Polarization-Sensitive Metasurfaces

• Polarization-sensitive metasurfaces are engineered planar arrays of subwavelength scatterers that manipulate light’s amplitude, phase, and polarization.
• They employ design strategies like birefringence, Pancharatnam–Berry phase, multipole interference, and inverse design to achieve tailored optical functionalities.
• Applications span advanced polarimetry, imaging, analog optical computing, and quantum devices, while addressing challenges in fabrication and dynamic tuning.

Polarization-sensitive metasurfaces are planar arrays of subwavelength scatterers engineered to impart a tailored, polarization-dependent optical response by deterministic control of the amplitude, phase, and momentum of electromagnetic waves. Functionality arises from structuring material at deeply subwavelength scales, enabling highly anisotropic, polarization-dependent responses that would be unattainable with bulk materials. Their operational versatility encompasses spectral and polarimetric measurements, wavefront shaping, analog optical computing, nonlinear optical processes, and real-time tuning of optical phenomena, serving applications from advanced sensing to quantum information.

1. Fundamental Principles of Polarization Sensitivity

Polarization-sensitive metasurfaces utilize engineered unit cells whose geometry, material composition, and arrangement dictate a spatially varying optical Jones matrix, generally represented as

$$\mathbf{E}_{\mathrm{out}}(x, y) = \mathbf{J}(x, y) \mathbf{E}_{\mathrm{in}}(x, y),$$

where $\mathbf{E}_{\mathrm{in}}$ and $\mathbf{E}_{\mathrm{out}}$ denote the incident and transmitted electric field Jones vectors, and $\mathbf{J}(x, y)$ is the local transformation. This matrix can be arbitrarily manipulated via spatially varying phase retardance, orientation, and local eigenbasis, yielding access to the full retarder space as described in (Rubin et al., 20 May 2025). Early diffractive elements were limited to controlling phase along fixed axes, but with metasurfaces built from high-index or plasmonic nanostructures—such as elliptical nanopillars, gold nanorods, or graphene patches—control of both the phase and amplitude becomes possible for incident polarization bases of choice.

Spatial polarization control mechanisms include:

• Birefringent response: independent control over orthogonal polarization components, enabling the realization of waveplates, polarization beam splitters, and orbital angular momentum (OAM) multiplexers (Achouri et al., 2016).
• Pancharatnam–Berry (PB) phase: geometric phase shift proportional to twice the local orientation angle of anisotropic meta-atoms, imparting polarization- and helicity-sensitive wavefront control (Gao et al., 2021).
• Multi-multipole interference: simultaneous engineering of electric and magnetic (Mie or plasmonic) multipoles ensures broadband, reflectionless, and polarization-converting operation (Kruk et al., 2016).
• Nonlinear engineering: third-order and higher nonlinear susceptibility tensors can be tailored via meta-atom symmetry to achieve desired polarization states of generated harmonic fields (Yue et al., 3 Sep 2025, Toftul et al., 14 Jan 2025).

2. Theoretical Framework and Methodologies

Design methodologies for polarization-sensitive metasurfaces span field-continuity-based synthesis, scattering coefficient optimization, and full-wave inverse design.

a. Field-Based and Scattering Coefficient Synthesis

For monoanisotropic birefringent metasurfaces, the rigorous approach sets electromagnetic continuity conditions across the interface: $$\hat{z} \times \Delta \mathbf{H} = j\omega\epsilon_0 \bar{\chi}_{ee} \cdot \mathbf{E}_{\mathrm{av}},\quad \Delta \mathbf{E} \times \hat{z} = j\omega\mu_0 \bar{\chi}_{mm} \cdot \mathbf{H}_{\mathrm{av}},$$ yielding unique, generally complex susceptibility tensors for each polarization channel (Achouri et al., 2016). The alternative, approximate approach uses inversion of reflection and transmission coefficients to assign real susceptibilities, simplifying fabrication.

b. Inverse Design and Topology Optimization

Recent developments employ topology optimization, using gradient-based algorithms to find geometries that maximize figures of merit reflecting desired polarization and angular response. For instance, angle-multifunctional dichroic metasurfaces are synthesized by maximizing

$$\mathrm{FOM} = (|J_{-\theta}|\mathrm{V}\rangle|^2 - |J_{-\theta}|\mathrm{H}\rangle|^2)(|J_{+\theta}|\mathrm{H}\rangle|^2 - |J_{+\theta}|\mathrm{V}\rangle|^2),$$

with appropriate regularization to ensure manufacturability (Li et al., 14 Oct 2024). For computational imaging, metasurfaces and digital weights are co-optimized via backpropagation to produce coded point spread functions for polarization channels (Hazineh et al., 2023).

c. Calibration and Instrument Matrices

Devices intended for polarimetry or spectropolarimetry require instrument matrix calibration. For the integrated plasmonic metasurface (IPM), measured channel intensities are connected to the incident Stokes vector by

$\vec{I} = \mathbf{A}\vec{S},$

with $\mathbf{A}$ a 6×4 matrix derived from known input states and output intensities (Chen et al., 2015).

