Second-harmonic-generation (SHG) metalenses nanoimprinted from sol-gel lithium niobate (LN) currently combine a record imprintable-material nonlinearity of deffd_{\mathrm{eff}} = 4.8 pm/V (14% of monocrystalline d33d_{33}) with deliberately non-resonant geometric-phase designs. The platform's two efficiency bottlenecks are precisely quantified by its inventors: the material value sits close to the theoretical maximum of ≈6.6 pm/V (20% of d33d_{33}) predicted for randomly oriented crystalline domains with bulk LN χ(2)\chi^{(2)} tensor values, and the unit cells exploit no resonant field enhancement. The open problem is to raise the SHG focusing and conversion efficiency of this scalable platform by (i) materials engineering that enhances the effective nonlinear properties of the imprint-compatible sol-gel material — through synthesis recipes that reduce porosity and shrinkage, post-molding treatments allowing localized crystallinity control (laser annealing, thermal scanning-probe annealing, or poling), increased nanocrystallite sizes, doping, or the integration of quantum dots or plasmonic nanoparticles — while retaining direct nanoimprint processability, and/or (ii) metalens designs with enhanced light–matter interaction, whether by optimizing the design for higher focusing efficiency or by exploiting Mie, lattice-coupled, Fano, or bound-states-in-the-continuum resonances, compatible with the process realities of ≈50% linear shrinkage, a residual porous film, and fabrication-induced phase-profile deviations. As of August 2026, neither route has been demonstrated on this imprinted polycrystalline LN platform.

Background

Second-harmonic generation (SHG) is the nonlinear-optical process in which a material lacking inversion symmetry converts two photons of a pump wave into one photon at twice the optical frequency; its strength is parametrized by an effective second-order coefficient deffd_{\mathrm{eff}} (in pm/V). Lithium niobate (LN) is a ferroelectric crystal with one of the largest transparent-window nonlinear coefficients, d33d_{33} ≈ 34 pm/V at 1064 nm, but it is chemically so inert that top-down nanofabrication requires aggressive plasma etching, which yields slanted sidewalls and blocks high-aspect-ratio freeform nanostructures. A metasurface is a two-dimensional array of sub-wavelength scatterers (meta-atoms) that shapes a wavefront by position-dependent phase; a metalens is a metasurface that focuses light. In a nonlinear geometric-phase (Pancharatnam–Berry phase) metalens, the SHG wavefront is controlled by rotating anisotropic meta-atoms, with the nonlinear phase proportional to rotation angle. Talts, Weigand, Occhiodori and Grange (arXiv:2409.16379; Advanced Materials 37, 2418957, 2025) introduced a bottom-up alternative to etching: a sol-gel (solution-derived, dried and crystallized by annealing at 600 °C) LN material that is directly molded by soft nanoimprint lithography (SNIL, replication of a master mold through an elastomeric PDMS stamp), yielding polycrystalline structures — many randomly oriented crystalline grains of 10–30 nm — with nearly vertical sidewalls and aspect ratios up to 6. Because the grain axes are randomly oriented, the orientational average of the nonlinear tensor limits deffd_{\mathrm{eff}}: following powder-SHG analysis by Sánchez-Dena et al. (2017), the maximum for randomly oriented LN domains with bulk LN χ(2)\chi^{(2)} tensor values is 20% of d33d_{33}, ≈6.6 pm/V, and the measured deffd_{\mathrm{eff}} = 4.8 pm/V — obtained at λpump\lambda_{\mathrm{pump}} = 880 nm by comparison with x-cut monocrystalline LN — sits close to this value. The same group had earlier nanoimprinted sol-gel barium titanate for electro-optic metasurfaces (Weigand et al. 2024). Their imprinted C3-symmetric geometric-phase metalenses focus SHG from the near-UV to the near-IR with focal intensity enhancement of up to 34× relative to the inhomogeneous, speckle-like SHG at the metalens surface, but deliberately avoid resonances, so they forgo the large local-field enhancements available from Mie resonances (electromagnetic modes of high-index dielectric particles), collective lattice resonances (wave-coupled array modes), Fano resonances (sharp asymmetric lines from interfering bright/dark modes), and bound states in the continuum (BIC, non-radiating localized modes that become high-Q when weakly perturbed) — mechanisms reviewed by Pertsch and Kivshar (2020) and already exploited in etched monocrystalline LN metasurfaces (Fedotova et al. 2020) and in other platforms such as the polycrystalline ZnO vacuum-ultraviolet nonlinear metalens of Tseng et al. (2022). The imprint process itself imposes constraints that any improved design must tolerate: ≈50% linear shrinkage from master to annealed part, a residual porous film (~50 nm) beneath the structures, and fabrication-induced deviations from the analytical phase profile. In their outlook the authors indicate reducing porosity and shrinkage through different imprint-compatible synthesis recipes, post-molding treatments allowing localized crystallinity control (laser annealing, thermal scanning-probe annealing, or poling), increased nanocrystallite sizes, doping, and the integration of quantum dots or plasmonic nanoparticles as routes to a stronger effective nonlinearity, and more complex metalens designs with enhanced light–matter interaction — including optimized focusing designs and Mie, collective lattice-coupled, Fano, or bound-states-in-the-continuum resonances — as the route to stronger SHG focusing. Beyond SHG efficiency, the authors propose (but do not demonstrate) extending the platform to spontaneous parametric down-conversion (SPDC, the inverse process generating photon pairs for quantum light) and to Pockels-effect (electro-optic) GHz free-space modulation — functionality-broadening directions treated separately from the efficiency problem posed here.

