Enhanced optical Kerr effect in metasurfaces featuring arrays of rotated rectangular holes via trapped-mode resonances

Recent advances in nanophotonics have demonstrated that various optical resonances in nanostructures can achieve strong field confinement with substantially suppressed scattering. This study investigates the optical Kerr effect (OKE) enhancement in high-refractive-index metasurfaces featuring non-BIC trapped-mode resonances, using gallium phosphide (GaP) as a model material. Three-dimensional finite-difference time-domain simulations reveal a significant enhancement of the effective second-order refractive index, reaching values up to 700 times greater than bulk GaP. The numerical results show strong electromagnetic field localization at the trapped-mode resonance, characterized by a wide transmittance dip (low Q-factor) and near-unity reflectance. Remarkable stability is observed, with the OKE enhancement maintaining less than 5% variation for moderate polarization angles and tolerating random nanohole rotations that model fabrication imperfections. Compared to bound states in the continuum (BIC), the non-BIC trapped mode demonstrates superior robustness to structural disorder while achieving comparable nonlinear enhancement. These findings suggest promising applications in reflective nonlinear optics, particularly for high harmonic generation and polarization-insensitive photonic devices.