We introduce a novel variant of the Lanczos method for computing a few eigenvalues of sparse and/or dense non-Hermitian systems arising from the discretization of Maxwell-or Helmholtz-type operators in electromagnetics. We develop a Krylov subspace projection technique built upon short-term vector recurrences that does not require full reorthogonalization and can approximate simultaneously both left and right eigenvectors. We report on experiments for solving eigenproblems arising in the

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... s of dielectric waveguides and scattering applications from PEC structures. The theoretical and numerical results reported in this study will contribute to highlight the potential and enrich the database of this technology for solving generalized eigenvalue problems in Computational Electromagnetics.