  The modified Maxwell's Stekloff eigenvalue problem arises recently from the
inverse electromagnetic scattering theory for inhomogeneous media. This paper
contains a rigorous analysis of both the eigenvalue problem and the associated
source problem on Lipschitz polyhedra. A new finite element method is proposed
to compute Stekloff eigenvalues. By applying the Babuska-Osborn theory, we
prove an error estimate without additional regularity assumptions. Numerical
results are presented for validation.
