  We propose an unfitted finite element method for numerically solving the
time-harmonic Maxwell equations on a smooth domain. The model problem involves
a Lagrangian multiplier to relax the divergence constraint of the vector
unknown. The embedded boundary of the domain is allowed to cut through the
background mesh arbitrarily. The unfitted scheme is based on a mixed interior
penalty formulation, where Nitsche penalty method is applied to enforce the
boundary condition in a weak sense, and a penalty stabilization technique is
adopted based on a local direct extension operator to ensure the stability for
cut elements. We prove the inf-sup stability and obtain optimal convergence
rates under the energy norm and the $L^2$ norm for both the vector unknown and
the Lagrangian multiplier. Numerical examples in both two and three dimensions
are presented to illustrate the accuracy of the method.
