Lithium Niobate Metasurface for GHz and Efficient Electro-Optical Modulation in the Linear and Nonlinear Regime

Optical metasurfaces emerged as the key platform to manipulate light at the nanoscale. A fast and efficient reconfiguration of metasurface properties is fundamental to realize ultrathin devices for free-space optical communications and optical computing. Among the tuning mechanisms, the electrically driven refractive index change caused by Pockels effect in nonlinear materials is advantageous, due to the wide modulation bandwidth and the ready integrability with electronic systems. Nowadays, fiber electro-optic (EO) modulators routinely reach 100 GHz modulation rate with CMOS compatibile voltages <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(V_{\text{EO}} &lt; 5\ \mathrm{V})$</tex>[1]. However, the inherently perturbative nature of the Pockels effect significantly limits the attained EO modulation efficiency in metasurfaces, characterized by a sub-wavelength thickness. This often results in a trade-off between modulation efficiency and device bandwidth. To bridge this gap, we propose a lithium niobate on insulator metasurface consisting in an asymmetric periodic grating, characterized by high quality-factor (Q) resonances, to modulate both the reflectivity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$R$</tex> and the second-harmonic generation (SHG) power <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W_{\text{SHG}}$</tex> by an external bias (see Fig. 1a) [2]. The realized Q > 8000 enables a modulation efficiency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\Delta R / R) / V_{\text{EO}} &gt; 10^{-2} \mathrm{V}^{-1}$</tex> (see Fig. 1b), a value achieved only in platforms sacrificing modulation bandwidth to enhance the driving field amplitude. The low device capacitance allows the achievement of 1 GHz of modulation bandwidth. Moreover, by leveraging the large optical nonlinearity of LiNbO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> in combination with the Pockels effect, we also efficiently modulate the SHG by the same platform. The high <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q$</tex> of our device is the key to excite SHG with the same continuous-wave source used for the linear modulation and attain a striking SHG modulation efficiency of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\Delta W_{\text{SHG}} / W_{\text{SHG}}) / V_{\text{EO}}=0.12 \mathrm{V}^{-1}$</tex> (see Fig. 1c and d). These findings pave the way toward efficient EO modulation of nonlinear signals driven by low-power CW lasers, establishing a technological milestone in nanophotonics.