Nonlocal Metasurfaces: Principles & Applications

Updated 2 October 2025

Nonlocal metasurfaces are engineered two-dimensional structures that exhibit collective, spatially extended electromagnetic responses rather than localized resonances.
They employ hydrodynamic, coupled mode, and transfer matrix models to achieve sharp spectral selectivity, tunable phase control, and high-Q resonances.
Applications span imaging, analog optical computation, and quantum light sources, offering functionalities beyond conventional local metasurface designs.

Nonlocal metasurfaces are engineered two-dimensional structures whose electromagnetic response is governed by spatially extended, collective, or spatially dispersive modes—rather than by localized (independent) resonances confined to individual meta-units. This class of metasurfaces exploits spatial or temporal nonlocality to enable functionalities inaccessible to conventional local designs, including sharp spectral selectivity, broadband wavefront control, enhanced light–matter interaction, compact analog computation, and tunable or active optical functionalities. Nonlocality can arise from hydrodynamic or quantum effects (in plasmonics), modal coupling across meta-units (in photonics and acoustics), intentional long-range elastic coupling (in elastic metasurfaces), or multilayer interference and spatial dispersion engineered at the macroscopic or microscopic scale. The field encompasses both linear and nonlinear, passive and active implementations, and extends to multifunctional, chiral, quantum, and programmable devices.

1. Fundamental Principles of Nonlocality in Metasurfaces

Nonlocality in metasurfaces refers to a situation where the response at a given spatial location depends not only on the local field but also on its distribution across a finite region or even the entire surface. In electromagnetic theory, this is mathematically described by a surface polarization or impedance that is a functional of the incident field’s spatial profile, i.e., $P(\mathbf{r}) = \int K(\mathbf{r},\mathbf{r'}) E(\mathbf{r'}) d\mathbf{r'}$ , where $K$ is a nonlocal kernel. Key mechanisms for nonlocality include:

Hydrodynamic/quantum nonlocality: In metallic (plasmonic) metasurfaces with sharp features or narrow gaps, nonlocality arises from the spatial dispersion in the electronic response (hydrodynamic model), characterized by a wavevector-dependent dielectric function $\epsilon_L(\omega,k)$ with a screening length on the order of $0.1~\rm{nm}$ for noble metals (Yang et al., 2019, Yang et al., 2019).
Bound states in the continuum (BICs) and extended resonances: In dielectric and photonic crystal metasurfaces, extended modes, such as quasi-BICs, are spatially delocalized over many unit cells and can give rise to high- $Q$ resonances with spatially nonlocal field distributions (Overvig et al., 2020, Zhang et al., 2022).
Intentional mechanical/elastic coupling: In elastic/acoustic metasurfaces, nonlocality can be engineered using flexible links or beams that create frequency or wavenumber-dependent coupling across multiple meta-units, thus tailoring the phase response as a function of incident wavenumber (Zhu et al., 2020).
Macroscopic spatial dispersion: Multilayer or cascaded metasurfaces can leverage multiple internal reflections and phase accumulation in subwavelength layers to achieve angular spatial dispersion (e.g., grid impedance $Z_s(\theta)$ dependent on angle), allowing wide-angle functionalities in anti-reflective coatings and radomes (Shaham et al., 22 Dec 2024, Zhuravlev et al., 16 Jul 2025).

Nonlocality fundamentally contrasts with conventional "local" metasurfaces, where the response at each point is determined solely by the local incident field and the independent scattering behavior of each meta-unit.

2. Theoretical Models and Analytical Frameworks

Several distinct analytical models capture the essence of nonlocal metasurface behavior:

Wavevector-Dependent Dielectric Response: In hydrodynamic models for plasmonic metasurfaces, the dielectric function for the longitudinal mode is wavevector dependent:

$\epsilon_L(\omega,k) = \epsilon_\infty - \frac{\omega_p^2}{\omega(\omega+i\Gamma)-\beta^2 |k|^2}$

where $\beta$ is the nonlocal parameter and $\delta = \beta/\omega_p$ is the decay/screening length, leading to smeared singularities and discrete modal spectra (Yang et al., 2019, Yang et al., 2019).

Coupled Mode Theory (TCMT, STCMT): Temporal coupled mode theory (TCMT) is extended to incorporate spatial nonlocality via spatio-temporal coupled mode theory (STCMT), where the modal amplitude $a(x,t)$ varies in space and time:

$\frac{d a(x, t)}{dt} + i[\omega_0 + i\gamma] a(x, t) - c\,\partial_x a(x, t) - i(b+i\Gamma/2) \partial_x^2 a(x, t) = \int K(x,x')s_+(x',t) dx'$

Enabling the mapping of the resonant, spatially extended response, phase gradients, and eigen-wave formation in nonlocal metasurfaces (Overvig et al., 2023).

