Fig. 3: Three-dimensional finite element simulations showing device performance.

a Electric field components in the xy plane (a) in the middle of the silicon waveguide, showing polarization rotation (vanishing E_x and emerging E_y). Window size: 7 × 1 μm². b Field intensity ∣E∣² in the middle of the spacer, showing nano-concentration of energy. Window size: 1.5 × 0.2 μm². c Time-averaged Poynting vector S_z at each of the locations (i)–(iv) and input as labeled in (a). Inset: relative contribution (in %) for each mode shown in Fig. 2³⁴.