This paper proposes a novel scheme for the solution of Maxwell equations in the time domain. A discretization scheme in time is developed to render implicit solution of system of equations possible.

The scheme allows for calculation of the field values at different time slices in an iterative fashion. This facilitates us to tackle problems whose solutions have harmonic or even more general dependency on time. The spatial grid is partitioned into finite number of elements with intrinsic shape functions to form the bases of solution. Furthermore, the finite elements are enriched with plane wave functions. This significantly reduces the number of nodes required to discretize the geometry, without compromising on the accuracy or allowed tolerance in the errors, as compared to that of classical FEM. Also, this considerably reduces the computational costs, viz. memory and processing time. Parametric studies, presented herewith, confirm the robustness and efficiency of the proposed method. The numerical scheme can thus be further developed for solution of problems where analytical solutions cannot be developed, or even when the solution cannot be categorized as time-harmonic in nature.