Effective Medium Theory with finite boundaries

In this study, we present a way to control the refractive index inside of an otherwise empty metallic waveguide by inserting dielectric slabs. We show how to predict the effective refractive index for a partially filled waveguide. These predictions are confirmed by explicit numerical FDTD calculations on the electromagnetic wave propagation inside the waveguide. Our work provides a simple rule to design effective medium inside finite boundaries, that can be used for metamaterial applications.