Mode converters (MCs) play an essential role in mode‐division multiplexing (MDM) systems. Numerous schemes have been developed on the silicon‐on‐insulator (SOI) platform, yet most of them focus solely on the conversion of fundamental mode to one or two specific higher‐order modes. In this study, we introduce a hybrid shape optimization (HSO) method that combines particle swarm optimization (PSO) with adjoint methods to optimize the shape of the S‐bend waveguide, facilitating the design of arbitrary‐order MCs featuring compactness and high performance. Our approach was validated by designing a series of 13 μm‐long MCs, enabling efficient conversion between various TE modes, ranging from TE ₀ to TE ₃ . These devices can be fabricated in a single lithography step and exhibit robust fabrication tolerances. Experiment results indicate that these converters achieve low insertion losses under 1 dB and crosstalks below −15 dB across bandwidths of 80 nm (TE ₀ –TE ₁ ), 62 nm (TE ₀ –TE ₂ ), 70 nm (TE ₀ –TE ₃ ), 80 nm (TE ₁ –TE ₂ ), 55 nm (TE ₁ –TE ₃ ), and 75 nm (TE ₂ –TE ₃ ). This advancement paves the way for flexible mode conversion, significantly enhancing the versatility of on‐chip MDM technologies.

Multimode waveguide bend (MWB) is one of the essential components for achieving high-density integration of on-chip mode-division multiplexing (MDM). This paper proposes a low-loss and compact MWB utilizing the hybrid shape optimization (HSO) method. The HSO combines particle swarm optimization (PSO) and the adjoint approach to optimize the shape of MWB efficiently. Two types of MWBs are designed, with effective radii of 6 $\mu$ m and 10 $\mu$ m, supporting three modes and four modes, respectively. Fabrication of these MWBs requires a single lithography step and exhibits excellent fabrication tolerances. Experimental results show that the MWB supporting three modes has an insertion loss of less than 0.6 dB over a broad bandwidth of 100 nm (1500-1600 nm), with crosstalk of below -20 dB between all modes. Similarly, the MWB supporting four modes has an insertion loss of less than 0.8 dB over the same bandwidth, with inter-mode crosstalk of below -20 dB. The proposed MWB exhibits the best overall performance considering footprint, loss, inter-mode crosstalk, and operation bandwidth.

In previous works, inverse design methods have primarily focused on manipulating the optical power to achieve specific design targets. In this paper, we use the inverse design method to enable the precise engineering of the optical phase. As a proof of concept, we present a series of phase shifters (PSs) with varying phase shifts, which are inversely designed and theoretically validated on the silicon-on-insulator (SOI) platform. The designed PSs exhibit remarkable accuracy, with deviations of below 1${}^{°}$. These proposed PSs feature an ultra-compact footprint of 3 µm in length and offer superior fabrication tolerances compared to conventional structures. Over the 1535–1565 nm bandwidth, the discrepancy between the actual and target phase shifts remains below ±1${}^{°}$ for all phase shifters, while the insertion loss is consistently below 0.035 dB. Moreover, the feasibility of the designed five PSs is verified using 2 × 2 multimode interference couplers (MMI).