Nonlinear Metasurface Platform

• Nonlinear metasurfaces are engineered two-dimensional platforms that manipulate light-matter interactions via subwavelength meta-atoms and resonant field enhancement.
• They enable efficient frequency conversion, phase manipulation, and quantum state engineering by integrating advanced materials like multi-quantum wells and ENZ films.
• Resonant designs combined with AI-assisted optimization facilitate dynamic, reconfigurable control over ultrafast optical processes, from holography to entangled photon pair generation.

A nonlinear metasurface platform is a two-dimensional engineered structure composed of arrays of subwavelength meta-atoms designed to enhance, manipulate, and control nonlinear light-matter interactions at the surface level. These platforms leverage the resonant, geometric, and symmetry properties of appropriately engineered nanostructures to achieve efficient frequency conversion, phase manipulation, polarization control, spatiotemporal modulation, and quantum state engineering, all within devices of subwavelength thickness. By integrating nonlinear materials—such as multi-quantum wells, van der Waals crystals, all-dielectric nanostructures, or epsilon-near-zero films—these metasurfaces circumvent limitations of bulk nonlinear optics (notably, phase matching and device footprint) and enable advanced functionalities for ultrafast photonics, quantum optics, wavefront shaping, and compact, reconfigurable optical components.

1. Fundamental Principles and Architectures

Nonlinear metasurfaces exploit local field enhancement and resonance phenomena to mediate nonlinear processes, such as second-harmonic generation (SHG), third-harmonic generation (THG), four-wave mixing (FWM), and spontaneous parametric downconversion (SPDC). Unlike linear metasurfaces, which tailor amplitude, phase, or polarization at the fundamental frequency, nonlinear metasurfaces utilize materials with strong second- ($\chi^{(2)}$) or third-order ($\chi^{(3)}$) susceptibilities to engineer the emergent wavefront at the generated harmonic or parametric frequencies.

Core architectural strategies include:

• Plasmonic Metasurfaces with Multi-Quantum Well (MQW) Substrates: Localized surface plasmon resonances in U-shaped or split-ring resonators supply giant field enhancements at both pump and harmonic frequencies, while embedded MQW media deliver ultrahigh $\chi^{(2)}$ or $\chi^{(3)}$ nonlinearities (Tymchenko et al., 2015).
• Chiral Huygens Metasurfaces: Asymmetric nanoantennas (e.g., "butterfly" configurations) serve as polarization-independent field concentrators and programmable nonlinear dipole emitters, enabling arrangement as arrays of Huygens sources for structured harmonic radiation (Lesina et al., 2016).
• All-Dielectric Metasurfaces: High-index semiconductor or van der Waals materials support Mie and quasi-bound-state-in-the-continuum (q-BIC) modes, enhancing nonlinear interactions with reduced losses and enabling efficient SHG and THG (Zograf et al., 28 Oct 2024, Gennaro et al., 2022).
• Nonlocal and Quasi-Trapped Mode (QTM) Metasurfaces: Nonlocal resonant architectures support narrowband high-Q modes extending over multiple meta-atoms, affording both large THG enhancement and meta-atom level geometric phase control (Sedeh et al., 8 Jul 2025).
• Epsilon-Near-Zero (ENZ) and Hybrid Platforms: Integration of plasmonic and ENZ materials offers strong field localization around the ENZ wavelength, boosting nonlinear quantum processes such as polarization-entangled photon pair generation (Jia et al., 6 May 2024).

2. Nonlinear Phase Engineering and Wavefront Control

One of the central innovations in nonlinear metasurface platforms is the ability to exert deterministic, local control over the phase of nonlinear polarization currents—thereby shaping the phase, amplitude, and polarization of the emitted nonlinear waves with subwavelength precision.

Pancharatnam–Berry (PB) Phase in Nonlinear Regimes

Rotation of meta-atoms imparts a geometric phase (PB phase) onto the nonlinear polarization, which, due to the nonlinear mapping, scales differently for various polarization channels. For a second-harmonic process excited with a circularly polarized field $E_L^{(\mathrm{inc})}$, the key relations are:

• For LHCP SH component: $$K_{2,L}^{(L)}(x,y) \propto [E_L^{(\mathrm{inc})}]^2 e^{i2\varphi(x,y)}$$
• For cross-polarized component: $$K_{2,R}^{(L)}(x,y) \propto [E_L^{(\mathrm{inc})}]^2 e^{i\varphi(x,y)}$$

This "phase-multiplier" effect enables full $0$–$2\pi$ phase coverage and subwavelength spatial control over nonlinear emission (Tymchenko et al., 2015, Matsudo et al., 2022, Sedeh et al., 8 Jul 2025).

