Wigner-Smith Time Delay Matrix for Electromagnetics: Theory and Phenomenology
arXiv:2003.06985 · doi:10.1109/TAP.2020.3008650
Abstract
Wigner-Smith (WS) time delay concepts have been used extensively in quantum mechanics to characterize delays experienced by particles interacting with a potential well. This paper formally extends WS time delay theory to Maxwell's equations and explores its potential applications in electromagnetics. The WS time delay matrix relates a lossless and reciprocal system's scattering matrix to its frequency derivative and allows for the construction of modes that experience well-defined group delays when interacting with the system. The matrix' entries for guiding, scattering, and radiating systems are energy-like overlap integrals of the electric and/or magnetic fields that arise upon excitation of the system via its ports. The WS time delay matrix has numerous applications in electromagnetics, including the characterization of group delays in multiport systems, the description of electromagnetic fields in terms of elementary scattering processes, and the characterization of frequency sensitivities of fields and multiport antenna impedance matrices.
arXiv commentPublished in the IEEE Trans. on Antennas \& Propag., vol. 69, no. 2, Feb. 2021
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- Time delays in anisotropic systems
- Perturbing scattering resonances in non-Hermitian systems: a generalized Wigner-Smith operator formulation
- Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies
- Wigner-Smith Time Delay Matrix for Electromagnetics: Guiding and Periodic Systems with Evanescent Modes