Temporal Transfer Matrix Method for Exceptional-Point Media via Canonical Basis Expansion

Abstract: We present a generalized temporal transfer matrix method (TTMM) for time-varying media that accurately captures wave dynamics in media operating at exceptional points (EPs). The method expands wave fields in the canonical basis of each temporal layer and derives the complete time evolution of all basis vectors. Temporal matching and phase-delay matrices are constructed from the generalized modal matrices and their corresponding eigenvalues. Additionally, an amplitude-boosting matrix is introduced to account for the power-law amplification of field amplitudes associated with EP dynamics. This matrix depends only on the order of the EP and naturally reduces to the identity matrix in its absence. The proposed TTMM is validated through two representative EP media, demonstrating its accuracy and broad applicability.