Inverse design of deformed silicon waveguides for multimode cyclic conversion.

Mode-division multiplexing has emerged as a powerful strategy for enhancing the capacity of photonic integrated circuits, where compact and versatile mode manipulation devices in bus waveguides play a central role. In this work, we present the inverse design of two ultra-compact mode cyclic converters with size of only 7 µm in length, enabled by the integration of the finite-element method, Bernstein polynomial-based deformation parameterization, and the gradient-based method of moving asymptotes. The first device, a dual-mode cyclic converter (DMCC) with efficient TE0/TE1 mutual conversion, is obtained within just 20 optimization iterations. Three-dimensional finite-difference time-domain simulations on a silicon-on-insulator platform confirm high conversion efficiencies of -0.053 dB (TE0-to-TE1) and -0.043 dB (TE1-to-TE0), with mode purities reaching 99.3%. Extending this approach, a triple-mode cyclic converter (TMCC) for TE0/TE1/TE2 cyclic conversion is realized through a two-stage optimization strategy, converging at around 100 iterations. The TMCC exhibits conversion efficiencies of -0.67 dB (TE0-to-TE1), -1.1 dB (TE1-to-TE2), and -0.67 dB (TE2-to-TE0), accompanied by high mode purities of 96.4%, 93.6%, and 98.3%, respectively. Robustness analyses further demonstrate tolerance to fabrication deviations of ±10 nm. These results highlight the potential of inverse design in deformed multimode silicon waveguides for realizing efficient mode cyclic conversion, thereby advancing mode-division multiplexing in photonic integrated circuits.