PB Phase at Higher Harmonics and Nonlinear Anisotropy

For THG, the nonlinear phase for co-polarized and cross-polarized harmonic channels obeys:

• $\Phi_{\text{co}} = 2\sigma\alpha$
• $\Phi_{\text{cross}} = 4\sigma\alpha$

where $\sigma$ is the input handedness and $\alpha$ is the meta-atom orientation (Matsudo et al., 2022, Sedeh et al., 8 Jul 2025). With careful symmetry breaking, geometric phase control becomes "selective", accumulating only at the resonance attributed to QTM modes, thus decoupling resonant and off-resonant behavior at the design level (Sedeh et al., 8 Jul 2025).

Acoustic and Quasicrystalline Analogues

Analogous control is achieved in nonlinear acoustic metasurfaces via phase profiles imparted through resonator mass-tuning, enabling steering, focusing, or even self-bending of generated harmonics in the transmission region (Lin et al., 2022). Spatially aperiodic arrangements (e.g., Penrose or HQC tilings) further allow the global symmetry of the metasurface to regulate the far-field nonlinear diffraction pattern, with local meta-atom orientation delivering geometric phase control on the constituent nonlinear dipoles (1901.10138).

3. Resonant Enhancement, Local Field Engineering, and Efficiency

Nonlinear conversion efficiency in metasurface platforms is primarily determined by the ability to confine and enhance local electromagnetic fields at the pump and generated frequencies:

• High-Q Resonances: Both Mie-like and q-BIC resonances support field localization and allow substantial enhancement of nonlinear processes. Achieving $Q > 50$ in high-index dielectrics enables multi-order THG efficiency enhancement, with bandwidths tunable by geometry and material contrast (Abdelraouf, 12 Jun 2025, Zograf et al., 28 Oct 2024). BICs are used as symmetry-protected, low-loss field concentrators, with intentional symmetry breaking introducing radiative coupling (quasi-BIC).
• Modal Overlap and Double Resonance: Efficient nonlinear emission requires coincident resonances at multiple interacting frequencies (e.g., both pump and harmonic). This is achieved through structural design (e.g., vertical stacking, spatial positioning, or material composition) and verified in doubly resonant ENZ metasurfaces boosting SPDC and SHG (Jia et al., 6 May 2024).
• AI-Assisted Optimization: Neural network tools (e.g., NanoPhotoNet-NL) enable optimization of complex multilayer metasurface geometries to maximize both field localization and effective nonlinear overlaps—Facilitating DUV THG with Q-factors exceeding 50, greatly expediting inverse design (Abdelraouf, 12 Jun 2025).
• Nonlocal and Hybrid Plasmonic Effects: In hybrid graphene-gold architectures, electrically tunable plasmon modes further enhance nonlinear field localization at mid-IR and visible frequencies; the tunable overlap integral $$E_{\text{far}}(\omega_{\text{FWM}}) \propto \int E_{\text{near}}(\omega_{\text{FWM}}) \cdot P_{\text{NL}}(\omega_{\text{FWM}}) dV$$ links design to FWM efficiency (Feinstein et al., 23 Jul 2024).

4. Dynamical and Reconfigurable Nonlinear Functionality

Modern nonlinear metasurface platforms incorporate mechanisms for dynamic and even real-time control of their nonlinear response:

• Electro–Optical Tuning: Integration of electrodes with materials such as lithium niobate enables modulation of SHG via the electro-optic (Pockels) effect, with refractive index modulation $\Delta n = -\frac{1}{2} n^3 \gamma_{33} E$ shifting the resonance condition and thus controlling SHG output (He et al., 11 Apr 2024). Such schemes also permit programmability at the metasurface level for dynamic holography, modulation, and quantum light sources.
• All-Optical Reconfigurability: In As$_2$S$_3$ and other Kerr nonlinear materials, intensity-dependent refractive index changes allow for ultrafast switching of optical functionalities, such as on-demand imparting or removal of orbital angular momentum onto a beam (Xu et al., 2018).
• Power-Dependent (Self-Biased) Switching: At microwaves, the use of PIN diodes embedded in meta-atoms enables a self-biased platform that transitions between quarter-wave plate behavior and digital metasurface operation depending solely on the incident field intensity—effectively realizing an all-passive, gainless nonlinear switch (Kiani et al., 2020).
• AI-Enabled Spectral Adaptivity: The combination of multilayer structure, phase-change materials, and AI-accelerated design allows for the realization of fast, broadband, and spectrally tunable DUV sources via dynamic refractive index switching (Abdelraouf, 12 Jun 2025).