Transfer Matrix and Scattering Models: Elastic and acoustic nonlocal metasurfaces are modeled using lumped-parameter mass–spring chains and transfer matrices, generalizing to higher dimension matrices when inter-unit coupling is non-negligible (Zhu et al., 2020, Ding et al., 2021).
Circuit Models and GSTCs: Macroscopic spatial dispersion and normal susceptibility effects are described analytically using generalized sheet transition conditions (GSTCs) and rational-function expressions for the reflection/transmission coefficients, with explicit mapping to multilayer circuit models (Shaham et al., 22 Dec 2024, Zhuravlev et al., 16 Jul 2025).
Inverse Design and Topology Optimization: Freeform nonlocal metasurfaces supporting accidental BICs and tailored near-field distributions are discovered using adjoint-based topology optimization and neural parametric boundary representations (Jiang et al., 18 Jun 2025).

These theoretical approaches provide design tools for both fundamental understanding and engineering of metasurface functionalities beyond local paradigms.

The incorporation of nonlocality into metasurface design leads to fundamental modifications in field localization, spectrum, and device performance:

Spectrum Discretization and Reduced Field Enhancement: For singular plasmonic metasurfaces, nonlocality discretizes the continuum of SPP modes, resulting in a set of discrete absorption peaks instead of a continuum, and removes field divergences at singularities, yielding large but finite field enhancement (Yang et al., 2019). In near-touching metasurfaces, nonlocality leads to a blueshift of resonance peaks and a saturation in the density of states (DOS) (Yang et al., 2019).
High- $Q$ Extended Resonances and Spectral Selectivity: Nonlocal photonic/metasurface designs leveraging quasi-BICs generate ultra-high- $Q$ resonances, supporting selective, narrowband manipulation (e.g., geometric phase imparted only at certain wavelengths) while devices remain transparent elsewhere (Overvig et al., 2020, Song et al., 2021, Zhang et al., 2022).
Broadband and Wavevector-dependent Phase Gradients: Intentional nonlocality in elastic metasurfaces leads to wavenumber-dependent phase shifts that can be designed to achieve broadband suppression or steering of waves (e.g., broadband total internal reflection) by manipulating the frequency-dependent coupling between units (Zhu et al., 2020).
Spatially and Temporally Dispersive Transfer Functions: Space-time nonlocal metasurfaces enable analog computations such as mixed spatio-temporal differentiation ( $\partial_x^2 \partial_t^2$ ) and selective event-based edge detection, with the transfer function engineered for desired operations in the $(k_x, \Delta\omega)$ domain (Esfahani et al., 12 Jan 2024, Cotrufo et al., 14 Mar 2024).
Thermal and Nonlinear Emission Enhancement: The presence of spatially extended nonlocal resonances dramatically increases field localization and energy storage, benefiting spontaneous parametric down-conversion efficiency and thermal emission focusing (Zhang et al., 2022, Overvig et al., 2023).

The engineering of nonlocal responses allows metasurfaces to overcome limitations of local designs related to spectral bandwidth, field concentration, and functional selectivity.

4. Practical Implementations and Characteristic Metasurface Architectures

A diverse range of architectures and materials platforms have been reported for nonlocal metasurfaces, including:

Material/System	Nonlocality Mechanism	Functionality/Features
Noble metals	Hydrodynamic quantum model	Discrete SPP spectrum, controlled energy localization (Yang et al., 2019, Yang et al., 2019)
Dielectric photonics	Extended photonic modes, BICs	Multifunctional, narrowband phase control, nonlocal lenses (Overvig et al., 2020, Chen et al., 2020, Luca et al., 7 May 2025)
Elastic/acoustic	Mechanical coupling	Broadband wave control, tunable phase gradients (Zhu et al., 2020, Ding et al., 2021)
Quantum nonlinear	Nonlocal GMRs in LiNbO₃	Enhanced photon-pair generation, engineered angular entanglement (Zhang et al., 2022)
PCB/Meta-atom array	Macroscopic multilayer	All-angle control (radomes, PMCs), spatial-dispersion engineering (Shaham et al., 22 Dec 2024, Zhuravlev et al., 16 Jul 2025)
Inverse design	Freeform topology opt.	Accidental BICs, tailored near-field, multifunctionality (Jiang et al., 18 Jun 2025)
Optomechanical	GHz acoustic wave coupling	Dynamically tunable, non-metallic, low-loss operation (Pitanti et al., 2023)
Active/Phase-change	Sb₂S₃, Si, thermal/mechanical	Active, nonvolatile, multistate, tunable meta-optics (Liu et al., 2023, Malek et al., 2020)

Nonlocal metasurfaces frequently utilize high-index dielectrics (Si, Ge, LiNbO₃) for low-loss, high-Q performance, and their architectures often involve periodic, quasi-periodic, or aperiodic patterns supporting spatially delocalized eigenmodes or engineered spatial dispersion.

