We propose and demonstrate a high-performance asymmetrical multimode interference splitter on X-cut lithium niobate on insulator (LNOI) with an ultra-compact size of 5.8 μm × (26.4–35.6) μm. A rectangle with a small region is removed from the upper left corner of the multimode interference (MMI) coupler to achieve a variable splitting ratio. Here, we design and characterize MMIs in six different distribution ratios ranging from 50:50 to 95:5 on a 600 nm thick LNOI. Based on the cascade structure, the linear fitting method accurately shows the device loss (~0.1–0.9 dB). Our fabricated devices demonstrate robustness across a 30 nm optical bandwidth (1535–1565 nm). In addition, we numerically simulate the Z-cut LNOI, showing that the structure corresponding to the TM mode can also achieve a good variable splitting ratio.

Thin-film lithium niobate electro-optic modulators exhibit outstanding advantages such as large bandwidth, low insertion loss, and low half-wave voltage, demonstrating broad application prospects. However, due to internal defects in lithium niobate crystals, modulators exhibit electro-optic relaxation phenomena, with the relaxation time of thin-film structures being reduced by more than two orders of magnitude compared to bulk materials. In this study, we fitted and simulated the electro-optic relaxation behavior of thin-film lithium niobate modulators based on RC circuit model, effectively explaining their time-domain response characteristics under low-frequency conditions. By comparing thin-film modulators with and without silica cladding structures, the fitting results indicate that the relaxation time of modulators with cladding is approximately 11.9 ms, showing positive DC drift, whereas the relaxation time of modulators without cladding is significantly shortened to about 88.6 μs and exhibits negative DC drift. Additionally, the enhancement of optical intensity alters the photoconductivity of the material, thereby affecting its low-frequency electro-optic response behavior. This research provides important ideas for the design and optimization of next-generation integrated lithium niobate photonic modulators with high stability and controllability.

Diffractive deep neural networks (D ² NNs) are fundamentally constrained by diffraction-induced weight coupling, which restricts parameter updates to a low-dimensional realizable manifold and limits optimization efficiency. We analyze the geometry of gradient updates in such physically constrained systems and introduce the gradient cosine degree (GradCos) to quantify the alignment among mini-batch gradients. High gradient alignment is shown to be strongly associated with degraded performance in D ² NNs on simple datasets such as MNIST. To diversify realizable update directions, we employ teacher-generated soft labels to redistribute gradient components without altering the physical architecture. Numerical results reveal a strong negative correlation between GradCos and recognition accuracy. A single-layer D ² NN trained with soft labels achieves 91.1% accuracy on the MNIST dataset, comparable to an eight-layer model trained with hard labels. The softened-gradient geometry also improves robustness to phase quantization and enhances generalization to unseen categories. These findings indicate that modulating gradient geometry provides an effective algorithmic pathway to alleviate optimization bottlenecks imposed by optical weight coupling, supporting the miniaturization and practical deployment of D ² NNs.