SUPPLEMENTARY FIGURE CAPTIONS

Fig. S1. Full-vector solver benchmark for the reference ring-core fiber. Calculated effective refractive indices are compared with the published Fiber 3 reference values used for numerical validation.

Fig. S2. Local segment-length tolerance of the final five-layer design around the nominal operating point. The figure complements the main-text local transmission plot by emphasizing the narrow phase-matched length intervals under the stated target and competitor thresholds.

Fig. S3. Coherence factor C_q and bound-subspace coupling B_q for the four launched reference modes of the final five-layer structure at λ0 = 1550 nm and L = 2.025 mm. The target HE21-based family shows near-unity coherence, whereas the competing modes retain high bound-subspace coupling but low coherence. This comparison supports mode-dependent coherent recombination as the primary discrimination mechanism within the adopted forward bound-mode diagnostic.

Fig. S4. Reduced long-length modal-beat continuation of target transmission and worst-competitor transmission. This auxiliary 20–100 mm continuation illustrates recurrent interference rather than cumulative purification and is not an independent full-wave propagation calculation.
