arXiv:2610.34804v1 Announce Type: new Abstract: In this paper, we develop and analyze a numerical method for the Maxwell's transmission eigenvalue problem in dispersive media. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. For discretization, we employ the Nedelec elements. Convergence of the scheme is established via the abstract approximation theory of Karma. To compute the resulting nonlinear matrix eigenvalue problems, we employ a parallel multi-step contour integral method. Numerical experiments are presented to demonstrate the viability and accuracy of the proposed approach.