Nonlinear geometric phase control via high-Q quasi-BIC resonance in all-dielectric metasurfaces

Nonlinear geometric metasurfaces are an important platform for information encoding and light-field manipulation with wide applications in display encryption and beyond. Enhancing nonlinear conversion efficiency and controlling the nonlinear geometric phase are equally crucial for practical use. Recently, high-Q resonances in nonlocal metasurfaces have shown strong light-matter interactions, providing a foundation for efficient nonlinear conversion. However, simultaneously achieving high efficiency and effective phase control remains a key challenge. Here, based on the principle of geometric phase, we efficiently realize third-harmonic phase control, where the high-Q resonance corresponds to a magnetic dipole-related quasi-BIC mode. At the ultra-narrow resonance bandwidth, the electric field enhancement exceeds 50 times, with a quality factor over 3000 and high stability under rotation. A third-harmonic conversion efficiency of the order of 10^-3 is achieved at a peak pump density of 100 MW cm^-2, outperforming previously reported nonlinear geometric metasurfaces. This work holds significant potential for on-chip nonlinear information processing and wavefront control requiring strong light-matter interaction.