Extensions of immittance decompositions with additional high-frequency terms

Develop canonical circuit and Hamiltonian constructions for impedance matrices containing an additional pole at infinity or a constant nonreciprocal term.

Background

The presented impedance construction extracts zero-frequency, finite-frequency, and regular high-frequency contributions under a restricted response form. More general impedance matrices can contain an inductive pole at infinity or a constant nonreciprocal contribution, which require circuit-synthesis and quantization steps beyond those developed in the manuscript.

The authors identify these additional response structures as an explicit extension that remains unresolved.

References

More general impedance matrices containing an additional pole at infinity, $L_{Z,\infty}s$, or a constant nonreciprocal term, $B_\infty$, require additional steps (see Refs. for some particular cases) that are left for future work.

— Immittance formulas for exact blackbox quantization and divergence-free effective models in circuit QED  (2608.26027 - Gigon et al., 26 Aug 2026) in Section 2, subsection “Brief review of Cauer expansions for nonreciprocal multiport environments,” paragraph following the finite-frequency impedance decomposition