Problem Statement

For the nanoimprinted sol-gel lithium niobate metasurface platform of Talts et al., whose measured effective nonlinearity deffd_{\mathrm{eff}} = 4.8 pm/V at λpump\lambda_{\mathrm{pump}} = 880 nm (14% of monocrystalline d33d_{33}, calibrated against x-cut monocrystalline LN) is close to the theoretical maximum of 6.6 pm/V — the maximally achievable 20% of d33d_{33} for randomly oriented domains with bulk LN χ(2)\chi^{(2)} tensor values — and whose metalens designs deliberately avoid resonances: (1) by what materials engineering — synthesis recipes that reduce porosity and shrinkage while remaining imprint-compatible, post-molding treatments allowing localized crystallinity control such as laser annealing, thermal scanning-probe annealing or poling, increased nanocrystallite sizes, doping, or incorporation of quantum dots or plasmonic nanoparticles — can a directly nanoimprint-compatible LN-based material raise its effective second-order nonlinearity above the demonstrated 4.8 pm/V while retaining the molded high-aspect-ratio nanofabrication and the direct nanoimprint scalability of the process; and/or (2) can meta-atom and lattice designs with enhanced light–matter interaction — designs optimized for higher focusing efficiency, or resonances such as Mie, lattice-coupled, Fano, or bound-states-in-the-continuum modes — realized within the process constraints of ≈50% linear shrinkage, a residual porous film, and fabrication-induced phase-profile deviations, deliver higher second-harmonic focusing and conversion efficiency, quantified by the focal intensity enhancement relative to the speckle-like SHG at the metalens surface, than the demonstrated non-resonant geometric-phase metalenses, whose focal intensity enhancement reaches up to 34×? The two routes jointly serve one objective — higher nonlinear conversion efficiency from the scalable imprinted platform — and either one, or their combination, would advance it.

