A simple and robust technique to retrieve effective refractive index of heterogeneous dielectrics for millimeter-wave applications

In this paper a simple methodology to retrieve the effective refractive index of a heterogeneous dielectric substrate is proposed. The host dielectric material is filled with small spherical dielectric inclusions which are arranged in a cubic lattice to form a heterogeneous dielectric. The proposed technique relies on the determination of the dispersion diagram (DD) of a unit cell that consists of a dielectric cube with a dielectric spherical inclusion at its center. The inhomogeneous substrate results from a 3D periodic repetition of the unit cell. Since only waves those propagate parallel to one of the faces of the unit cell are considered, the DD is 2D. The DD is then restricted to the ΓXMΓ spectral triangle that borders the irreducible first Brillouin zone, due to the symmetry of the structure. The effective refractive index can readily be determined through the slope of the DD, without using scattering parameters.