5. Applications: Imaging, Sensing, Computation, and Quantum Optics

The unique capabilities of nonlocal metasurfaces have enabled several advanced applications:

Meta-Optics and Imaging: Nonlocal dielectric metasurfaces act as space-compressing "spaceplates", lenses, or imaging elements, decoupling focal length and device thickness for ultra-compact optical systems (Chen et al., 2020, Luca et al., 7 May 2025). Multifunctional devices can focus and filter at distinct wavelengths with near-transparency outside select bands (Overvig et al., 2020, Luca et al., 7 May 2025).
Spectrally Decoupled and Selective Displays: Spectral decoupling allows metasurfaces patterned on eyewear to redirect light in the NIR for eye tracking without impacting visible light transmission (Song et al., 2021).
Analog Optical Computation: Nonlocal metasurfaces serve as compact, passive processors—performing spatio-temporal differentiation, event-based edge detection tailored to object speed, and temporal signal processing using engineered transfer functions (Esfahani et al., 12 Jan 2024, Cotrufo et al., 14 Mar 2024).
Acoustic/Sound Manipulation: Deep learning-optimized nonlocal acoustic metasurfaces achieve multi-channel energy redistribution with engineered coupling (Ding et al., 2021).
Quantum Light Sources: Nonlocal guided-mode resonant metasurfaces support enhanced, spatially entangled photon-pair emission via SPDC, with engineered spatial quantum correlations for quantum imaging and sensing (Zhang et al., 2022).
Active and Dynamic Functionality: Thermally and mechanically reconfigurable nonlocal metasurfaces enable wavefront switching, variable focusing, and holography, including phase-change implementation for multistate control (Malek et al., 2020, Liu et al., 2023).
Robust Spatial Filtering: Nonlocal non-Hermitian metasurfaces act as compact spatial filters, insensitive to lateral/longitudinal misalignment, replacing bulk pinhole setups (Chen et al., 26 Jun 2025).

These functionalities often rely on features unattainable by local metasurfaces, such as ultra-high Q, broadband and/or selective phase engineering, and tunable or programmable responses.

6. Design Strategies, Trade-Offs, and Limitations

The design of nonlocal metasurfaces requires careful balancing of competing factors:

Spectral–Angular Trade-Offs: Enhancing the Q-factor or spatial selectivity can limit the angular bandwidth over which the device is effective; for example, single-resonance nonlocal metasurfaces are fundamentally constrained by:

$\frac{L}{\lambda_0}\cdot\left(\frac{k_{t,\max}}{k_0}\right)^2 \le n$

where $n$ is the number of coupled resonators/layers (Chen et al., 2020).

Fabrication Tolerances and Losses: Many designs are sensitive to nanometer-scale tolerances; for instance, the nonlocal response in guided-mode resonant structures depends critically on precise geometrical control (Song et al., 2021). Losses or deviations can reduce efficiency or Q.
Phase and Transmission Constraints: Achieving both amplitude and phase control across wide angular or spectral ranges—necessary for applications such as all-angle transparent radomes or wide-angle anti-reflection coatings—requires precise engineering of spatially dispersive impedance, potentially at the expense of device bandwidth (Shaham et al., 22 Dec 2024, Zhuravlev et al., 16 Jul 2025).
Trade-offs in Active Devices: The range and speed of tuning (thermal, mechanical, or phase-change) and maximum repeatability are limited by material properties—e.g., maximum refractive index change or activation time in Sb₂S₃ or Si (Liu et al., 2023, Malek et al., 2020).
Modal Overlap and Functionality Multiplexing: Multiplexed functionality (e.g., multi-wavelength or chiral designs) can require complex optimization and may be limited by modal overlap and spectral crowding (Jiang et al., 18 Jun 2025).

Working within these constraints, various paradigms—symmetry-protected or accidental BICs, neural topology optimization, macroscopic/microscopic dispersion engineering—enable high-performance nonlocal metasurfaces for specific applications.

7. Outlook and Future Directions

Current research on nonlocal metasurfaces is advancing toward increased complexity, integration, and active/on-demand reconfigurability:

Programmable Nonlocal Metasurfaces: The integration of phase-change materials, mechanical actuation, or electrical tuning points to programmable, multistate devices capable of rapid and reversible multifunctional reconfiguration (Liu et al., 2023, Pitanti et al., 2023).
Quantum Nonlinear and Entangled-Photon Devices: Progress in nonlinear nonlocal metasurfaces supporting engineered SPDC is driving miniaturization and integration of quantum light sources (Zhang et al., 2022).
All-Angle and Broadband Control: Advances in PCB-compatible and multilayer metasurface synthesis open pathways to universal spatial-dispersion engineering for radomes, PMCs, and space-compressive "spaceplates" (Shaham et al., 22 Dec 2024, Zhuravlev et al., 16 Jul 2025).
Neuromorphic and Analog Optical Computing: Nonlocal metasurfaces that perform in situ, passive analog computations with tunable spatio-temporal selectivity are being explored for neuromorphic image processing and integrated photonic neural networks (Esfahani et al., 12 Jan 2024, Cotrufo et al., 14 Mar 2024).
Topological Structured-Light Generation: High-Q nonlocal metasurfaces are enabling topological and non-diffracting beam shaping, including vortex Bessel beams with enhanced propagation lengths and spatiotemporal control (Kim et al., 30 Sep 2025).

A continued convergence of inverse design, topology optimization, advanced materials, and quantum or nonlinear science is expected, with future metasurfaces exhibiting unprecedented functionalities and integration levels for photonics, acoustics, quantum information, and analog computing.