Programmable heterogeneous lithium niobate photonic circuits via active–passive joint inverse design

Realizing densely integrated, programmable photonic circuits on thin-film lithium niobate on insulator (LNOI) is essential for next-generation high-speed optical information processing. However, it remains highly challenging due to LNOI’s limited optical confinement, fabrication constraints, and the poor scalability of conventional design approaches. Here, we experimentally demonstrate an active–passive joint inverse design method on a heterogeneous silicon-LNOI platform to overcome these limitations. By co-optimizing dynamic electro-optic phase variables with the topology of silicon metastructures integrated onto LNOI slab waveguides, this approach enables efficient control of optical energy distribution and spatial modes while ensuring fabrication robustness. We experimentally demonstrate 2×2 and 4×4 phase-programmable spatial routers with routing regions of 15×8µm 2 and 35×14µm 2 , respectively, achieving up to 86% size reduction while maintaining high transmission efficiency. Furthermore, we demonstrate a reconfigurable 4×1 mode synthesizer that supports diverse composite modal states and fast reconfiguration among four guided modes (TE 0 −TE 3 ). The architecture is inherently scalable, enabling the dynamic manipulation and processing of highly complex mode states and extension to larger-scale photonic circuits. Our results establish a general route toward densely integrated, multidimensional photonic networks, and open opportunities for programmable photonic information processing on LNOI platforms.