Complete-basis expansion for higher-order nonclassical waveguide corrections

Develop an expansion theory for nonclassical waveguide modes under the nonclassical electromagnetic boundary condition that incorporates a sufficiently large number of unbound or non-propagative classical waveguide modes, including radiative and evanescent modes, to form a complete basis and accurately account for higher-order contributions of the Feibelman d-parameters.

Background

The paper develops a first-order perturbation theory for nonclassical waveguide modes supported by mesoscale plasmonic waveguides. The theory uses classical waveguide modes satisfying the classical electromagnetic boundary condition as basis functions and treats the Feibelman d-parameters in the nonclassical electromagnetic boundary condition as a first-order perturbation.

The authors report that the discrepancy between the perturbative predictions and rigorous full-wave calculations increases as the nanogap becomes smaller, indicating that higher-order d-parameter contributions become important. Including only bound and propagative classical waveguide modes in the expansion theory does not significantly improve the accuracy. The unresolved task is therefore to incorporate unbound or non-propagative modes so that the basis is complete, despite the associated increase in computational cost and reduction in physical insight.

References

Therefore, to ensure the accuracy of the expansion theory so as to fully account for the higher-order contributions of the d-parameters, it is necessary to incorporate not only bound and propagative CWMs but also a large number of unbound or non-propagative (i.e., radiative or evanescent) CWMs into the expansion theory, so that the considered CWMs can constitute a complete set of basis functions [32]. This, however, comes at the cost of increased computational cost and diminished physical insight, which falls beyond the scope of this work and is left for future investigations.

— Perturbation theory of mesoscale plasmonic waveguide with an analytical treatment of nonclassical electromagnetic boundary condition  (2608.18856 - Xue et al., 19 Aug 2026) in Main text, Verification section, discussion following Fig. 2(b) (page 5)