Fig. 1. Top view and simulated mode field distribution of straight waveguide and circular-arc bent waveguide. (a) Top view of straight waveguide and circular-arc bent waveguide; (b) simulated mode field distribution of straight waveguide; (c) simulated mode field distribution of circular-arc bent waveguide

Fig. 2. Schematic diagram of refractive index distribution of bent waveguides before and after conformal transformation, influence of n₁-n₂ on αr, and writing strategy of modification lines. (a) Refractive index distribution before and after conformal transformation without modification lines; (b) change of αr with n₁-n₂; (c) schematic diagram of writing strategy for modification lines; (d) refractive index distribution before and after conformal transformation when adding modification lines

Fig. 3. Simulation results of S-shaped bent waveguide. (a),(b) Cross-sectional refractive index distribution and bending loss simulation diagrams of bent waveguide without modification lines; (c),(d) cross-sectional refractive index distribution and bending loss simulation diagrams of bent waveguide with modification lines; (e) relationship between bending loss and curvature radius of bent waveguides with and without modification lines

Fig. 4. Optical microscope photos and mode field distribution pictures. (a1),(b1) Cross-sectional optical microscope photos of bent waveguide before and after adding modification line, respectively; (a2),(b2) mode field distribution pictures corresponding to (a1) and (b1), respectively; (a3),(b3) simulated mode field distribution images of bent waveguide before and after adding modification line, respectively

Fig. 5. Different schemes of writing order of waveguide and modification lines and their corresponding bending losses. (a) Schematic diagram of writing order of waveguide and modification lines; (b) bending losses of waveguides under different writing schemes

Fig. 6. Bending losses of waveguides under different R, P2, and dis. (a) Variation of bending loss with P2 and dis when R=10 mm; (b) variation of bending loss with P2 and dis when R=20 mm. Horizontal thick solid line and thin solid lines represent magnitude of bending loss for bent waveguide without modification lines and measurement error, respectively

Fig. 7. Bending losses of waveguide under different R, θ, and σ conditions. (a) Bending losses of waveguide under different R and θ conditions; (b) bending losses of waveguide under different R and σ conditions

Fig. 8. Bending losses of waveguide under different writing methods of modification lines, R and m. (a) Writing symmetrically on both sides; (b) only writing from outside of bend; (c),(d) optical microscope images of cross section of bent waveguide when two layers of modification lines are written on both sides and from outside of bending, respectively