5. Quantum State Generation and Structured-Field Applications

Nonlinear metasurface platforms have emerged as compact, scalable sources for nonclassical light and structured beams:

• Photon Pair Generation and Entanglement: Subwavelength-thickness metasurfaces utilizing SPDC in lithium niobate or ENZ-coupled plasmonic platforms achieve color, angular, and polarization tunability of quantum photon pair sources. These platforms enable all-optical or electro-optic tuning of emission angle (via pump wavelength or EO effect), momentum path-entanglement, and direct generation of Bell states through engineered $\chi^{(2)}$ tensor anisotropy (Weissflog et al., 12 Mar 2024, Jia et al., 6 May 2024).
• Orbital Angular Momentum and Wavefront Structuring: Chiral metasurfaces and PB-phase architectures enable programmable implementation of vortex beams, polarization-multiplexed structured beams, and controllable holographic elements—transforming the output nonlinear beam into arbitrary, multiplexed field patterns with high efficiency (Lesina et al., 2016, Matsudo et al., 2022).
• Topological Photonics: Nonlinear metasurfaces designed for the generation and dynamical switching of skyrmionic textures (electric vs. magnetic) in terahertz toroidal pulses demonstrate the feasibility of topological information encoding and robust data transmission (Niu et al., 29 Aug 2025).

6. Fabrication, Material Platforms, and Practical Integration

Implementation of nonlinear metasurface platforms depends on advances in top-down and hybrid fabrication methodologies, as well as the identification of optimal material systems:

• Top-Down Nanofabrication: Electron-beam lithography and FIB milling are used for precise definition of meta-atom geometries (e.g., arrays of equilateral triangles with atomically precise zigzag edges in 3R–MoS₂), followed by anisotropic wet etching to induce designed symmetry breaking and q-BIC modes (Zograf et al., 28 Oct 2024).
• Material Systems: III–V semiconductors (GaAs, AlGaAs), van der Waals materials (3R–MoS₂), lithium niobate, ENZ materials (ITO), chalcogenide glasses (As$_2$S$_3$), and hybrid plasmonic/dielectric structures are leveraged for their respective nonlinear coefficients and refractive indices (Gennaro et al., 2022, He et al., 11 Apr 2024, Zograf et al., 28 Oct 2024).
• Integration with Photonic Circuits: The subwavelength thickness of metasurfaces enables monolithic integration into photonic chips, compatibility with fiber/coupler interfaces, and stacking in multilayer architectures for increased functionality (Abdelraouf, 12 Jun 2025, Weissflog et al., 12 Mar 2024).

7. Prospects, Challenges, and Outlook

Nonlinear metasurface platforms are advancing the frontier of nanoscale photonics, yet present ongoing challenges:

• Optimization Complexity: Concurrent control over nonlinear efficiency, wavefront manipulation, polarization, bandwidth, and fabrication constraints necessitates multi-objective and AI-driven inverse design approaches (Li et al., 21 Mar 2024, Abdelraouf, 12 Jun 2025).
• Scalability and Loss: Achieving ultrahigh Q-factors, high field enhancement, and minimal scattering/absorption losses in realistic nanostructures, while respecting fabrication limits, remains a central engineering challenge.
• Dynamic and Quantum Applications: Extending these concepts to actively programmable or topological metasurfaces (e.g., for mode-encoded data transfer, ultrafast switching, quantum transduction) presents new requirements in terms of phase-stability, electrical control, and quantum efficiency (Feinstein et al., 23 Jul 2024, Niu et al., 29 Aug 2025).
• Interplay of Local and Global Symmetries: The full utilization of local symmetry (meta-atom level) and global lattice symmetry (quasicrystalline arrangements) enables complex far-field functionalities, yet modeling and controlling these interactions for higher-order and cascaded processes is a subject of ongoing research (1901.10138).

In aggregate, nonlinear metasurface platforms offer a rigorous, application-enabling approach to engineer and enhance nonlinear optical interactions, bringing transformative capabilities to integrated photonics, quantum technologies, ultrafast optics, and structured-field engineering.