a Color-coded electric field and its contours upon applying a bias of 25 V. The electrostatic field extends stronger along the depth-direction (z-axis), as compared to the isotropic case, due to the anisotropy in the relative permittivity of z-cut lithium niobate (LiNbO3, LN). b In-plane (Ex) and out-of-plane electric-field component (Ez) in the LN substrate 100 nm below the surface (along the dashed red line shown in Fig. 2a). The yellow bars indicate the position of the Au wires. The in-plane field component Ex shows highest amplitude in between the two electrodes, while the out-of-plane component Ez exhibits highest amplitude underneath the wires with opposite sign. c, d Due to the linear electro-optic (Pockels) effect in the LN substrate, the extraordinary (ne) and ordinary (no) refractive index underneath the left wire is decreased, while being increased by an equal amount in the right guide. Consequently, the waveguides lose their optical identity, which influences the power transfer in the directional coupler.