands [2407.19249].
- **Limitations:** Current challenges include chromatic and polarization crosstalk in complex multiplexing, efficiency loss in multi-layer stacks (glass/alignment losses), spot uniformity for $N \gg 10$ without inverse design, fabrication tolerances ($<$10-20 nm) for high-NA, and limitations in simultaneous bandwidth, efficiency, and focus count [2505.10953][2503.09176].
- **Atomic array approaches:** Offer the prospect of ultra-low-loss, robust multifocal metasurfaces with efficiency $\sim$80–90%, provided the subwavelength lattice engineering is experimentally achievable [2410.22469].

In concluding, the multi-foci metalens framework unifies a broad class of metasurface-based focusing devices under a phase-engineered, subwavelength-thick paradigm, with demonstrated scalability, reconfigurability, and application reach spanning classical and quantum photonics [2503.09176][2011.04790][2402.11559][2410.22469][2505.10953].

Source: https://www.emergentmind.com/topics/multi-foci-metalens