Generalized Modal Ports

Origins in Mode Matching

The idea of modal representation on subdomain interfaces is inspired by the Mode Matching technique, a method extensively studied in the 1990s for waveguide and resonator analysis. In Mode Matching, interface fields are expanded in terms of eigenfunctions of the transverse Laplacian, defined on the cross-section and satisfying specific boundary conditions (typically PEC or PMC).

While suitable for canonical structures, these strict boundary conditions limit generalization to arbitrary geometries or interfaces extracted from generic decompositions. This called for a more flexible formulation with basis functions well suited to represent equivalent tangential electric currents on the subdomain interfaces.

Basis Completeness and Current Continuity

The surface modal functions used in EmCAD are defined under PMC-like boundary conditions, which ensure that the normal component of current across interface edges vanishes — thus guaranteeing continuity of current across neighboring faces. However, a basis formed exclusively by these surface modes is generally incomplete.

Edge related functions are therefore added to enrich the modal space and provide a complete basis for the representation of equivalent surface currents. They are specifically constructed to preserve the current continuity across shared edges, complementing the surface modes.

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