Barium Titanate-Based Active Transmissive Metasurfaces in the Visible Spectrum

We report the design of an electro-optically tunable barium titanate (BTO)-based transmissive metasurface for subwavelength amplitude and phase modulation at a wavelength of 630 nm. To date, most active metasurfaces have focused on controlling the properties of light in reflection. However, in recent years, there has been considerable interest in developing dynamically tunable transmissive metasurfaces that integrate seamlessly into optical systems with minimal insertion losses. In particular, there has been an increased demand for visible frequency optical modulators that can be readily integrated into imaging and augmented reality systems. Liquid crystals (LCs) have been widely used for achieving dynamic control in transmission. However, LC-based modulators typically consist of large unit cells ranging from 2-4 μm, which strongly limit the field-of-view for visible frequency operation. Additionally, LC modulators are restricted to kHz modulation frequencies. Electro-optic materials relying on the Pockels effect provide a promising alternative for reconfigurable transmissive metasurfaces with high efficiencies and subwavelength unit cell control at visible frequencies.<br/><br/>Here, we propose the integration of barium titanate nanoblock resonators, which exhibit higher order Mie resonances, into transmissive metasurfaces. Barium titanate is a high-index birefringent material with a wide transmission range across the visible and near-infrared spectrum, from 0.4 to 5 μm. The non-centrosymmetric crystal structure of BTO gives rise to its strong Pockels coefficient, dominated by the values of <i>r</i>₄₂ = <i>r</i>₅₁ = 1300 pm/V in bulk crystals. Recently, significant progress has been made in the fabrication of BTO thin films, with electro-optic coefficients as high as <i>r</i>₄₂ = 942 pm/V reported using molecular beam epitaxy [1]. We first derive the crystal orientation and incident light polarization with respect to the applied field which yield the strongest electro-optic response in BTO. We find that an in-plane electric field in a-axis oriented crystals produces the maximal refractive index change when the electrodes are oriented at 54° with respect to the in-plane optical axis (c-axis). Assuming experimentally realized Pockels coefficients, this configuration corresponds to a maximal index change of 0.1-0.2 at 630 nm with applied fields ranging between 0.2-0.5 MV/cm. Using this response, we design subwavelength nanoblock resonators on top of a silicon nitride membrane and low-index dielectric thin film. The resonator dimensions and the dielectric thickness are chosen to engineer an avoided crossing between two resonant modes, yielding maximal phase shift at high transmittance values. The resonators are individually addressed in one dimension through lateral ITO electrodes. The resulting metasurface exhibits transmittance values of over 50% for index changes of +/- 0.2 and an associated phase shift of more than 240°. Full-wave simulations of the metasurface are complemented by electrostatic simulations confirming the desired polarization of the optical mode with respect to the incident light polarization. In a next step, we alter the refractive indices between adjacent metasurface elements to mimic the effect of independent resonator biasing and engineer spatial phase gradients that steer the transmitted beam in desired directions. We discuss design choices to mitigate crosstalk between individual resonators and maximize beam directivity. Finally, we explore experimental pathways to realize the proposed BTO metasurface and analyze the impact of fabrication imperfections – such as sidewall angles, deviation from target crystal orientation, and electrode configuration – on the achieved performance.<br/><br/>[1] Abel et al., <i>Nat. Mater.</i> <b>18</b>, 42–47 (2019).