Low-Loss Multimode Waveguide Bends with Direct Laser Writing in Polymer

Waveguide bends are critical components for compact routing in integrated photonic circuits, yet their design in air-clad polymer waveguides fabricated by two-photon polymerization direct laser writing (2PP-DLW) is challenging due to multimode behavior. We address this by systematically modeling Bézier-shaped 90° bends and S-bends using a variational FDTD solver, exploring bend span, curvature, and waveguide dimensions. Our results show that smaller waveguides (widths 2-4 µm) and lower Bézier parameters (B = 0-0.2) consistently yield superior performance, enabling sharper bends with minimal loss. For 90° bends, spans as small as 20-30 µm achieve near-unity transmission, while for S-bends, aspect ratios below 1 are feasible, allowing highly compact layouts. Although all configurations transmit energy to the fundamental mode, wider waveguides exhibit stronger higher-order mode excitation and greater sensitivity to fabrication imperfections. Smaller waveguides reduce these effects but approach the resolution limits of 2PP-DLW. Thus, a 2 µm wide waveguide represents an optimal compromise between fabrication feasibility and optical performance. Experimental demonstrations confirm the practicality of these design rules, illustrating trends predicted by simulations. These findings establish clear guidelines for designing low-loss, space-efficient 3D photonic circuits and highlight the critical role of simulation-driven optimization in fully exploiting 2PP-DLW technology, while providing deeper insight for future device architectures.