Fundamental impossibility of shared-RF mode-transfer pairs

Determine whether mode-transfer pairs for which no common RF configuration was found within the explored RF parameter range are fundamentally impossible to support simultaneously under the modeled shared-RF resonator architecture, rather than merely missed by the bounded numerical search.

Background

The physical switching model assigns multiple optical connections to a common RF-control group, so all associated frequency conversions must be realized by one multimode resonator scattering matrix. The paper compares transfers optimized individually with pairs optimized jointly using a common RF configuration and finds that a substantial fraction of individually feasible pairs cannot be simultaneously supported above selected target-mode thresholds within the explored parameter range.

The reported failure to find a common RF configuration is explicitly not interpreted as proof of fundamental impossibility. Resolving whether these pairs are intrinsically incompatible or merely require RF parameters outside the bounded search range remains unresolved.

References

Conversely, failure to identify a common solution within the bounded numerical search does not establish that the corresponding pair is fundamentally impossible; it only indicates that no compatible RF configuration was found within the modeled parameter family and search range.

— Design and Physical Constraints of Synthetic-Frequency Photonic Switching Fabrics  (2609.01130 - Parra, 1 Sep 2026) in Supplementary Note 4, subsection “Compatibility under a shared RF configuration”