  We introduce a new numerical method for solving time-harmonic Maxwell's
equations via the modified weak Galerkin technique. The inter-element functions
of the weak Galerkin finite elements are replaced by the average of the two
discontinuous polynomial functions on the two sides of the polygon, in the
modified weak Galerkin (MWG) finite element method. With the dependent
inter-element functions, the weak curl and the weak gradient are defined
directly on totally discontinuous polynomials. Optimal-order convergence of the
method is proved. Numerical examples confirm the theory and show effectiveness
of the modified weak Galerkin method over the existing methods.
