Inverse Design of Deformed Silicon Waveguide for Mode Cycling

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 cyclers with size of only 7 μm, 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 cycler, achieves efficient TE0/TE1 bidirectional conversion within just 20 optimization iterations. Three-dimensional Finite-difference time-domain simulations on a silicon-on-insulator platform confirm low conversion losses 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 cycler for TE0/TE1/TE2 cyclic conversion is realized through a two-stage optimization strategy, converging within 100 iterations. The triple-mode cycler 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-designed deformed multimode silicon waveguides for realizing efficient mode cycling, thereby advancing mode-division multiplexing enabled photonic integrated circuits.