Breaking the Size-Tolerance Trade-off in Vertical Couplers via Adjoint-Based Inverse Design.

Heterogeneous integration of III-V lasers on silicon is pivotal for scaling next-generation photonic systems, yet it faces a fundamental bottleneck: the inherent trade-off between coupler compactness and misalignment tolerance. In this work, we break this longstanding barrier by combining multi-start adjoint optimization with a physics-guided strategy that places dense control points in near-phase-matched regions. This approach produces a more extended phase-near-matched region that spatially overlaps with the region of controlled odd supermode excitation, which is the key condition for simultaneously achieving compactness and tolerance. Our design achieves 98.11% coupling efficiency within a footprint of just 20 μm. Remarkably, it sustains over 80% efficiency under substantial misalignments up to ± 1.1 μm and waveguide width variations of ± 0.4 μm-representing the highest tolerance per unit length reported for vertical III-V-on-silicon couplers. This achievement decouples the traditional conflict between size and robustness, offering a critical solution for high-yield micro-transfer printing and dense photonic integration. The successful extension of our optimization framework to the lithium niobate-on-silicon nitride platform confirms its generality, positioning it as a versatile and transformative design strategy for a broad range of heterogeneous photonic platforms.