3. Device Classes and Functional Implementations

Device / Functionality	Meta-atom Platform	Polarization Principle
Waveplates & polarization splitters	Si/graphene nanopillars	Birefringence, PB phase
Analog edge detectors	Silicon holes/rods	Angular momentum filtering
Nonlinear harmonic generators	a-Si/c-Si nanocuboids	Tensorial nonlinear suscept.
Polarimetric sensors	Hybrid metasurface stack	Instrument matrix inversion
Programmable polarimeters	VO₂ digital microwires	Digitally set anisotropy
Plasmonic spectropolarimeters	Gold nanorod gratings	Diffraction, phase gradients
Photocatalytic yield modulators	Au–TiO₂ elliptical rods	LSPR polarization tuning

Strong polarization conversion or analysis can be demonstrated in various modalities:

• Broadband dielectric designs achieving near-unity (99%) polarization conversion efficiency via multi-mode Huygens metasurfaces (Kruk et al., 2016).
• Birefringence-derived devices for programmable polarization beam splitting or OAM channel multiplexing, where the meta-atom shape and orientation locally control Jones matrix eigenstates (Achouri et al., 2016, Hazineh et al., 2023).
• Quarter- and half-wave plates in the THz regime using plasmonic or graphene patches, with tunability from electrostatic gating (Guo et al., 2016).
• Multifunctional dichroic metasurfaces with angle-dependent selectivity for linear or circular bases; simulation ER > 50, measured ER ~10 at select angles (Li et al., 14 Oct 2024).

4. Nonlinear and Spectral-Polarimetric Capabilities

Nonlinear metasurfaces enable emission with tailored polarization at harmonic frequencies through symmetry-controlled effective nonlinear susceptibility tensors. In amorphous Si metasurfaces, the THG process can be described analytically: $$P_{3\omega} = a_1(V_R e^{4i a}|L\rangle + V_L e^{-4i a}|R\rangle ) + a_2( V_R e^{2i a}|R\rangle + V_L e^{-2i a}|L\rangle ) + ...$$ where $a_i$ are functions of the extracted tensor elements $X_{ij}$ and meta-atom rotation angle $a$, $V_{R,L}$ are right and left-circular field components (Yue et al., 3 Sep 2025). Monoclinic chiral arrangements further amplify linear-to-elliptical conversion in both the fundamental and THG, with ellipticity ($\sigma$) shifts of up to 0.7 observed near resonance (Toftul et al., 14 Jan 2025). This denotes a pathway for nonlinear vector beam shaping or polarization-multiplexed harmonic imaging.

Polarization-resolved spectropolarimetry is realized by IPMs which diffract polarization and spectral components into spatially distinct domains using phase-gradient metasurfaces optimized for six analyzer states (Chen et al., 2015). The instrument matrix approach enables recovery of the Müller matrix of unknown samples, providing complete characterization of diattenuation, retardance, and depolarization.

5. Sensing and Imaging Applications

Polarization-sensitive metasurfaces serve as non-destructive sensors for material anisotropy, alignment, and molecular structure. Guided-mode-resonant colorimetric metasurfaces, when coupled with fibrous samples (e.g., PCL nanofibers), enable quantitative extraction of alignment via correlation of reflected colorimetric change ($\Delta E_{ab}$ in CIELAB space) and polarization conversion properties—bypassing the need for destructive crystallographic or microscopy methods (Kirya et al., 15 Apr 2025). Dielectric metasurface polarimeters provide direct measurement of all Stokes parameters with fidelity exceeding 99% in single-shot fashion by mapping arbitrary polarization inputs to unique far-field diffraction signatures, allowing fast, compact, and integrated polarization imaging (Shah et al., 2022).

In analog optical computing, image-processing metasurfaces implement edge detection (Laplacian operation) with polarization-asymmetric or polarization-independent transfer functions. This allows for real-time, polarization-dependent directional differentiation, and operation on unpolarized images, with efficiency near passive device theoretical bounds (Cotrufo et al., 2023).

6. Programmable and Dynamically Tunable Metasurfaces

Dynamic or reconfigurable polarization-sensitive control is achievable through materials exhibiting phase transitions (e.g., VO₂ in Babinet-invertible metasurfaces (Nakata et al., 2016) and conformal digital metasurfaces (Shabanpour et al., 2021)). By switching bias states of orthogonally oriented wires, devices can encode distinct reflectivity states for each input polarization, enabling ultrafast, programmable polarimetric sensors compatible with curved surfaces and oblique angles. Angle-selective dichroic metasurfaces based on topology-optimized phase patterns further harness incidence direction as a tuning parameter for polarization selectivity, enabling multifunctional optical elements that operate differently by steering input angle (Li et al., 14 Oct 2024).

In plasmonic applications, the ellipticity of metasurface nanopillars (Au–TiO₂) sets LSPR wavelengths for each polarization axis. The photocatalytic yield is actively modulated by rotating the input polarization, effectively doubling N-demethylation product yield when switching between TE and TM modes (yield from 4.7 to 9.98, SERS detected), with product selection tunable in multi-pathway reactions (Lyu et al., 26 Sep 2025).

7. Implications, Limitations, and Future Directions

Current metasurfaces extend polarization control beyond form birefringence and spatially variant geometric phase to cover arbitrary points in Jones retarder space, providing unprecedented flexibility in phase, amplitude, and eigenaxis modulation (Rubin et al., 20 May 2025). This full-space control is not achievable with historic diffractive or form-birefringent optics, leading to new paradigms in polarization imaging, quantum state tomography, and analog optical processing.

Challenges remain in scaling fabrication for high fidelity of complex nanostructures, minimizing cross-talk between polarizations, compensating for chromatic aberrations in broadband applications, and optimizing nonlinear and dynamic response. Inverse-designed and multilayer architectures are under exploration for expanding bandwidth, efficiency, and functional density. The integration of polarization-sensitive metasurfaces is anticipated in next-generation cameras, spectrometers, polarimetric imagers, quantum devices, nonlinear light sources, analog optical processors, and advanced photonic sensors.

Polarization-sensitive metasurfaces thus constitute a versatile, foundational platform for controlling and exploiting the polarization degree of freedom in light, enabling compact, efficient, and multifunctional photonic systems across classical and quantum domains.