References

  1. Ülle-Linda Talts, Helena C. Weigand, Irene Occhiodori, Rachel Grange: Scalable Lithium Niobate Nanoimprinting for Nonlinear Metalenses. arXiv:2409.16379 (2024); published as Advanced Materials 37, 2418957 (2025). DOI 10.1002/adma.202418957, https://doi.org/10.1002/adma.202418957
  2. O. Sánchez-Dena, E. V. García-Ramírez, C. D. Fierro-Ruiz, E. Vigueras-Santiago, Rurik Farías, J. A. Reyes-Esqueda: Effect of size and composition on the second harmonic generation from lithium niobate powders at different excitation wavelengths. Materials Research Express 4, 035022 (2017). DOI 10.1088/2053-1591/aa62e5, https://doi.org/10.1088/2053-1591/aa62e5
  3. Ming Lun Tseng, Michael Semmlinger, Ming Zhang, Catherine Arndt, Tzu-Ting Huang, Jian Yang, Hsin Yu Kuo, Vin-Cent Su, Mu Ku Chen, Cheng Hung Chu, Benjamin Cerjan, Din Ping Tsai, Peter Nordlander, Naomi J. Halas: Vacuum ultraviolet nonlinear metalens. Science Advances 8, eabn5644 (2022). DOI 10.1126/sciadv.abn5644, https://doi.org/10.1126/sciadv.abn5644
  4. Anna Fedotova, Mohammadreza Younesi, Jürgen Sautter, Aleksandr Vaskin, Franz J. F. Löchner, Michael Steinert, Reinhard Geiss, Thomas Pertsch, Isabelle Staude, Frank Setzpfandt: Second-Harmonic Generation in Resonant Nonlinear Metasurfaces Based on Lithium Niobate. Nano Letters 20, 8608–8614 (2020). DOI 10.1021/acs.nanolett.0c03290, https://doi.org/10.1021/acs.nanolett.0c03290
  5. Thomas Pertsch, Yuri Kivshar: Nonlinear optics with resonant metasurfaces. MRS Bulletin 45, 210–220 (2020). DOI 10.1557/mrs.2020.65, https://doi.org/10.1557/mrs.2020.65
  6. Helena C. Weigand, Ülle-Linda Talts, Anna-Lydia Vieli, Viola V. Vogler-Neuling, Alfonso Nardi, Rachel Grange: Nanoimprinting Solution-Derived Barium Titanate for Electro-Optic Metasurfaces. Nano Letters 24, 5536–5542 (2024). DOI 10.1021/acs.nanolett.4c00711, https://doi.org/10.1021/acs.nanolett.4c00711
  7. Bohan Li, Zhuoqun Wang, Qingtao Fang, Ning Lu, Zhanghua Han, Weijin Chen, Yuechen Jia, Feng Chen: Meta-Atom Rotation Unlocks Nonlinear Optical Chirality in Lithium Niobate Metasurfaces. Laser & Photonics Reviews 20, e71170 (2026). DOI 10.1002/lpor.71170, https://doi.org/10.1002/lpor.71170
  8. Rana Faryad Ali, Guillermo Aguilar: Direct Photochemical Patterning of Lithium Niobate Structures for Scalable Nonlinear Optical Metasurfaces. Small Science 6, e202500606 (2026). DOI 10.1002/smsc.202500606, https://doi.org/10.1002/smsc.202500606
  9. Eleni Prountzou, Helena C. Weigand, Virginia Falcone, Ülle-Linda Talts, Morgan Trassin, Rachel Grange: Electro-optic Modulation in Polycrystalline Barium Titanate Metasurfaces Enhanced by Poling. ACS Photonics 13, 2928–2936 (2026). DOI 10.1021/acsphotonics.6c00340, https://doi.org/10.1021/acsphotonics.6c00340
  10. Jumin Qiu, Meibao Qin, Tingting Liu, Lun Qu, Xintong Shi, Feng Wu, Tianbao Yu, Qiegen Liu, Shuyuan Xiao: Doubly resonant nonlinear metasurfaces enabling NIR-to-UV upconversion for reconfigurable Fourier optical processing. arXiv:2603.01609 (submitted 2026-03-02). arXiv ID 2603.01609, https://arxiv.org/abs/2603.01609
  11. Dong Kyo Oh, Hyunjung Kang, Dohyun Kang, Joohoon Kim, Junsuk Rho: Nanoprinting metasurfaces with engineered optical materials. Nature Reviews Materials 11, 375–392 (2026). DOI 10.1038/s41578-025-00874-3, https://doi.org/10.1038/s41578-025-00874-3
  12. Yong Wang, Zi Wang, Yang Liu, Lina Yang, Kaixuan He, Lifan Zhang, Guodong Wang, Lei Zhang: Heterogeneous integration of 8-inch LiNbO3 films for second harmonic generation. Journal of Materials Chemistry C 13, 15948–15956 (2025). DOI 10.1039/d5tc01952d, https://doi.org/10.1039/d5tc01952d
  13. Yaping Hou, Yigong Luan, Yu Fan, Alfonso Nardi, Attilio Zilli, Bobo Du, Jinyou Shao, Marco Finazzi, Chunhui Wang, Lei Zhang, Michele Celebrano: Efficient and tunable narrowband second-harmonic generation by a large-area etchless lithium niobate metasurface. arXiv:2602.00830 (submitted 2026-01-31). arXiv ID 2602.00830, https://arxiv.org/abs/2602.00830